Saturday, 17 March 2018

On This Day in Math - March 17


St. Patrick’s Day. The equation of the day is the four-leaved rose r = sin(2θ). Work on this curve was first published by the Italian priest Guido Grandi in 1723. *VFR

"Spirit of '76" by Archibald McNeal Willard, 189

The 76th day of the year; 76 is an automorphic number because the square of 76 ends in 76. (5 and 6 are automorphic because 52 ends in five and 62 ends in six).
There is one other two digit automorphic number (it should be easy to find) but can you find the three digit ones?

76= 8 + 13 + 21 + 34 the sum of four consecutive Fibonacci numbers

76 is the number of 6 X 6 symmetric permutation matrices.


1694 L’Hospital hires his former tutor Johann Bernoulli to “work on what I shall ask you ... and also to communicate to me your discoveries, with the request not to mention them to others.” The first calculus text resulted in 1696. It contained the famous “L’Hospital’s rule,” which, we now know, is the work of Bernoulli. [Eves, Circles, 208◦] VFR
(Because L'Hospital is so often discredited by Intro Calculus teachers for his role, I wanted to add more detail in the hopes they will share a more enlightened presentation of his work.)
In a letter from March 17, 1694, l'Hôpital made the following proposal to Johann Bernoulli: in exchange for an annual payment of 300 Francs, Bernoulli would inform L'Hôpital of his latest mathematical discoveries, withholding them from correspondence with others, including Varignon. Bernoulli's immediate response has not been preserved, but he must have agreed soon, as the subsequent letters show. L'Hôpital may have felt fully justified in describing these results in his book, after acknowledging his debt to Leibniz and the Bernoulli brothers, "especially thle younger one" (Johann). Johann Bernoulli grew increasingly unhappy with the accolades bestowed on l'Hôpital's work and complained in private correspondence about being sidelined. After l'Hôpital's death, he publicly revealed their agreement and claimed credit for the statements and portions of the text of Analyse, which were supplied to l'Hôpital in letters. Over a period of many years, Bernoulli made progressively stronger allegations about his role in the writing of Analyse, culminating in the publication of his old work on integral calculus in 1742: he remarked that this is a continuation of his old lectures on differential calculus, which he discarded since l'Hôpital had already included them in his famous book. For a long time, these claims were not regarded as credible by many historians of mathematics, because l'Hôpital's mathematical talent was not in doubt, while Bernoulli was involved in several other priority disputes. For example, both H. G. Zeuthen and Moritz Cantor, writing at the cusp of the 20th century, dismissed Bernoulli's claims on these grounds. However, in 1921 Paul Schafheitlin discovered a manuscript of Bernoulli's lectures on differential calculus from 1691–1692 in the Basel University library. The text showed remarkable similarities to l'Hôpital's writing, substantiating Bernoulli's account of the book's origin.
L'Hôpital's pedagogical brilliance in arranging and presenting the material remains universally recognized. Regardless of the exact authorship (one should also note that the book was first published anonymously), Analyse was remarkably successful in popularizing the ideas of differential calculus stemming from Leibniz. *Wik

1856 Joseph Lacomme, a French well-sinker, and illiterate laborer who asked a mathematics professor to tell him the amount of stone needed to cover the bottom of a circular cistern, and unsatisfied with the reply that it would be impossible to tell him exactly, set about experimenting and determined the "True" ratio of the circumference to diameter of a circle. Teaching himself arithmetic and writing to confirm the results he obtained by experimentation he shared his computation with the commissioner of police in Paris. The commissioner introduced Lacomme to his father, who presented him to the Academie and after consideration by a committee, Lacomme received a silver medal from the French Academie for his discovery of the true ratio of diameter to circumfrence of a circle. He would later receive three more medals from other societies for his value of 3 1/8. *Augustus DeMorgan, A Budget of Paradoxes, pgs 46-47
The Kindle edition of A Budget of Paradoxes, Volume I is currently free.

1889 A political cartoon in the New York World lampooned President Benjamin Harrison's advisers and cabinet members showing the group sitting around playing the game, Pigs in Clover which had recently been invented by Charles Martin Crandall. The caption read "Will Mr. Harrison be able to get all these hungry pigs in the official pen?"
The events which prompted the story were related in a New York Tribune's March 13, 1889 issue:
Senator William M. Evarts purchased one from a street fakir in order to get rid of him. He took the puzzle home and worked it for hours. The following morning he brought it with him into senate chambers where Senator George Graham Vest stopped by Evarts' desk, borrowed the puzzle and took it to a cloak room. Soon thereafter he was joined by Senators James L. Pugh, James B. Eustis, Edward C. Walthall and John E. Kenna. A page was sent out to buy five of the puzzles and upon his return, the group engaged in a "pig driving contest". About 30 minutes later, Senator Vest announced his accomplishment of driving the last pig in the pen.
*Antique Toy Collectors of America *Wik (Will negotiate trade of my off-spring or other not-to-valuable property for a imageof this cartoon. )

1905 Albert Einstein submits his paper "On a Heuristic Point of View Concerning the Production and Transformation of Light" to the Annalen der Physik. In this revolutionary paper he proposes that light can be conceived both as waves and as discrete quanta (later to be called photons) which are localized at points in space. This paper was the primary reason for his Nobel Prize.

1914 Ramanujan boarded the S.S. Nevasa on 17 March 1914, and at 10 o'clock in the morning, the ship departed from Madras. He arrived in London on 14 April, with E. H. Neville waiting for him with a car. A tweet from @amanicdroid pointed out that, "this was significant for him culturally as a high-caste Hindu as crossing the ocean was taboo. "

1941 The National Gallery of Art opened its doors on the mall in Washington D.C. The gallery was a gift of Pittsburgh financier Andrew W. Mellon. His personal collection of 152 masterpieces has grown to 80,000 priceless works today. Today it is a good place to see some mathematics, from the lack of perspective in its medieval works, to The Lady in the Red Hat with its camera obscura technique, to the geometric starkness of the East Wing. *VFR

1988 Apple Computer sues Microsoft Corporation for copyright infringement in its Windows design. After Apple developed a highly successful graphical user interface for its Macintosh computer released in 1984, Microsoft fought back with an operating system of its own, called "Windows." In 1995, Apple lost the lawsuit, in which it claimed that the similarities of the Windows and Macintosh environments extended too far.*CHM

2013 Flash of Meteor hitting moon visible to naked eye. Scientists monitoring the moon for meteorite impacts spotted the biggest impact event to date: a space rock the size of a basketball slammed into the lunar surface at a speed of 56,000 miles per hour (90,000 km/hr), creating a new crater around 20 meters wide.
The flash was impressive — it unleashed the equivalent energy of 5 tons of TNT exploding and would have been visible to anyone casually looking at the moon, no telescope required. *NASA The impact hit almost exactly on a crater already present. This animated gif shows before and after shots of the site.

1733 Carsten Niebuhr(March 17, 1733 Lüdingworth – April 26, 1815 Meldorf, Dithmarschen), German mathematician, cartographer, and explorer in the service of Denmark. Niebuhr's first book, Beschreibung von Arabien, was published in Copenhagen in 1772, the Danish government providing subsidies for the engraving and printing of its numerous illustrations. This was followed in 1774 and 1778 by the two volumes of Niebuhr's Reisebeschreibung von Arabien und anderen umliegenden Ländern. These works (particularly the one published in 1778), and most specifically the accurate copies of the cuneiform inscriptions found at Persepolis, were to prove to be extremely important to the decipherment of cuneiform writing. Before Niebuhr's publication, cuneiform inscriptions were often thought to be merely decorations and embellishments, and no accurate decipherments or translations had been made up to that point. Niebuhr demonstrated that the three trilingual inscriptions found at Persepolis were in fact three distinct forms of cuneiform writing (which he termed Class I, Class II, and Class III) to be read from left to right. His accurate copies of the trilingual inscriptions gave Orientalists the key finally crack the cuneiform code, leading to the discovery of Old Persian, Akkadian, and Sumerian. *Wik

1876 Ernest Benjamin Esclangon (March 17, 1876 – January 28, 1954) was a French astronomer and mathematician. During World War I, he worked on ballistics and developed a novel method for precisely locating enemy artillery. When a gun is fired, it initiates a spherical shock wave but the projectile also generates a conical wave. By using the sound of distant guns to compare the two waves, Escaglon was able to make accurate predictions of gun locations.
After the armistice, Esclangon became director of the Strasbourg Observatory and professor of astronomy at the university the following year. In 1929, he was appointed director of the Paris Observatory and of the International Time Bureau, and elected to the Bureau des Longitudes in 1932. In 1933, he initiated the talking clock telephone service in France. He was elected to the Académie des Sciences in 1939.
Serving as director of the Paris Observatory throughout World War II and the German occupation of Paris, he retired in 1944. He died in Eyrenville, France.
The binary asteroid 1509 Esclangona and the lunar crater Esclangon are named after him.*Wik

1915 Wolfgang Döblin, known in France as Vincent Doblin, (17 March 1915 – 21 June 1940) was a German-French mathematician. Wolfgang was the son of the Jewish-German novelist, Alfred Döblin. His family escaped from Nazi Germany to France where he became a citizen. Studying probability theory at the Institute Henri Poincaré under Fréchet, he quickly made a name for himself as a gifted theorist. He became a doctor at age 23. Drafted in November 1938, after refusing to be exempted of military service, he had to stay in the active Army when World War II broke out in 1939, and was quartered at Givet, in the Ardennes, as a telephone operator. There, he wrote down his latest work on the Chapman-Kolmogorov equation, and sent this as a "pli cacheté" (sealed envelope) to the French Academy of Sciences. His company, sent to the sector of the Saare on the ligne Maginot in April 1940, was caught in the German attack in the Ardennes in May, withdrew to the Vosges, and capitulated on June 22, 1940. On June 21, Doblin had committed suicide in Housseras (a small village near to Epinal), at the moment where German troops came in sight of the place. In his last moments, he burned his mathematical notes.
The sealed envelope was opened in 2000, revealing that Döblin was ahead of his time in the development of the theory of Markov processes. In recognition of his results, Itō's lemma is now referred to as the Itō–Doblin Theorem.
His life was recently the subject of a movie by Agnes Handwerk and Harrie Willems, A Mathematician Rediscovered. *Wik

1972 Kalpana Chawla (March 17, 1962 – February 1, 2003) was an American astronaut and the first indian woman in space. She first flew on Space Shuttle Columbia in 1997 as a mission specialist and primary robotic arm operator. In 2003, Chawla was one of the seven crew members killed in the Space Shuttle Columbia disaster. *Wik

1652 Benjamin Bramer (15 Feb 1588 in Felsberg, Germany - 17 March 1652 in Ziegenhain, Germany) was an architect who published work on the calculation of sines. He was tutored by Jost Bürgi in a wide range of subjects but it was mathematics that he loved and he passed this love on to Bramer. (Bramer married Bürgi's daughter) Bramer followed Alberti (1435), Dürer (1525) and Bürgi (1604) when in 1630 he constructed a device that enabled one to draw accurate geometric perspective. The instrument had been described in a 1617 publication Trigonometrica planorum mechanica oder Unterricht und Beschreibung eines neuen und sehr bequemen geometrischen Instrumentes zu allerhand Abmessung. Bramer designed several other mathematical instruments, for example a description of the pantograph appears in the same 1617 publication. The instrument is designed to copy a geometric shape and reproduce it at a reduced or enlarged scale. It consists of an assemblage of rigid bars adjustably joined by pin joints; as the point of one bar is moved over the outline to be duplicated, the motion is translated to a point on another bar, which makes the desired copy according to the predetermined scale. Bramer has not been recognised as the inventor of the pantograph, this distinction going to the Jesuit Christoph Scheiner who describes a similar instrument in his 1631 publication Pantographice seu acre delineandi res quaslibet by parallelogrammum linear seu cavum mechanicum, mobile. Although Scheiner's publication did much to spread knowledge of the pantograph, the instrument he describes is technically inferior to the earlier instrument as described by Bramer. *SAU

1767 George Parker (born 1697, 17 Mar 1764) [2nd Earl of Macclesfield] English astronomer who was instrumental in changing the computation of current chronology, subsequently enacted as the British Calendar Act of 1751 which co-authored and co-promoted. (Shortly thereafter, he was elected President of the Royal Society, 1752-1764). Since 1582, the new calendar of Pope Gregory XIII had been used in most of Europe. In England the new calendar was rejected as popish. By 1750, the old calendar became 11 days out of sequence with the position of the Earth in its orbit due to its lack of leap years. Parker was assisted in these calculations by his friend James Bradley, the astronomer royal, and received influential support from Philip Dormer Stanhope, 4th Earl of Chesterfield. *TIS

1771 Chester Moor Hall, (Dec. 9, 1703, Leigh, Essex, Eng.— March 17, 1771, Sutton, Surrey), English jurist and mathematician who invented the achromatic lens, which he utilized in building the first refracting telescope free from chromatic aberration (colour distortion).
Convinced from study of the human eye that achromatic lenses were feasible, Hall experimented with different kinds of glass until he found (1729) a combination of crown glass and flint glass that met his requirements. In 1733 he built several telescopes with apertures of 2.5 inches (6.5 cm) and focal lengths of 20 inches (50 cm).*

1782 Daniel Bernoulli (29 January 1700 (8 Feb new style), 8 March 1782) was a Dutch-Swiss mathematician and was one of the many prominent mathematicians in the Bernoulli family. He is particularly remembered for his applications of mathematics to mechanics, especially fluid mechanics, and for his pioneering work in probability and statistics. Bernoulli's work is still studied at length by many schools of science throughout the world. The son of Johann Bernoulli (one of the "early developers" of calculus), nephew of Jakob Bernoulli (who "was the first to discover the theory of probability"), and older brother of Johann II, He is said to have had a bad relationship with his father. Upon both of them entering and tying for first place in a scientific contest at the University of Paris, Johann, unable to bear the "shame" of being compared as Daniel's equal, banned Daniel from his house. Johann Bernoulli also plagiarized some key ideas from Daniel's book Hydrodynamica in his own book Hydraulica which he backdated to before Hydrodynamica. Despite Daniel's attempts at reconciliation, his father carried the grudge until his death.
He was a contemporary and close friend of Leonhard Euler. He went to St. Petersburg in 1724 as professor of mathematics, but was unhappy there, and a temporary illness in 1733 gave him an excuse for leaving. He returned to the University of Basel, where he successively held the chairs of medicine, metaphysics and natural philosophy until his death.
In May, 1750 he was elected a Fellow of the Royal Society. He was also the author in 1738 of Specimen theoriae novae de mensura sortis (Exposition of a New Theory on the Measurement of Risk), in which the St. Petersburg paradox was the base of the economic theory of risk aversion, risk premium and utility.
One of the earliest attempts to analyze a statistical problem involving censored data was Bernoulli's 1766 analysis of smallpox morbidity and mortality data to demonstrate the efficacy of vaccination. He is the earliest writer who attempted to formulate a kinetic theory of gases, and he applied the idea to explain Boyle's law. He worked with Euler on elasticity and the development of the Euler-Bernoulli beam equation. *Wik

1846 Friedrich Wilhelm Bessel (22 Jul 1784, 17 Mar 1846 at age 61). He is noted for the special class of functions that have become an indispensable tool in applied mathematics. This, like all of his mathematical work, was motivated by his work in astronomy. *VFR In 1809, at the age of 26, Bessel was appointed director of Frederick William III of Prussia's new Königsberg Observatory and professor of astronomy, where he spent the rest of his career. His monumental task was determining the positions and proper motions for about 50,000 stars, which allowed the first accurate determination of interstellar distances. Bessel's work in determining the constants of precession, nutation and aberration won him further honors. Other than the sun, he was the first to measure the distance of a star, by parallax, of 61 Cygni (1838). In mathematical analysis, he is known for his Bessel function. *TIS

1853 Christian Doppler (29 Nov 1803; 17 Mar 1853) Austrian physicist who first described how the observed frequency of light and sound waves is affected by the relative motion of the source and the detector, known as the Doppler effect. In 1845, to test his hypothesis, Doppler used two sets of trumpeters: one set stationary at a train station and one set moving on an open train car, all holding the same note. As the train passed the station, it was obvious that the frequency of the notes from the two groups didn't match. Sound waves would have a higher frequency if the source was moving toward the observer and a lower frequency if the source was moving away from the observer. Edwin Hubble used the Doppler effect of light from distant stars to determine that the universe is expanding.*TIS

1922 Heinrich Suter (4 January 1848, Hedingen near Zurich, Switzerland – 17 March 1922) was a historian of science specializing in Islamic mathematics and astronomy.*Wik

1956 Irène Joliot-Curie (12 Sep 1897; 17 Mar 1956) French physicist and physical chemist, wife of Frédéric Joliot-Curie, who shared the 1935 Nobel Prize for Chemistry "in recognition of their synthesis of new radioactive elements." For example, in their joint research they discovered that aluminium atoms exposed to alpha rays transmuted to radioactive phosphorus atoms. She was the daughter of Nobel Prize winners Pierre and Marie Curie. From 1946, she was director of the Radium Institute, Paris, founded by her mother. She died of leukemia, like her mother, resulting from radiation exposure during research.*TIS

1956 Henry Frederick Baker FRS (3 July 1866 – 17 March 1956) was a British mathematician, working mainly in algebraic geometry, but also remembered for contributions to partial differential equations (related to what would become known as solitons), and Lie groups.
Baker was born in Cambridge, England and educated at The Perse School before winning a scholarship to St John's College, Cambridge in October 1884. Baker graduated as Senior Wrangler in 1887, bracketed with 3 others.
Baker was elected Fellow of St John's in 1888 where he remained for 68 years.
In June, 1898 he was elected a Fellow of the Royal Society. In 1911, he gave the presidential address to the London Mathematical Society.
In January 1914 he was appointed Lowndean Professor of Astronomy. *Wik
In the 1920's and 30's before the war Baker's graduate students would meet at what they called Professor Baker’s "Tea Party". They met each Saturday to discuss the areas of research in which they were working. It was to one of these meetings that a young Donald Coxeter brought his "Aunt Alice", the 69 year old Alicia Boole to co-present on the subject of Polytopes in higher dimensions.

1962 Wilhelm Blaschke (13 Sep 1885; 17 Mar 1962) German mathematician whose major contributions to geometry concerned kinematics and differential geometry. Kinetic mapping (important later in the axiomatic foundations of various geometries) he both discovered and established it as a tool in kinematics. He also initiated topological differential geometry (the study of invariant differentiable mappings)*TIS

Credits :
*CHM=Computer History Museum
*FFF=Kane, Famous First Facts
*NSEC= NASA Solar Eclipse Calendar
*RMAT= The Renaissance Mathematicus, Thony Christie
*SAU=St Andrews Univ. Math History
*TIA = Today in Astronomy
*TIS= Today in Science History
*VFR = V Frederick Rickey, USMA
*Wik = Wikipedia
*WM = Women of Mathematics, Grinstein & Campbell

Thursday, 15 March 2018

On This Day in Math - March 16

Memorial for Ohm ,

Whenever I meet in Laplace with the words 'Thus it plainly appears', I am sure that hours and perhaps days, of hard study will alone enable me to discover how it plainly appears.
~Nathaniel Bowditch

The 75th day of the year; the aliquot divisors of 75 are 1,3,5,15, and 25. Their sum is a perfect square, 49. Their product is also a perfect square, 5625. (Can you find other numbers with this property?)

75 is also the larger of the smallest pair of betrothed (quasi-amicable) numbers. 48 and 75 are a betrothed pair since the sum of the proper divisors of 48 is 76 and 75+1 = 76 and the sum of the proper divisors of 75 is 49, with 48+1=49. (There is only a single other pair of betrothed numbers that can be a year day)

75 and 76 form the first pair of adjacent numbers in base ten which are NOT a palindrome in any base \( 2 \leq b \leq 10 \)

275 + 75 is prime

75 is a Keith # or repfigit (75 appears in a Fibonacci-like sequence created by its digits) 7, 5, 12, 17, 29, 46, 75 ...  (75 is the sixth of seven year days which are repfigits.  Can you find the others?)


1713 Saunderson to Jones: “There has been nothing published here since my last to you, excepting a treatise, which is not worth mentioning, by one Mr. Green, fellow of Clare Hall of this university. If there had been anything in it instructive or diverting I should have sent it to you; but I can find nothing in it but ill manners and elaborate nonsense from one end to the other. The gentelman has been reputed mad for these two years last past, but never gave the world such ample testimony of it before.” [Rigaud, Correspondence of Scientific Men of the Seventeenth Century, I, *263] *VFR

1763 Jerome Lalande writes in his diary about a visit to England, and "I went to see the Tower, and from there by water to Surrey Street to see Mr Short (James Short FRS was an optician who had been called to London to teach mathematics to William, Duke of Cumberland)
who spoke to me about the difficulty in giving his mirrors a parabolic figure. It is done only by guess-work." *Richard Watkins

1802 The United States Military Academy at West Point established by act of congress. This school was the first engineering school in the U.S. Charles Davies, a noted math textbook writer, taught there.*VFR (The academy opened on July 4, 1802. Before 1812 it was conducted as an apprentice school for military engineers and, in effect, as the first U.S. school of engineering.)

1830 The New York Stock Exchange had its slowest trading day, only 31 shares trading hands. *VFR

1916 On his seventieth birthday in 1916, Mittag-Leffler and his wife signed their last will and testament. They gave their entire fortune to found a Mathematical Institute which now bears their names. It is in their villa in Djursholm, near Stockholm, Sweden. A sumptuous volume giving a complete calatogue of Mittag-Leffler’s library was also published at this time, and this library is now housed in the Institute. Naturally it is a favorite haunt of historians of mathematics. *VFR (See Births,1846 below)

1926 Clark University Physics Professor, Robert H. Goddard, conducted the first successful open-air test of a liquid-fuel rocket. “The rocket soared only forty-one feet, hardly the ‘extreme altitudes’ Goddard had envisioned, yet the occasion was anologous to the first flight of the Wright brothers at Kitty Hawk nearly a quarter of a century earlier.” *William A. Koelsch, Clark University, 1887–1987
He thought stable flight could be obtained by mounting the rocket ahead of the fuel tank. The tank was shielded from the flame by a metal cone and was pulled behind the rocket by the lines for gasoline fuel and oxygen. The design worked, but did not produce the hoped-for stability. The rocket burned about 20 seconds before reaching sufficient thrust (or sufficiently lightening the fuel tank) for taking off. During that time it melted part of the nozzle. It took off to a height of 41-ft, leveled off and within 2.5 seconds hit the ground 184 feet away, averaging about 60 mph. The camera ran out of film, so no photographic record of that flight remains. *TIS

1928 Chandrasekhara Raman presented the results from his Feb 28 ground breaking experiments in light scattering at a meeting of scientists in Bangalore on 16 March 1928. The results would lead to his wining the Nobel Prize in Physics in 1930. *Wik

1986 The Manchester Guardian Weekly announces that Colin Rourke of Warwick and his student Eduardo Rego of Oporto University in Portugal have solved the 82 year old Poincare conjecture which states that loops on spheres in n-dimensions can be shrunk to points. Obviously, Mr. Rego will get his Ph.D. *VFR The article in the Guardian was by Ian Stewart. In November 1986, Rourke was at the University of California, Berkeley, conducting a seminar to explain and defend his proof. By the end of the week, Rourke's audience, which included some of the world's top topologists, had pointed out a gap in his proof, one that Rourke could not fill. In the end, there was no valid proof. The problem was solved by the reclusive Russian mathematician Grigori Perelman in November of 2002

1990 Internet Extends Beyond U.S. to Europe: The National Science Foundation announces it will extend its network with a high-speed data link to Europe. Five years earlier, the Internet in its modern form had started to develop rapidly thanks to the formation of the NSFNET, which linked five supercomputer centers in the United States. Later in 1990, Europe contributed to the growth of the Internet when CERN's Tim Berners-Lee developed HTML, the language used for the World Wide Web.*CHM


1750 Caroline Lucretia Herschel (16 Mar 1750, 9 Jan 1848) German-born British astronomer, sister of Sir William Herschel, who assisted in his astronomical researches making calculations associated with his studies. In her own telescope observations, she found three nebulae (1783) and eight comets (1786-97). In 1787, King George III gave Caroline a salary of 50 pounds per year as assistant to William. She published the Index to Flamsteed's Observations of the Fixed Stars and a list of his mistakes in 1797. At the age of 10 she had been struck with typhus, which subsequently stunted her growth. She never grew taller than 4' 3" and remained frail throughout her life. *TIS
[The following inscription is engraved on Miss Herschel's tomb. It begins: "Hier ruhet die irdische Hülle von CAROLINA HERSCHEL, Geboren zu Hannover den 16ten Marz 1750, Gestorben, den 9ten Januar 1848." But, for the convenience of our young readers, we give it in English:—





"The eyes of her now glorified were, while here below, directed towards the starry heavens. Her own discoveries of comets, and her share in the immortal labours of her brother, William Herschel, bear witness of this to succeeding ages.

"The Royal Irish Academy of Dublin, and the Royal Astronomical Society of London, enrolled her name among their members.

"At the age of 97 years 10 months, she fell asleep in calm rest, and in the full possession of her faculties; following into a better life her father, Isaac Herschel, who lived to the age of 60 years, 2 months, 17 days, and has lain buried not far off since the 29th of March 1767."

This epitaph was mainly written by Miss Herschel herself, and the allusion to her brother is characteristic.]
*from The Project Gutenberg EBook of The Story of the Herschels, by Anonymous

1789 Georg Simon Ohm (16 Mar 1789; 6 Jul 1854 at age 65) German physicist (high school teacher) who showed by experiment (1825) that there are no “perfect” electrical conductors. All conductors have some resistance. He stated the famous Ohm's law (1826): “If the given temperature remains constant, the current flowing through certain conductors is proportional to the potential difference (voltage) across it.” or V=iR. *Tis

1821 Heinrich Eduard Heine (16 March 1821 in Berlin, Germany - 21 Oct 1881 in Halle, Germany) Heine is best remembered for the Heine-Borel theorem. He was responsible for the introduction of the idea of uniform continuity.*SAU

1846 Magnus Gösta Mittag-Leffler (16 Mar 1846; 7 Jul 1927 at age 81) Swedish mathematician who founded the international mathematical journal Acta Mathematica and whose contributions to mathematical research helped advance the Scandinavian school of mathematics. Mittag-Leffler made numerous contributions to mathematical analysis (concerned with limits and including calculus, analytic geometry and probability theory). He worked on the general theory of functions, concerning relationships between independent and dependent variables. His best known work concerned the analytic representation of a one-valued function, this work culminated in the Mittag-Leffler theorem. *TIS One of the stories that circulates from time to time about Mittag-Leffler and the fact that there is no Nobel Prize in mathematics is that Nobel disliked Mittag-Leffler for having an affair with Nobel's wife and so he did not create a prize in Mathematics. Only problem; Nobel never married, and there is little if any evidence that Mittag-Leffler ever met Nobel's mistress, Sophie Hess.

1853 Heinrich (Gustav Johannes) Kayser (16 Mar 1853, 14 Oct 1940) was a German physicist who discovered the presence of helium in the Earth's atmosphere. Prior to that scientists had detected helium only in the sun and in some minerals. Kayser's early research work was on the properties of sound. In collaboration with the physicist and mathematician Carl D.T. Runge, Kayser carefully mapped the spectra of a large number of elements. He wrote a handbook of spectroscopy (1901–12) and a treatise on the electron theory (1905).*TIS

1915 Kunihiko Kodaira(16 Mar 1915; 26 Jul 1997 at age 82) Japanese mathematician who was awarded the Fields Medal in 1954 for his work in algebraic geometry and complex analysis. Kodaira's work includes applications of Hilbert space methods to differential equations which was an important topic in his early work and was largely the result of influence by Weyl. Through the influence of Hodge, he also worked on harmonic integrals and later he applied this work to problem in algebraic geometry. Another important area of Kodaira's work was to apply sheaves to algebraic geometry. In around 1960 he became involved in the classification of compact, complex analytic spaces. One of the themes running through much of his work is the Riemann-Roch theorem. He won the 1985 Wolf Prize. *TIS

1947 Dr. Keith Devlin (March 16, 1947, Kingston upon Hull, UK; ) is a co-founder and Executive Director of Stanford University's H-STAR institute, a co-founder of the Stanford Media X research network, and a Senior Researcher at CSLI. He is a World Economic Forum Fellow and a Fellow of the American Association for the Advancement of Science. His current research is focused on the use of different media to teach and communicate mathematics to diverse audiences. He also works on the design of information/reasoning systems for intelligence analysis. Other research interests include: theory of information, models of reasoning, applications of mathematical techniques in the study of communication, and mathematical cognition. He has written 32 books and over 80 published research articles. Recipient of the Pythagoras Prize, the Peano Prize, the Carl Sagan Award, and the Joint Policy Board for Mathematics Communications Award. In 2003, he was recognized by the California State Assembly for his "innovative work and longtime service in the field of mathematics and its relation to logic and linguistics." He is "the Math Guy" on National Public Radio. *Stanford Edu

1954 John E. Laird (March 16, 1954 Ann Arbor, Michigan - ) is a computer scientist who, with Paul Rosenbloom and Allen Newell, created the Soar cognitive architecture at Carnegie Mellon University. Laird is a Professor of the Computer Science and Engineering Division of the Electrical Engineering and Computer Science Department of the University of Michigan. He was the director of the Artificial Intelligence Laboratory there from 1994 to 1999. *Wik


 Bowditch gravestone,Mount Auburn Cemetery
Middlesex County
Massachusetts, USA

1838 Nathaniel Bowditch (26 Mar 1773, 16 Mar 1838 at age 65) Self-educated American mathematician and astronomer. He learned Latin to study Newton's Principia and later other languages to study mathematics in these languages. Between 1795 and 1799 he made four sea voyages and in 1802 he was in command of a merchant ship. He was author of the best book on navigation of his time, New American Practical Navigator (1802), and his translation (assisted by Benjamin Peirce) of Laplace's Mécanique céleste gave him an international reputation. Bowditch was the discoverer of the Bowditch curves (more often called Lisajous figures for their co-discoverer), which have important applications in astronomy and physics.*TIS Bowditch was a navigator on the Wilkes Expedition and an island in the Stork Archipelago in the South Pacific is named for him (and sometimes called Fakaofu)
(I can give no explanation for the discrepancy in the date of death on his tombstone.)

1841 Félix Savart (30 Jun 1791, 16 Mar 1841 at age 49)French physicist who researched various manifestations of vibration. With Jean-Baptiste Biot, he developed the Biot-Savart Law (1820) concerning the magnetic field intensity around a current-carrying wire. After earning a degree in medicine (1816), he took an interest in physics, beginning with a study of the violin to explain the contributions from its components to the sound from the strings. He presented a memoir on the subject to the Paris Academy of Sciences in 1819. He conducted extensive research in acoustics, the nodal patterns of vibrating systems (including air columns), and related enquiries into the elasticity of substances. He also investigated the voice and hearing. He devised a rotating toothed wheel to produce a sound of any frequency by a reed held against it, to measure high frequency hearing limits. *TIS

1914 Edward Singleton Holden (November 5, 1846 – March 16, 1914) was an American astronomer. Born in St. Louis, Missouri in 1846 to Jeremiah and Sarah Holden. From 1862-66, he attended Washington University in St. Louis, where he obtained a B.S. degree. He later trained at West Point in the class of 1870.In 1873 he became professor of mathematics at the US Naval Observatory, where he made a favorable impression on Simon Newcomb. He was director of Washburn Observatory at the University of Wisconsin–Madison from 1881 to 1885. He was elected a member of the American National Academy of Sciences in 1885.
On August 28, 1877, a few days after Asaph Hall discovered the moons of Mars Deimos and Phobos, he claimed to have found a third satellite of Mars. Further analysis showed large mistakes in his observations.
He was president of the University of California from 1885 until 1888, and the first director of the Lick Observatory from 1888 until the end of 1897. Meanhwile in 1893 while at the observatory he published a book on Mughal Emperors, The Mogul emperors of Hindustan, A.D. 1398- A.D. 1707. He resigned as a result of internal dissent over his management among his subordinates. While at the Lick Observatory, he was the founder of the Astronomical Society of the Pacific and its first President (1889–1891).
In 1901 he became the librarian of the United States Military Academy at West Point, where he remained until his death.
His cousin, George Phillips Bond, was director of Harvard College Observatory.
He discovered a total of 22 NGC objects during his work at Washburn Observatory.
He wrote many books on popular science (and on other subjects, such as flags and heraldry), including science books intended for children. For example the book Real Things In Nature. A Reading Book of Science for American Boys and Girls published in 1916.*Wik

1922 George Bruce Halsted (23 Nov 1853 in Newark, New Jersey, USA - 16 March 1922 in New York, USA) His main interests were the foundations of geometry and he introduced non-euclidean geometry into the United States, both through his own research and writings as well as by his many important translations. Halsted gave commentaries on the work of Lobachevsky, Bolyai, Saccheri and Poincaré and made translations of their works into English. His work on the foundations of geometry led him to publish Demonstration of Descartes's theorem and Euler's theorem in the Annals of Mathematics in 1885. His other main interest was in mathematical education and, as a mathematics educator, he criticised the careless way that mathematics was presented in the textbooks of the time. He contributed over ninety article to the American Mathematical Monthly and wrote many biographies of mathematicians such as Lambert, Farkas Bolyai, Lobachevsky, De Morgan, Sylvester, Chebyshev, Cayley, Hoüel and Klein. *SAU

1933 Alfréd Haar (11 Oct 1885 in Budapest, Hungary - 16 March 1933 in Szeged, Hungary) was a Hungarian mathematician who is best remembered for his work on analysis on groups, introducing a measure on groups, now called the Haar measure. *SAU

1940 Sir Thomas Little Heath (5 October 1861 – 16 March 1940) was a British civil servant, mathematician, classical scholar, historian of ancient Greek mathematics, translator, and mountaineer. Heath translated works of Euclid of Alexandria, Apollonius of Perga, Aristarchus of Samos, and Archimedes of Syracuse into English.
He was distinguished for his work in Greek Mathematics and author several books on Greek mathematicians. It is primarily through Heath's translations that modern English-speaking readers are aware of what Archimedes did.
He died in Ashtead, Surrey. *Wik

1941 Edward Lindsay Ince (30 Nov 1891 in Amblecote, Staffordshire, England
- 16 March 1941 in Edinburgh, Scotland) Ince graduated from Edinburgh and researched at Edinburgh and Cambridge. He worked at universities in Leeds, Liverpool, Cairo, Edinburgh and Imperial College London before moving back to Edinburgh as Head of Technical Mathematics. He worked on Special Functions. *SAU

1980 William Prager (May 23, 1903, Karlsruhe - 16 March 1980 in Zurich, Switzerland) was a German-born US applied mathematician. He was a lecturer at Darmstadt, a deputy director at University of Göttingen, professor at Karlsruhe, University of Istanbul, the University of California, San Diego and Brown University, where he advised Bernard Budiansky.
The Society of Engineering Science has awarded the Wiliam Prager Medal in Solid Mechanics since 1983 in his honor.*Wik

1992 Yves-André Rocard (22 May 1903 in Vannes, France - 16 March 1992 in Paris, France) French mathematician and physicist who

Credits :
*CHM=Computer History Museum
*FFF=Kane, Famous First Facts
*NSEC= NASA Solar Eclipse Calendar
*RMAT= The Renaissance Mathematicus, Thony Christie
*SAU=St Andrews Univ. Math History
*TIA = Today in Astronomy
*TIS= Today in Science History
*VFR = V Frederick Rickey, USMA
*Wik = Wikipedia
*WM = Women of Mathematics, Grinstein & Campbell

On This Day in Math - March 15

1659 title page of one of Argoli's books.*Wik

...there is no study in the world which brings into more harmonious action all the faculties of the mind than [mathematics], ... or, like this, seems to raise them, by successive steps of initiation, to higher and higher states of conscious intellectual being ...
~James J Sylvester

The 74th day of the year.
74 is related to an open question in mathematics since 742 + 1 is prime. Hardy and Littlewood conjectured that asymptotic number of elements in this sequence, primes = n2 + 1, not exceeding n is approximately \(c \frac {\sqrt{n}} {log(n)}\) for some constant c. There was a $1000 prize for best solution to an open sequence during 2015 and submitting it to OEIS, details here

74 is the sum of the squares of two consecutive prime numbers. 
A hungry number is number in the form 2n  that eats as much pi as possible, for example 25 is the smallest power of two that contains a 3.  The smallest power that contains the first three digits of pi, 314 is 27 4
(eating e seems much harder for powers of 2)

22796996699 is the 999799787th prime. Note that the sum of digits of the nth prime equals the sum of digits of n. The number 74 is the largest known digit sum with this property (as of August 2004). *Prime Curios

44 B.C. Julius Caesar assassinated on the Ides of March, a phrase which came to denote an ill omen. The word “ides” is from the Etruscan for one-half (it is the middle of the lunar month).

1758 March 15th was the earliest date in the prediction of the return of Halley's comet by the team of Clairaut, La Lande and Lepaute. After incremental computations of the gravitational influences and motion of Jupiter and Saturn on the predicted return of Halley's comet, Alexis-Claude Clairaut presents the results to the Academies de Sciences. The computational work of the team of Clairaut, with La Lande and Nicole-Reine Lepaute, (having removed Saturn from the last few months calculations to speed the results) had predicted a window of arrival between March 15 and May 15 (1758).
The unruly comet reached perihelion on the 13th of March. *David A Grier, When Computers Were Human

In 1806, a 6-kg chondritemeteorite - carrying carbon-based, organic chemicals - was unequivocally identified for the first time. Its arrival on earth was noted at 5:30 pm, outside Alais, France. The organic chemicals it carried suggested the possibility of life on whatever body was the source, somewhere in the universe. According to the observations of Berzelius and a commission appointed by the French Academy it "emits a faint bituminous substance" when heated. Berzelius reported his analysis of the Alais meteorite in 1833 that destructive distillation yielded a blackish substance, indiginous water, carbon dioxide gas, a soluble salt containing ammonia, and a blackish-brown sublimate, which Berzelius confessed was unknown to him. *TIS

1871 James Clerk Maxwell in a letter to C. J. Monro comments on the fourth dimension, "The peculiarity of our space is that of its three dimensions, none is before or after another. As is x, so is y, and so is z."
Later in the same message he adds, "I am quite sure that the kind of continuity which has four dimensions all co-equal is not to be discovered by merely generalizing Cartesian space equations." Alfred M. Bork, The Fourth Dimensions in Ninetenth-Century Physics, Isis, Sept. 1964, pg 326-338
Matt Parkers fun book on the Fourth Dimension

1873 Lewis Carroll in a letter to fourteen year old Helen Fielden offers a tempting geometric problem,
I don’t know if you’re fond of puzzles, or not. If you are, try this. If not, never mind. A gentlemen (a nobleman let us say, to make it more interesting) had a sitting-room with only one window in it — a square window, 3 feet high and 3 feet wide. Now, he had weak eyes, and the window gave too much light,  so (don’t you like “so” in a story?) he sent for the builder, and told hm to alter it, so  as to give half the light. Only, he was to keep it square — he was to keep it 3 feet high — and he was to keep it 3 feet wide. How did he do it? Remember, he wasn’t allowed to use curtains, or shutters, or colored glass, or anything of that sort.

I must tell you an awful story of my trying to set a puzzle to a little girl the other day. It was at a dinner party, at dessert. I had never seen her before, but, as she was sitting next me, I rashly proposed to her to try the puzzle (I daresay you know of it) of “the fox, the goose, and bag of corn.” And I got some biscuits to represent the fox and the other things. Her mother was sitting on the other side, and said, “Now you take pains, my dear, and do it right!” The consequences were awful! She shrieked out, “I can’t do it! I can’t do it! Oh, Mamma! Mamma!” threw herself into her mother’s lap, and went off into a fit of sobbing which lasted several minutes! That was a lesson to me about trying children with puzzles. I do hope the square window won’t produce any awful effect on you! I am.

*Robin Wilson, Lewis Carroll in Numberland: His Fantastical Mathematical Logical Life (If the puzzle stumps you, I put a helpful hint at the bottom after credits.)

1955 John von Neumann sworn in as one of the first Atomic Energy Commissioners. In August he learned that he had bone cancer. *Goldstein, The Computer from Pascal to von Neumann

1933 Winston Churchill was very interested in science and wrote often and popularly on the subject. He chaired a conference in on the atomic discoveries in the Cavendish Laboratory in Cambridge. On this date his scientific friend, Frederick Lindemann said of him, "All the qualities … of the scientist are manifest in him. The readiness to face realities, even though they contradict a favourite hypothesis; the recognition that theories are made to fit facts, not facts to fit the theories; the interest in phenomena and the desire to explore them, and above all the underlying conviction that the world is not just a jumble of events but that there must be some higher unity." *Graham Farmelo, Churchills Bomb

1994 Aldus Corporation and Adobe Systems Inc. Merge:
Aldus Corporation and Adobe Systems Inc. announce they will merge. Aldus revolutionized desktop publishing (DTP) when founder Paul Brainerd released the PageMaker program in 1985. Computer Scientists John Warnock and Charles Geschke applied knowledge learned in their graduate work to similar products and founded Adobe in 1982.CHM

2012 Every year on March 15 since 1957, the city of Hinckley, Ohio has eagerly awaited the return of the buzzards at "Buzzards' Roost" at the Hinckley Reservation, part of the Cleveland Metroparks. *

1570 Andrea Argoli a versatile Italian scholar. He was a jurist, mathematician, astronomer and astrologer, and medical writer.
He was professor of mathematics at the University of Rome La Sapienza, from 1622 to 1627, and then the University of Padua 1632 to 1657. His astrology pupils may have included Placido Titi, and Giambattista Zenno, astrologer to Wallenstein.*Wik
From 1622 to 1627 he held a chair of mathematics in Rome, but lost it because of his enthusiasm for astrology. *VFR

1713 Abbé Nicolas Louis de La Caille (15 Mar 1713; 21 Mar 1762 at age 48) was a French astronomer who named 15 of the 88 constellations in the sky. He spent 1750-1754 mapping the constellations visible from the Southern Hemisphere, as observed from the Cape of Good Hope, the southernmost part of Africa. In his years there, he was said to have observed over 10,000 stars using just his 1/2-inch refractor. He established the first southern star catalogue containing 9776 stars (Caelum Australe Stelliferum, published partly in 1763 and completely in 1847), and a catalogue of 42 nebulae in 1755 containing 33 true deep sky objects (26 his own discoveries).*TIS

1855 Sir Charles Vernon Boys (15 Mar 1855; 30 Mar 1944 at age 88) English physicist and inventor of sensitive instruments. He graduated in mining and metallurgy, self-taught in a wide knowledge of geometrical methods. In 1881, he invented the integraph, a machine for drawing the antiderivative of a function. Boys is known particularly for his utilization of the torsion of quartz fibres in the measurement of minute forces, enabling him to elaborate (1895) on Henry Cavendish's experiment to improve the values obtained for the Newtonian gravitational constant. He also invented an improved automatic recording calorimeter for testing manufactured gas (1905) and high-speed cameras to photograph rapidly moving objects, such as bullets and lightning discharges. Upon retirement in 1939, he grew weeds.*TIS

A reproduction of his wonderful book, Soap-Bubbles: Their Colours and the Forces Which Mould Them : Being the Substance of Many Lectures Delivered to Juvenile and Popular Audiences with the Addition of Several New and Original Sections

1860 Walter Frank Raphael Weldon DSc FRS (Highgate, London, 15 March 1860 – Oxford, 13 April 1906) generally called Raphael Weldon, was an English evolutionary biologist and a founder of biometry. He was the joint founding editor of Biometrika, with Francis Galton and Karl Pearson.*Wik Pearson said of him, "He was by nature a poet, and these give the best to science, for they give ideas." *SAU

1868 Grace Chisholm Young (née Chisholm; 15 March 1868 – 29 March 1944) was an English mathematician. She was educated at Girton College, Cambridge, England and continued her studies at Göttingen University in Germany, where in 1895 she became the first woman to receive a doctorate in any field in that country. Her early writings were published under the name of her husband, William Henry Young, and they collaborated on mathematical work throughout their lives. For her work on calculus (1914–16), she was awarded the Gamble Prize.
Her son, Laurence Chisholm Young, was also a prominent mathematician. One of her living granddaughters, Sylvia Wiegand (daughter of Laurence), is also a mathematician (and a past president of the Association for Women in Mathematics.)*Wik

1897 James Joseph,(Sylvester) (3 Sep 1814; 15 Mar 1897) youngest child of Abraham Joseph, born in London. The eldest son, an actuary, eventually migrated to the U.S. where, for unknown reasons, he took the surname Sylvester. The rest of the family soon followed suit, so that is how James Joseph Sylvester got his name. *VFR British mathematician who, with Arthur Cayley, founded the theory of algebraic invariants, algebraic-equation coefficients that are unaltered when the coordinate axes are translated or rotated. Beginning in 1833, he studied at St John's College, Cambridge. However, at this time signing a religious oath to the Church of England was required to graduate. Being Jewish, he refused and so he did not graduate. He taught physics at the University of London (1838-41), one of the few places which did not bar him because of his religion. Sylvester did important work on matrix theory, in particular, to study higher dimensional geometry. In 1851 he discovered the discriminant of a cubic equation. Earlier in his life, he tutored Florence Nightingale.*TIS (This idea of Sylvester tutoring Nightingale, to the best of my knowledge, originates from the Herbert Baker obituary. Karen Hunger Parshall, among others, has questioned the accuracy of this statement.)
James Joseph Sylvester died, at age 83, after earlier suffering a paralytic stroke while working at his mathematics. *VFR
I came across a nice story about Sylvester on the wonderful "Cut-the-Knot" blog of Alexander Bogomolny. He writes, "Sylvester was one the greatest British mathematicians of the 19th century. He was known for his absentmindedness and poor memory; on one occasion he even denied the truth of one of his own theorems."

1900 Elwin Bruno Christoffel (November 10, 1829 in Montjoie, now called Monschau – March 15, 1900 in Strasbourg) was a German mathematician and physicist. Christoffel worked on conformal maps, potential theory, invariant theory, tensor analysis, mathematical physics, geodesy, and shock waves. The Christoffel symbol, Riemann–Christoffel tensor, and Schwarz–Christoffel mapping are named after him. *

1960 Eduard Cech,(29 June 1893 in Stracov, Bohemia (now Czech Republic)- 15 March 1960 in Prague, Czechoslovakia (now Czech Republic)) Czech topologist. His research interests included projective differential geometry and topology. In 1921–1922 he collaborated with Guido Fubini in Turin. He died in Prague. *Wik

1955 Michele Angelo Besso (25 May 1873 Riesbach – 15 March 1955 Genoa) was a Swiss/Italian engineer of Jewish Italian (Sephardi) descent. He was a close friend of Albert Einstein during his years at the Federal Polytechnic Institute in Zurich, today the ETH Zurich, and then at the patent office in Bern. Besso is credited with introducing Einstein to the works of Ernst Mach, the sceptical critic of physics who influenced Einstein's approach to the discipline. Einstein called Besso "the best sounding board in Europe" for scientific ideas.
In a letter of condolence to the Besso family Albert Einstein wrote his now famous quote "Now Besso has departed from this strange world a little ahead of me. That means nothing. People like us, who believe in physics, know that the distinction between past, present and future is only a stubbornly persistent illusion" *Wik

1962 Arthur Holly Compton (10 Sep 1892; 15 Mar 1962) American physicist and engineer. He was a joint winner, with C.T.R. Wilson of England, of the Nobel Prize for Physics (1927) for his discovery and explanation of the change in the wavelength of X rays when they collide with electrons in metals. This so-called Compton effect is caused by the transfer of energy from a photon to a single electron, then a quantum of radiation is re-emitted in a definite direction by the electron, which in so doing must recoil in a direction forming an acute angle with that of the incident radiation. During WW II, in 1941, he was appointed Chairman of the National Academy of Sciences Committee to Evaluate Use of Atomic Energy in War, assisting in the development of the atomic bomb.*TIS

1992 Deane Montgomery (2 Sept 1909 - 15 March 1992 in Chapel Hill, North Carolina, USA) was a mathematician specializing in topology who was one of the contributors to the final resolution of Hilbert's fifth problem in the 1950s. He served as President of the American Mathematical Society from 1961 to 1962.
Born in the small town of Weaver, Minnesota, he received his B.S. from Hamline University in St. Paul, MN and his Masters and Ph.D. from the University of Iowa in 1933; his dissertation advisor was Edward Chittenden.
In 1941 Montgomery was awarded a Guggenheim Fellowship. In 1988, he was awarded the American Mathematical Society Leroy P. Steele Prize for Lifetime Achievement.*Wik

2004 William Hayward Pickering (24 Dec 1910; 15 Mar 2004) Engineer and physicist, head of the team that developed Explorer 1, the first U.S. satellite. He collaborated with Neher and Robert Millikan on cosmic ray experiments in the 1930s, taught electronics in the 1930s, and was at Caltech during the war. He spent the rest of his career with the Jet Propusion Laboratory, becoming its Director (1954) with responsibility for the U.S. unmanned exploration of the planets and the solar system. Among these were the Mariner spacecraft to Venus and Mercury, and the Viking mission to Mars. The Voyager spacecraft yielded stunning photographs of the planets Jupiter and Saturn.*TIS

2004 John A. Pople (31 Oct 1925; 15 Mar 2004) British mathematician and chemist who, (with Walter Kohn), received the 1998 Nobel Prize in Chemistry for his work on computational methodology to study the quantum mechanics of molecules, their properties and how they act together in chemical reactions. Using Schrödinger's fundamental laws of quantum mechanics, he developed a computer program which, when provided with particulars of a molecule or a chemical reaction, outputs a description of the properties of that molecule or how a chemical reaction may take place - often used to illustrate or explain the results of different kinds of experiment. Pople provided his GAUSSIAN computer program to researchers (first published in 1970). Further developed, it is now used by thousands of chemists the world over. *TIS

2006 George Whitelaw Mackey (February 1, 1916 in St. Louis, Missouri – March 15, 2006 in Belmont, Massachusetts) was an American mathematician.
Mackey's main areas of research were in the areas of representation theory, ergodic theory, and related parts of functional analysis. Earlier in his career Mackey did significant work in the duality theory of locally convex spaces, which provided tools for subsequent work in this area, including Alexander Grothendieck's work on topological tensor products.
He has written numerous survey articles connecting his research interests with a large body of mathematics and physics, particularly quantum mechanics and statistical mechanics. He was among the first five recipients of William Lowell Putnam fellowships in 1938.*Wik

Credits :
*CHM=Computer History Museum
*FFF=Kane, Famous First Facts
*NSEC= NASA Solar Eclipse Calendar
*RMAT= The Renaissance Mathematicus, Thony Christie
*SAU=St Andrews Univ. Math History
*TIA = Today in Astronomy
*TIS= Today in Science History
*VFR = V Frederick Rickey, USMA
*Wik = Wikipedia
*WM = Women of Mathematics, Grinstein & Campbell

(Hint for the Lewis Carroll puzzle, think of diamonds.) 

Wednesday, 14 March 2018

On This Day in Math - March 14

Two of my favorite guys celebrate Pi-Day

"It is nothing short of a miracle that modern methods of instruction have not yet entirely strangled the holy curiosity of inquiry."
~Albert Einstein

Today, have your Pi(e) both ways!

The 73rd day of the year; 73 is the alphanumeric value of the word NUMBER: 14 + 21 + 13 + 2 + 5 + 18 = 73 *Tanya Khovanova, Number Gossip;

The 73rd day is Pi day in non-leap years, the string 73 appears at the 299th and 300th digits after the decimal point of Pi.

Fans of the Big Bang Theory on TV know that Leonard refers to 73 as the "Chuck Norris of Numbers"  After Sheldon points out that : 73 is the 21st prime, and it's mirror image 37 is the 12th prime. This enigma is the only known such combination.

Sheldon failed to mention that 73 is also the 37th odd number.

And 73 is the smallest prime factor of a googol + 1 *Prime Curios

A good time to introduce you student's to a nice way to find many digits of pi, pick ) pick a relatively close apppx of pi (I'll use 2.5) and call it x, then x+ sin(x) is a better approximation, and repeating continues to give more and more digits of pi up to limits of calculator For 2.5 we get 3.098 -> 3.14157 -> 3.141592654 .  (student's might be challenged for why (and when) this works).

And of course, for Pi Day, we need the world's most accurate Pi Chart

1664 Isaac Barrow delivered his “Prefatory Oration” as the first Lucasion Professor at Cambridge. It lasted two hours, and contained the following plea for students to come to his office: “If it be then your Pleasure, ye Lovers of Study, come always; be not restrained through any Fear, or retarded too much by Modesty, what you may do by your Right, you shall make me do willingly, nay gladly and joyfully. Ask your Questions, make your Enquiries, bid and command; you shall neither find me adverse nor refractory to your Commands, but officious and obedient. If you meet with any Obstacles or Difficulties, or are retarded with any Doubts while you are walking in the cumbersome Road of this Study of Mathematics, I beg you to impart them, and I shall endeavor to remove every Hindrance out of your Way to the best of my Knowledge and Ability.” In closing and referring to himself he states that “An accomplished mathematician, is a most wretched orator.” * The Prefactory Oration' (address to the University of Cambridge upon being elected Lucasian Professor of Mathematics, 14 Mar 1664)

1667/8 Pepys records in his diary that he saw Sir. Samuel Morland’s adding machine for pounds, shillings and pence. Samuel Pepys also wrote in his diary, that the machine of Morland is very pretty, but not very useful, while the famous scientist Robert Hooke, for example, found the machines very silly.

1818 John Adams writes to Thomas Jefferson about David Rittenhouse and his Orrery, he says:
"Rittenhouse was a virtuous and amiable man, an exquisite mechanician, master of the astronomy known in his time, an expert mathematician, a patient calculator of numbers." U Penn Library website

In 1839, Sir John Herschel referred to "photography" in a lecture to the Royal Society—possibly the first use of the word. Following Fox Talbot's publication of his invention of what became known as the Calotype process, a number of scientific men made their own investigations, including not only Herschel but also Berard, Robert Hunt and Draper. Herschel used the name Chrysotype (from the Greek word for gold) for his process. It used paper washed in a solution of ammonio-citrate of iron and brought out the image with a solution of soda or chloride of gold, or with nitrate of silver, and fixing it in the first case by washing it with iodide of potassium and in the second, with hyposulphite of soda. It had technical difficulties in controlling the contrast, colour and fogging of the image. *TIS
Appropriately, it was an astronomer who coined the term photography, but the questoin is, which one. Some credit Johann Heinrich von Madler for combining “photo” (from the Greek word for “light”) and “graphy” (“to write”). *  Madler's claim rests on a paper supposedly written on 25 February 1839 in the German newspaper Vossische Zeitung. Many still credit Sir John Herschel both for coining the word and for introducing it to the public. His uses of it in private correspondence prior to 25 February 1839 and at his Royal Society lecture on the subject in London on 14 March 1839 have long been amply documented and accepted as settled facts.

1930 At breakfast in the family home in Oxford, 11-year-old Venetia Burney suggested a name for a newly discovered planet that her grandfather read about in his Times of London edition. Venetia’s grandfather, the retired head of the historic Bodleian Library at Oxford University, passed the idea along to an astronomer friend of his, who telegraphed his colleagues at the Lowell Observatory in Flagstaff, Arizona. They voted unanimously in favor of the name. Pluto, the solar system’s ninth planet, was born. Read more at *Washington Post.   In 1877, Venetia's grandfather's brother, Henry, a housemaster at Eton, had successfully proposed that the two dwarf moons of Mars be named Phobos and Deimos, two attendants of the Roman war god, whose names mean fear and terror.

1934 France issued a stamp for the centenary of the death of Joseph Jacquard (1752–1834), inventor of an improved loom for figured weaving. The punched cards that he invented provided the model for computer cards. [Scott #295] *VFR

1951 Kurt G¨odel shared the first Einstein award with Julian Schwinger. *VFR

1955 Bell Labs Announces TRADIC "Giant Brain":
AT&T Bell Laboratories announces the completion of the first fully transistorized computer, TRADIC. TRADIC contained nearly 800 transistors, which replaced the standard vacuum tube and allowed the machine to operate on fewer than 100 watts -- or one-twentieth the power required by a comparable vacuum tube computer.*CHM

1962 Norway issued a pair of stamps commemorating the centenary of the birth of Vilhelm Bjerknes (1862–1951), physicist, meterologist, and mathematician. [Scott #403–4] *VFR

1988 The earliest known official or large-scale celebration of Pi Day was organized by Larry Shaw in 1988 at the San Francisco Exploratorium, where Shaw worked as a physicist, with staff and public marching around one of its circular spaces, then consuming fruit pies. The Exploratorium continues to hold Pi Day celebrations.
On March 12, 2009, the U.S. House of Representatives passed a non-binding resolution (HRES 224), recognizing March 14, 2009, as National Pi Day *Wik

1995 On Tuesday, March 14, Speaking at the string theory conference at University of Southern California , Edward Witten made the surprising suggestion that the five existing string theories were in fact not distinct theories, but different limits of a single theory which he called M-theory. Witten's proposal was based on the observation that the five string theories can be mapped to one another by certain rules called dualities and are identified by these dualities. "E. Witten: Some problems of strong and weak coupling" *Wik

2012 Judge rules you can't copyrite Pi... The story stripped from Devlin's Angle by Keith Devlin:
The story begins on Pi Day (March 14, or 3.14) 2011, when New Scientist posted a video by a musician called Michael John Blake, in which he played a piano rendering of the first 31 decimal places of pi, played at a tempo of 157 beats per minute (314 divided by two).

The video immediately went viral, but a few hours later, YouTube was contacted by a lawyer representing jazz musician Lars Erickson, who claimed that Blake's work sounded very similar to his 1992 composition "Pi Symphony", which he had registered with the US copyright office. With a claim of copyright infringement, YouTube removed the video. But Blake decided to lodge an appeal.
One year later, on March 14 of this year, US district court judge Michael H. Simon, deliberately choosing to announce his decision on Pi Day, dismissed Erickson’s claim of copyright infringement. "Pi is a non-copyrightable fact, and the transcription of pi to music is a non-copyrightable idea," Simon wrote in his legal opinion.
So now, without fear of prosecution, is the first 31 digits of Pi.

What Pi Sounds Like from Michael John Blake on Vimeo.

2015 Pi day on this day will have a special moment (or two such moments for folks with 12 hour clocks), at 9:26:53 of 3/14/15. Approximating \( \pi \approx 3.14159265 \)

2015 This day is the planned first day issue of a Danish stamp showing the popular Hanson writing ball from 1878. The writing ball was invented in 1865 by the reverend Rasmus Malling-Hansen (1835–1890) principal of the Royal Institute for the Deaf-Mutes in Copenhagen. The machine included an electromagnetic escapement for the Ball, thus making Malling-Hansen's machine the first electric typewriter. It was exhibited at a great industrial exhibition in Copenhagen in 1873, at the world exhibition in Vienna in 1873, and at the Paris exhibition or Exposition Universelle. All through the 1870s it won several awards. It was sold in many countries in Europe, and it is known that it was still in use in offices in London as late as 1909. *Wik

2016 Sphere packing for eight dimensions is solved by Maryna Viazovska. In 1611, Kepler conjectured that here was no way to pack spheres more densly than the way we would normally stack oranges or cannonballs, with every triangle of three supporting another nestled above (and below) tangent to all of the first three. By 1831 Gauss had managed to prove the conjecture for 3d. In her paper Viazovska proved no packing of unit balls in Euclidean space R8 has density greater than that of the E8-lattice packing. One week later, (March 21) building on her work, with collaboration of four others, they were able to prove that the Leech lattice is the densest packing of congruent spheres in twenty-four dimensions, and that it is the unique optimal periodic packing. *arxiv.

1692 Pieter van Musschenbroek (14 Mar 1692; 19 Sep 1761 at age 69) Dutch mathematician and physicist who invented the Leyden jar, the first effective device for storing static electricity. He grew up in a family that manufactured scientific instruments such as telescopes, microscopes and air pumps. Before Musschenbroek's invention, static electricity had been produced by Guericke using a sulphur ball, with minor effects. In Jan 1746, Musschenbroek placed water in a metal container suspended on silk cords, and led a brass wire through a cork into the water. He built up a charge in the water. When an unwary assistant touched the metal container and the brass wire, the discharge from this apparatus delivered a substantial shock of static electricity. The Leyden name is linked to the discovery having being made at the University of Leiden. *TIS

1835 Giovanni Virginio Schiaparelli (14 Mar 1835; 4 Jul 1910 at age 75) Italian astronomer who is remembered for his observations of Mars over seven oppositions and named the "seas" and "continents". In 1877, he saw on the surface of the planet Mars the markings that he called canali (channels), later misinterpreted as "canals." He made extensive studies, both observational and theoretical, of comets, determining from the shapes of their tails that there was a repulsive force from the sun. He showed that meteor swarms travel through space in cometary orbits. He explained the regular meteor showers as the result of the dissolution of comets and proved it for the Perseids. He suggested that Mercury and Venus rotate on their axes, discovered the asteroid Hesperia (1861) and was a major observer of double stars. *TIS

1838 Rev U Jessee Kniseley (March 14, 1838 - May 19, 1881) was born in New Philadelphia, Ohio March 14 1838 He was a self made man and in a very great measure self educated. The degree of MA was conferred on him by Marietta College and that of PhD by Wittenberg College in which latter institution he had formerly been a classical and theological student. He also attended Jefferson College Pa but was not a graduate of any college. He was chosen President and Professor of Mathematics of Luther College, an institution of ephemeral existence. Rev Dr Knisely was a Lutheran preacher of marked ability and great eloquence and for fourteen years previous to his death he was the loved pastor of the church of that denomination at Newcomerstown. He was a very fine mathematician and excelled especially in the solution of algebraic and geometrical problems The elegant solution of a Diophantine problem on pp 105 and 106 of the Mathematical Visitor Vol I No 4 and of the celebrated Malfatti's Problem pp 189 and 190 of No 6 are admirable samples of his superior skill in these departments of analysis. Rev Dr Knisely was also a master of language and the author of several works. Copies of his Parser's Manual and Arithmetical Questions for the Recreation of the Teacher and the Discipline of the Pupil are possessed by the writer. It is stated in the Tuscarawas Chroical from which the substance of a portion of this notice is taken that he was also author of Kniseley's Arithmetic and Mrs Knisely states that he had in preparation a work on the Carculus, but of these works the writer knows nothing. His last work was the revision of Ray's Higher Arithmetic and the Key which he completed but a short time before his death. He died May 19, 1881 at the age of 43 years 2 months and 5 days The disease that caused his death was a general prostration of the nervous system. *Artemas Martin, Mathematical Visitor January 1882

1862 Vilhelm F(riman) K(oren) Bjerknes (14 Mar 1862; 9 Apr 1951 at age 89) was a Norwegian meteorologist and physicist, one of the founders of the modern science of weather forecasting. As a young boy, Bjerknes assisted his father, Carl Bjerknes (a professor of mathematics) in carrying out experiments to verify the theoretical predictions that resulted from his father's hydrodynamic research. After graduating from university, Bjerknes moved on to his own work applying hydrodynamic and thermodynamic theories to atmospheric and hydrospheric conditions in order to predict future weather conditions. His work in meteorology and on electric waves was important in the early development of wireless telegraphy. He evolved a theory of cyclones known as the polar front theory with his son Jakob. *TIS

1864 József Kürschák (14 March 1864 – 26 March 1933) was a Hungarian mathematician noted for his work on trigonometry and for his creation of the theory of valuations. He proved that every valued field can be embedded into a complete valued field which is algebraically closed. In 1918 he proved that the sum of reciprocals of consecutive natural numbers is never an integer. Extending Hilbert's argument, he proved that everything that can be constructed using a ruler and a compass, can be constructed by using a ruler and the ability of copying a fixed segment. He was elected a member of the Hungarian Academy of Sciences in 1897. *Wik

1879 Albert Einstein (14 Mar 1879; 18 Apr 1955 at age 76) German-American physicist who developed the special and general theories of relativity and won the Nobel Prize for Physics in 1921 for his explanation of the photoelectric effect. Recognized in his own time as one of the most creative intellects in human history, in the first 15 years of the 20th century Einstein advanced a series of theories that proposed entirely new ways of thinking about space, time, and gravitation. His theories of relativity and gravitation were a profound advance over the old Newtonian physics and revolutionized scientific and philosophic inquiry.*TIS

1882 WacLlaw Sierpinski (14 March 1882 in Warsaw, - 21 Oct 1969 in Warsaw) His grave carries—according to his wish—the inscription: Investigator of infinity. [Kuratowski, A Half Century of Polish Mathematics, p. 173; Works, p. 14] *VFR Sierpinski's most important work is in the area of set theory, point set topology and number theory. In set theory he made important contributions to the axiom of choice and to the continuum hypothesis. *SAU He is also remembered for his Sierpinski gasket or Triangle

1889 Oscar Chisini (March 14, 1889 – April 10, 1967) was an Italian mathematician. He introduced the Chisini mean in 1929. In 1929 he founded the Institute of Mathematics (Istituto di Matematica) at the University of Milan, along with Gian Antonio Maggi and Giulio Vivanti. He then held the position of chairman of the Institute from the early 1930s until 1959.The Chisini conjecture in algebraic geometry is a uniqueness question for morphisms of generic smooth projective surfaces, branched on a cuspidal curve. A special case is the question of the uniqueness of the covering of the projective plane, branched over a generic curve of degree at least five. *Wik

1911 Akira Yoshizawa (吉澤 章 Yoshizawa Akira; 14 March 1911 – 14 March 2005) was a Japanese origamist, considered to be the grandmaster of origami. He is credited with raising origami from a craft to a living art. According to his own estimation made in 1989, he created more than 50,000 models, of which only a few hundred designs were presented as diagrams in his 18 books. Yoshizawa acted as an international cultural ambassador for Japan throughout his career. In 1983, Emperor Hirohito awarded him the Order of the Rising Sun, 5th class, one of the highest honors bestowed in Japan.
In March 1998, Yoshizawa was invited to exhibit his origami in the Louvre Museum. Although he had previously disliked his contemporaries, he was not opposed to having his photo taken with them. Many of his patterns had been diagrammed by his professional rivals, which angered Yoshizawa when he was younger.[citation needed] However, as he had aged, he found that he now enjoyed the company of his peers.
Yoshizawa died on 14 March 2005 in a hospital in Itabashi Ward, Tokyo due to complications of pneumonia on his 94th birthday *Wik Some of his work is shown in this video:

1927 Marcel Berger (14 April 1927 – 15 October 2016) was a French mathematician, doyen of French differential geometry, and a former director of the Institut des Hautes Études Scientifiques (IHÉS), France. Formerly residing in Le Castera in Lasseube, Berger was instrumental in Mikhail Gromov's accepting positions both at the University of Paris and at the IHÉS. His contributions to geometry were both broad and deep. The classification of Riemannian holonomy groups provided by his thesis has had a lasting impact on areas ranging from theoretical physics to algebraic
geometry. *Wik *AMS

1874 Johann Heinrich von Mädler (29 May 1794, 14 Mar 1874 at age 79) German astronomer who (with Wilhelm Beer) published the most complete map of the Moon of the time, Mappa Selenographica, 4 vol. (1834-36). It was the first lunar map to be divided into quadrants, and it remained unsurpassed in its detail until J.F. Julius Schmidt's map of 1878. Mädler and Beer also published the first systematic chart of the surface features of the planet Mars (1830). *TIS

1973 Howard Hathaway Aiken (9 Mar 1900; 14 Mar 1973 at age 72) American mathematician who invented the Harvard Mark I, forerunner of the modern electronic digital computer. While a graduate student and instructor Harvard University, Aiken's research had led to a system of differential equations which could only be solved using numerical techniques, for which he began planning large computer. His idea was to use an adaptation of Hollerith's punched card machine. When eventually built, (1943) it weighed 35 tons, had 500 miles of wire and could compute to 23 significant figures. There were 72 storage registers and central units to perform multiplication and division. It was controlled by a sequence of instructions on punched paper tapes, and used punched cards to enter data and give output from the machine. *TIS

2005 Akira Yoshizawa (吉澤 章 Yoshizawa Akira; 14 March 1911 – 14 March 2005) (See birth in 1911 above)

2018 Stephen W. Hawking (8 Jan 1942, 14 Mar 2018 )English theoretical physicist who is one of the world's leaders in his field. His principal areas of research are theoretical cosmology and quantum gravity. Hawking is the Lucasian Professor of Mathematics at Cambridge University (formerly held by Sir Isaac Newton). Afflicted with Lou Gehrig's disease (amyotrophic lateral sclerosis; ALS), Hawking is confined to a wheelchair and is unable to speak without the aid of a computer voice synthesizer. However, despite his challenges, he has utilized his intelligence, knowledge and abilities to make remarkable contributions to the field of cosmology (the study of the universe as a whole). *TIS Hawking was the first to set out a theory of cosmology explained by a union of the general theory of relativity and quantum mechanics. He was a vigorous supporter of the many-worlds interpretation of quantum mechanics. Born on the 300th anniversary of Galileo's death, and died on the birth anniversary of Albert Einstein.

Credits :
*CHM=Computer History Museum
*FFF=Kane, Famous First Facts
*NSEC= NASA Solar Eclipse Calendar
*RMAT= The Renaissance Mathematicus, Thony Christie
*SAU=St Andrews Univ. Math History
*TIA = Today in Astronomy
*TIS= Today in Science History
*VFR = V Frederick Rickey, USMA
*Wik = Wikipedia
*WM = Women of Mathematics, Grinstein & Campbell