## Wednesday, 28 June 2017

### On This Day in Math - June 28

In my opinion, a mathematician, in so far as he is a mathematician, need not preoccupy himself with philosophy -- an opinion, moreover, which has been expressed by many philosophers.
Henri Lebesgue

The 179th day of the year; 179 is a prime whose square has one each of the digits from 0 to 4.

179 is a "Knockout Prime" of the form K(3,2) since 17, 19, and 79 are all prime.

179 is an emirp, a prime whose reversal, 971 is also prime, and the combination sum and product 179 * 971 + 179 + 971=174959 is also an emirp.

1793 has all odd digits, 5735339. *Derek Orr

EVENTS

1451 Sort of the American version of the Medes and Lydians. The Seneca and Mohawk tribes were preparing for war when a total solar eclipse swept over both their camps late in the afternoon of this early summer day. Both immediately sued for peace. (ref. DB 6/97: "A star Called the Sun" by George Gamow). *NSEC

1489 Last total solar eclipse on Easter Island before the one on 11 July 2012. The next will be on 25 February 2324. Ref. More Mathematical Astronomical Morsels by Jean Meeus; Willmann-Bell, 2002. *NSEC

1751 The ﬁrst volume of Diderot’s and d’Alembert’s Encyclopedie appeared. See Hawkins, Jean d’Alembert p. 69.*VFR

1774 A Bill passed by Parliament included a clause to pay John Harrison for inventing a Timekeeper for finding Longitude at Sea. H5 was put on trial by the King himself in 1772, and performed superbly. The Board of Longitude, however, had refused to recognize the results of this trial, so John and William petitioned Parliament. They were finally awarded £8750 by this Act of Parliament. Perhaps more importantly, John Harrison was finally recognized as having solved the longitude problem. *Nat. Maritime Museum ‏@NMMGreenwich, *ticktocktony.com

1832, the first American case of a cholera epidemic was reported in New York City. Previously, Europe and the Americas were unaffected by the First Cholera pandemic of 1817 when cholera, long endemic to the Indian subcontinent, spread to Arabia, Syria, and southern Russia. This abated in the early 1820's, but a new cholera cycle began in 1826. It invaded the British Isles in Oct 1831. Canada was struck shortly before cholera reached New York. Cholera was a horrible disease, spread through fouled water. Its victims died after hours of cramps, diarrhea, and vomiting. Crowded into unsanitary slums, the poor suffered most. Many of the city's elite fled to the countryside. In America, the disease's hold broke by Dec 1832.*TIS

1884 Sonya Kovalevskaya officially appointed extraordinary professor at Stockholm University. [The Mathematical Intelligencer, vol. 6, no. 1, p. 29; *VFR ]

1949 Wolfgang Pauli writes to Carl Jung to with theories of the "Pauli effect", which Jung described as synchronicity. Pauli was famous among his colleagues for the numerous instances in which demonstrations involving equipment suffered technical problems only when he was present. He was actually banned from the laboratory of Otto Sturn a frequent dinner companion. Pauli and Jung both believed there was an effect, and tried to explain it. In this letter Pauli uses an example from the I-ching, the Chinese book of changes, to describe his thoughts on the effect. *Charles P. Enz, No Time to be Brief: A Scientific Biography of Wolfgang Pauli,

In 1958, the Mackinac Bridge, the world longest suspension bridge, was dedicated. Ceremonies began on 24 Jun with the first "Governor's Walk" across the bridge. (It had opened to traffic on 1 Nov 1957.) This bridge joins the upper and lower peninsulas of the state of Michigan, reducing the crossing time, from a couple of hours, to just 10 minutes. Ceremonial groundbreaking took place at the St. Ignace end of the bridge on 7 May 1954, and on the opposite shore at Mackinaw City the next day. Meanwhile caissons and superstructures were assembled as far away as Indiana, Pennsylvania and Ohio. Including approaches, the total length is 26,444-ft, needing 34 bridge support foundations. The main span is 3,800-ft long. *TIS

2009 Stephen Hawking gave a party for time travelers at 12:00 UT on this day. He did not announce the event until after it was over, and it appears that no one else cared to attend. Below is the invitation, so if you missed it up until now, it's not to late to choose not to attend. (So much for free will)
*daily Mail online

2011 "6.28" has become popular as Tau day with many people who think 2 pi (or 6.28...) is more appropriate, or just a nice addition to Pi-day, on March 14 (or 3.14... )

Births

1875 Henri Lebesgue (June 28, 1875 – July 26, 1941) He introduced the concept of Lebesgue Measure, a device for measuring the ‘length’ of complicated sets of points on the line, and so is known as the father of modern integration theory. *VFR French mathematician whose generalization of the Riemann integral revolutionized the field of integration. He was maître de conférences (lecture master) at the University of Rennes until 1906, when he went to Poitiers, first as chargé de cours (assistant lecturer) of the faculty of sciences and later as...*TIS

1894 Einar Hille (28 June 1894 – 12 February 1980) born. In the preface of his Analytic Function Theory (1959) he wrote “It is my hope that students of this book may come to respect the historical continuity of the subject.” More authors should include historical footnotes as good as those in this book.*VFR Hille's main work was on integral equations, differential equations, special functions, Dirichlet series and Fourier series. Later in his career his interests turned more towards functional analysis. His name persists among others in the Hille–Yosida theorem. *Wik

1920 Nicolaas Hendrik "Nico" Kuiper (28 June 1920, Rotterdam - 12 December 1994, Utrecht) was a Dutch mathematician, known for Kuiper's test and proving Kuiper's theorem. He also contributed to the Nash embedding theorem.
Kuiper completed his Ph.D. in differential geometry from the University of Leiden in 1946 under the supervision of Willem van der Woude.
He served as director of the Institut des Hautes Études Scientifiques from 1971 to 1985.*Wik

1948 Kenneth Alan "Ken" Ribet (June 28, 1948 -) is an American mathematician, currently a professor of mathematics at the University of California, Berkeley. His mathematical interests include algebraic number theory and algebraic geometry.
He earned his bachelor's degree and master's degree from Brown University in 1969, and his Ph.D. from Harvard University in 1973.
Ribet is credited with paving the way towards Andrew Wiles's proof of Fermat's last theorem. Ribet proved that the epsilon conjecture formulated by Jean-Pierre Serre was indeed true, and thereby proved that Fermat's Last Theorem would follow from the Taniyama–Shimura conjecture. Crucially it also followed that the full conjecture was not needed, but a special case, that of semistable elliptic curves, sufficed. An earlier theorem of Ribet's, the Herbrand–Ribet theorem, the converse to Herbrand's theorem on the divisibility properties of Bernoulli numbers, is also related to Fermat's Last Theorem. *Wik

1972 Ngô Bảo Châu (June 28, 1972 - ) is a Vietnamese and French mathematician at the University of Chicago, best known for proving the fundamental lemma for automorphic forms proposed by Robert Langlands and Diana Shelstad. In 2004, Chau and Laumon were awarded the Clay Research Award for their achievement in solving the fundamental lemma proposed by Robert Langlands for the case of unitary groups. Chau also became the youngest professor in Vietnam in 2005. His proof of the general case was selected by Time as one of the Top Ten Scientific Discoveries of 2009. In 2010, he received the Fields Medal and in 2012, the Legion of Honour He is the first Vietnamese to receive the Fields Medal *Wik

DEATHS

1768 George Hadley (12 Feb 1685; 28 Jun 1768 at age 83) English physicist and meteorologist who first formulated an accurate theory describing the trade winds and the associated meridional circulation pattern now known as the Hadley cell.*TIS Hadley died at Flitton and was buried in the chancel of Flitton church.

1889 Maria Mitchell (August 1, 1818 – June 28, 1889) First American professional woman astronomer, born Nantucket, Mass. While pursuing an amateur interest, on 1 Oct 1847, she gained fame from the observation of a comet which she was first to report. She was also the first female member of the American Association of Arts and Sciences. She died at age 70 in Lynn, Mass.

1930 William J Greenstreet graduated from Cambridge and became headmaster of Marling School Stroud. He is best-known as the long-running editor of the Mathematical Gazette.

1956 Friedrich Riesz (Jan. 22, 1880, in Győr; Feb. 28, 1956, in Budapest)
One of the most significant personalities among Hungarian mathematicians.
At the beginning he studied engineering at the Technical University of Zurich, but he soon realized that he was much more interested in mathematics than in technical subjects. So he continued to study at the Royal Hungarian University of Sciences in Budapest. For him the lectures of Gyula Kőnig and József Kürschák meant the most. Then he studied for a year in Göttingen and attended the lectures of David Hilbert and Hermann Minkowski. He obtained his PhD degree and diploma of secondary school teacher of mathematics and physics in Budapest.

1952 William Watson (15 June 1884, Musselburgh, East Lothian, Scotland
- 28 June 1952 , Edinburgh, Scotland) graduated in Mathematics and Physics from Edinburgh University. He became head of the Physics department at Heriot Watt College in Edinburgh.*SAU

1972 Prasanta Chandra Mahalanobis FRS (29 June 1893 – 28 June 1972) was an Indian scientist and applied statistician. He is best remembered for the Mahalanobis distance, (a statistical measure of the distance between a point P and a distribution D, - a multi-dimensional generalization of the idea of measuring how many standard deviations away P is from the mean of D. ) and for being one of the members of the first Planning commission of free india. He made pioneering studies in anthropometry in India. He founded the Indian Statistical Institute, and contributed to the design of large-scale sample surveys *Wik

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

1984 Claude Chevalley (11 February 1909, Johannesburg – 28 June 1984, Paris) had a major influence on the development of several areas of mathematics including Ring Theory and Group Theory *SAU

1974  Vannever Bush (March 11, 1890 – June 28, 1974) American electrical engineer and administrator who and oversaw government mobilization of scientific research during World War II. At the age of 35, in 1925, he developed the differential analyzer, the world's first analog computer. It was capable of solving differential equations. He put into concrete form that which began 50 years earlier with the incomplete efforts of Babbage, and the theoretical details developed by Kelvin. This machine filled a 20 x 30 foot room. He innovated one of the largest growing media in our time, namely hypermedia as fulfilled in the Internet with hypertext links *TIS

1989 Charles Wilderman Trigg,(Feb 7, 1898 Baltimore, Md; June 28, 1989 San Diego, Ca.) American engineer, mathematician and educator. Educated in engineering, mathematics and education at University of Pittsburgh, University of Southern California and University of California at Los Angeles. Worked as an industrial chemist and engineer, 1917-1943, and as an educator and administrator, 1946-1963. Served in the United States Navy during World War II. Book review editor of the Journal of Recreational Mathematics. Considered one of the foremost recreational mathematicians of the twentieth century. *U of Calgary Archives

2015 Louis Norberg Howard, (12 March, 1929; Chicago, Il - June 28,2015) emeritus professor of mathematics at MIT, and McKenzie emeritus professor at Florida State University, died on Sunday, at the age of 86.
Howard joined the MIT mathematics faculty in 1955 as an assistant professor, and was promoted to full professor in 1964. He retired from MIT in 1984.
Howard was an applied mathematician who worked primarily in the field of fluid dynamics. He made fundamental contributions to a broad range of subjects, including hydrodynamic stability and geophysical flows. He made a number of key advances in our understanding of turbulent convection, flows in Hele-Shaw cells, salt-finger zones, rotating flows, and reaction-diffusion equations. The power of his mathematical modeling was evident when he transformed qualitative ideas about the bounds on turbulent transport into rigorous mathematical arguments that initiated the field of upper-bound theory.
He received his BA in physics from Swarthmore College in 1950, and his MA and PhD in mathematical physics from Princeton, in 1952 and 1953, respectively, under the supervision of Donald Spencer. He took an appointment as a Higgins lecturer in mathematics at Princeton in 1953, after which he became a research associate in mathematics and aeronautics at Caltech in 1955.
Howard was named a fellow of the American Academy of Arts and Sciences in 1965 and the American Physical Society in 1984, and was elected to the National Academy of Sciences in 1977. In 1997, he was honored with the prestigious Fluid Dynamics Prize of the American Physical Society. *MIT News

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

## Tuesday, 27 June 2017

### On This Day in Math - June 27

Every science that has thriven has thriven upon its own symbols: logic, the only science which is admitted to have made no improvements in century after century, is the only one which has grown no symbols.
Augustus de Morgan

The 178th day of the year; 178 = 2 x 89. Note that 2 and 89 are the smallest and the largest Mersenne prime exponents under 100. *Prime Curios

178 is a palindrome in base 6,$[454]_6$ and in base 8 $[262]_8$

Strangely enough, 178 and 196 are related... In fact, 178 has a square with the same digits as 196:
1782 = 31,684
1962 = 38,416
178 has also a cube with the same digits as 196:
1783 = 5,639,752
1963 = 7,529,536
*Zoo of Numbers

EVENTS

432 B.C. Meton observed the summer solstice and began his cycle. Meton was one of the first Greek astronomers to make accurate astronomical observations. It is widely believed that, working with Euctemon, he observed the summer solstice, which marked the Athenian New Year, in 432 BC.
The Metonic cycle appears in the oldest known astronomical device, the Antikythera Mechanism (2nd century BC) together with its multiple the Callippus cycle of 76 years.
The foundations of Meton's observatory in Athens are still visible just behind the podium of the Pnyx, the ancient parliament. Meton found the dates of equinoxes and solstices by observing sunrise from his observatory. The bisectrice of the observatory lies in an easterly direction, between the Acropolis and the Lycabetus hill.*Wik

1739 "Heavens!, Maupertuis is a flea. Is he ever in one place?" So wrote Francoise de Graffigny to a friend about the French mathematician/man of letters, Pierre-Louis Moreau de Maupertuis. Graffigny affectionately gave the nickname to describe his "frenetic ubiquity." *Mary Terrall, The Man Who Flattened the Earth.

In 1847, New York and Boston were linked by telegraph wires. This enabled the New York newspapers to receive foreign news brought by Cunard's steamers to the Boston port about 190 miles away. When the Cambria next arrived in Boston, three New York Newspapers on 18 Jul 1846 carried identical brief first-day telegraphic summaries of the Cambia's news*. This telegraph link opened three years after the first U.S. telegraph line was opened on 24 May 1844 with a message sent by Samuel Morse 80 miles from Washington D.C. and Baltimore, Md.*TIS

1908 The academy of sciences of Gottingen announced a prize of one hundred thousand marks, according to the will of Dr. Paul Wolfskehl, of Darmstadt, for the proof of Fermat’s great theorem. A German industrialist and amateur mathematician, Wolfskehl bequeathed 100,000 marks to the Göttingen Academy of Sciences to be offered as a prize for a complete proof of Fermat's Last Theorem. On 27 June 1908, the Academy published nine rules for awarding the prize. Among other things, these rules required that the proof be published in a peer-reviewed journal; the prize would not be awarded for two years after the publication; and that no prize would be given after 13 September 2007, roughly a century after the competition was begun. Wiles collected the Wolfskehl prize money, then worth \$50,000, on 27 June 1997.
Prior to Wiles' proof, thousands of incorrect proofs were submitted to the Wolfskehl committee, amounting to roughly 10 feet (3 meters) of correspondence. In the first year alone (1907–1908), 621 attempted proofs were submitted, although by the 1970s, the rate of submission had decreased to roughly 3–4 attempted proofs per month. According to F. Schlichting, a Wolfskehl reviewer, most of the proofs were based on elementary methods taught in schools, and often submitted by "people with a technical education but a failed career". In the words of mathematical historian Howard Eves, "Fermat's Last Theorem has the peculiar distinction of being the mathematical problem for which the greatest number of incorrect proofs have been published."*Wik

1966 An almost 300 year old conjecture of Leonhard Euler is proven wrong. Euler had conjectured that, in the fashion that $x^2 + y^2 = z^2$ it always takes n terms to sum to an n-th power: two squares, three cubes, four fourth powers,etc. In 1966, L. J. Lander and T. R. Parkin found the first counterexample: four fifth powers that sum to a fifth power. They showed that $27^5 + 84^5 + 110^5 + 133^5 = 144^5.$ In 1988 Noam Elkies of Harvard University found a counterexample for fourth powers: \(2,682,440^4 + 15,365,639^4 + 187,960^4 = 20,615,673^4. Subsequently, Roger Frye of Thinking Machines Corporation did a computer search to find the smallest example: 95,800^4 + 217,519^4 + 414,560^4 = 422,481^4.*David Darling

1967 The first ATM in England that was put into use was by Barclays Bank in Enfield Town in North London, United Kingdom, on 27 June 1967. This machine was the first in the UK and was used by English comedy actor Reg Varney, at the time so as to ensure maximum publicity for the machines that were to become mainstream in the UK. This instance of the invention has been credited to John Shepherd-Barron of printing firm De La Rue, who was awarded an OBE in the 2005 New Year's Honours List. His design used special cheques that were matched with a personal identification number, as plastic bank cards had not yet been invented. *Wik (The plaque posted at the sight makes the claim to be the first cash machine in the world, but cash dispensing machines had been installed in Tokyo and another shortly after in Upsalla.)

1977 Italy issued a postage stamp honoring Filippo Brunelleschi (1377–1446). [Scott #1266]. *VFR

1980 Creighton Carvello recited 20,013 digits of π from memory in nine hours and one minute. *VFR

BIRTHS
1767 Alexis Bouvard (27 June 1767 – 7 June 1843) French astronomer and director of the Paris Observatory, who is noted for discovering eight comets and writing Tables astronomiques of Jupiter and Saturn (1808) and of Uranus (1821). Bouvard's tables accurately predicted orbital locations of Jupiter and Saturn, but his tables for Uranus failed, leading him to hypothesize that irregularities were caused by an unknown perturbing body. This spurred observations leading to the discovery of Neptune by Adams and Leverrier.*TIS

1806 Augustus de Morgan (27 June 1806 – 18 March 1871) born in Madura (now Madurai), India, son of a colonel in the Indian Army. He is best known for his work in Formal Logic. “De Morgan’s Laws”, are contained in his ﬁrst book (1847), although they were known to Peter of Spain in the fourteenth century. *VFR

The rules can be expressed in English as:
"The negation of a conjunction is the disjunction of the negations." and
"The negation of a disjunction is the conjunction of the negations."
*Wik
When he defined and introduced the term "mathematical induction" (1838), he gave the process a rigorous basis and clarity that it had previously lacked. He originated the use of the slash to represent fractions, as in 1/5 or 3/7. In Trigonometry and Double Algebra (1849) he gave a geometric interpretation of complex numbers. *TIS  A nice blog about De Morgan's life and relationships is at The Renaissance Mathematicus.

1850 Jorgen Pedersen Gram.(June 27, 1850 – April 29, 1916) Danish mathematician. Today he is best known for his criterion of linear independence of functions. The Gram-Schmidt Orthonormal Basis Theorem in Linear Algebra was ﬁrst published by him in 1883.
1940 Daniel G. Quillen bon in Orange, New Jersey. In 1978 he won a Fields Medal as the “prime architect of the higher algebraic K-theory, a new tool that successfully employed geometric and topological methods and ideas to formulate and solve major problems in algebra, particu¬larly ring theory and module theory.” *VFR French mathematician who is known for her work in number theory and contributions to the applied mathematics of acoustics and elasticity. Germain was self-taught from books, and from lecture notes supplied by male friends attending the Ecole Polytechnique which she, as a woman, was not permitted to attend. Using a male pseudonym, M. LeBlanc, she corresponded with Lagrange who recognised her skill, and subsequently sponsored her work. She accomplished a limited proof of Fermat's last theorem, for any prime under 100 where certain conditions were met. In 1816, she won a prize sponsored by Napoleon for a mathematical explanation of Chladni figures, the vibration of elastic plates. She died at age 55, from breast cancer. TIS

1931 Martinus Justinus Godefriedus Veltman (born June 27, 1931 in Waalwijk) is a Dutch theoretical physicist. He shared the 1999 Nobel Prize in physics with his former student Gerardus 't Hooft for their work on particle theory. In 1963/64, during an extended stay at SLAC he designed the computer program Schoonschip for symbolic manipulation of mathematical equations, which is now considered the very first Computer algebra system. He was awarded the Nobel Prize for Physics in 1999 together with 't Hooft, "for elucidating the quantum structure of electroweak interactions in physics". Veltman is now retired and holds a position of Emeritus Professor at the University of Michigan. Asteroid 9492 Veltman is named in his honor. *Wik

DEATHS
1829 James Smithson (ca. 1765 – 27 June 1829) English scientist who provided funds in his will for the founding of the Smithsonian Institution, Washington, D.C. "for the increase and diffusion of knowledge." He had inherited his fortune chiefly through his mother's family. He was a chemist and minerologist who published 27 scientific papers. The mineral smithsonite (carbonate of zinc) was named for him.*TIS

1831 Sophie Germain (April 1, 1776 – June 27, 1831)died before she could receive the honorary doctorate Gauss had persuaded the University of Gottingen to give her. *VFR

1880 Carl Borchardt (22 February 1817 – 27 June 1880) was a German mathematician who worked in a variety of areas in analysis. He edited Crelle's Journal for more than 30 years.*SAU

1952 Max Dehn died (November 13, 1878 – June 27, 1952). He solved Hilbert’s third problem in 1900 (shortly after receiving his Ph.D. un¬der Hilbert on another topic in the foundations of geometry): a tetrahedron cannot be cut up into ﬁnitely many pieces and reassembled into a cube of equal volume. Thus Dehn became the ﬁrst mathematician to join “the honors class” of mathematicians who had solved one of the twenty-three problems Hilbert posed in Paris in 1900.

1975 Sir Geoffrey Ingram Taylor OM (7 March 1886 – 27 June 1975) was a British physicist, mathematician and expert on fluid dynamics and wave theory. His biographer and one-time student, George Batchelor, described him as "one of the most notable scientists of this (the 20th) century". His final research paper was published in 1969, when he was 83. In it he resumed his interest in electrical activity in thunderstorms, as jets of conducting liquid motivated by electrical fields. The cone from which such jets are observed is called the Taylor cone for his namesake. In the same year Taylor was appointed to the Order of Merit. He suffered a stroke in 1972 which effectively put an end to his work; he died in Cambridge in 1975.*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

## Monday, 26 June 2017

### On This Day in Math - June 26

When you measure what you are speaking about and express it in numbers,
but when you cannot express it in numbers
.
William Thompson, Lord Kelvin

The 177th day of the year; there are 177 graphs with seven edges.  *What's So Special About This Number.  (only 79 of these are connected graphs)
• 177 is the smallest magic constant for a 3 x 3 prime magic square
$\begin{bmatrix} 17 & 89 & 71 \\ 113 & 59 & 5 \\ 47 & 29 & 101 \end{bmatrix}.$

EVENTS

1424 Of the 20 total eclipses to visit the Orkneys and Shetland Islands in the period 1 - 3000AD it was the 13th longest in the whole of the UK at 3 minutes 56 seconds it was surpassed in Orkney by those of 364, 885, 1185, 1433, 2681. The eclipse track traveled across Denmark, Germany, Poland, Ukraine, Moldavia, and the Black Sea. (ref. SW-UK eclipses) *NSEC

1614   The first lottery of significance in the new world was held on this date by the Virginia Company.  The first Great Prize was 4,500 Crowns. *JN Kane, Famous First Facts (I have seen the date of this lottery also given as 1612)

1765 Benjamin Franklin writes to Peter Collinson about numerous topics including Accounts of Spouts and Whirlwinds, and a comment on his earlier kite experiments; but includes, "I am endeavouring to answer Dr. Parsons’s Request relating to the Indian Names of the Cardinal Numbers." *franklinpapers

In 1819, The first US patent for a velocipede, a predecessor of the bicycle, was issued to William K. Clarkson Jr. of New York. Little information remains available, however, because a fire at the Patent Office in 1836 destroyed the patent record, and it was not restored. The photo shows the Draisine design of the period (Europe, 1816). Bicycles were introduced to the US also in 1819 and were manufactured by David and Rogers in Troy, NY*TIS

1881 The great comet of 1881. Observed on the night of June 25-26 at 1h. 30m. A.M. from a print by Étienne Léopold Trouvelot, a French artist, astronomer and amateur entomologist. He is noted for the unfortunate introduction of the Gypsy Moth into North America. *The New York Public Library Digital Collections

1896 An early x-ray photograph of Sir William Crookes’s hand, taken with a cathode tube that bears his name, the Crookes Tube. The man taking these pioneering radiographs was the engineer Alan Archibald Campbell Swinton, later a Fellow of the Royal Society. He took the first x-ray images in Britain in January 1896 and by a year later the medical professions were bringing him surgical cases for analysis. *Keith Moore, Royal Society Blog

In 1974, at 8:01 a.m., a package of Wrigley's chewing gum with a bar code printed on it passed over a scanner at the Marsh Supermarket, Troy, Ohio, and became the first product ever logged under the new Universal Product Code (UPC) computerized recognition system. Invented by IBM, and approved for use in 1973, the UPC is a 12-number bar code representing the manufacturer's identity and an assigned product number. Within nanoseconds, this information is read with a laser beam moving at around 10,000 inches per second and transfers it to the store's database computer for price lookup and inventory management*TIS

In 1984, the National Maritime Museum, of which the Royal Observatory, Greenwich is a part, encouraged people up and down the Line to organise events in order to mark the so-called ‘centenary’ of the Prime Meridian. Although the International Meridian conference took place in October 1884, the Museum designated Tuesday 26 June as ‘Meridian Day’, on the grounds that any outdoor events would be less likely to be affected by the weather.
Commemorative six-inch diameter plastic plaques were offered to any individual who could show that the Meridian passed through the curtilage of their property. Potential claimants were required to write to their regional office of the Ordnance Survey to verify their claim and send this as proof of authenticity to the English Tourist Board who were distributing them. No records of how many were issued can be traced. The locations of just four are known, along with the existence of a fifth.
The National Maritime Museum also arranged for the Enfield Foundry to cast a bronze plaque as a more enduring alternative. At the time, it was stated that they would only be produced if 20 or more orders were received. How many were made is unknown, the Foundry’s records having been destroyed. Only three have been located to date. (If you are aware of one of these locations, please informe me, thanks PB)

In 2000, the completion of a working draft reference DNA sequence of the human genome was announced at the White House by President Bill Clinton, and representatives from the Human Genome Project (HGP) and the private company Celera Genomics. Clinton stated that even greater discoveries would follow from the working draft. As a draft, it contained some gaps and errors, but represented about 95% of all genes. HGP expected to use it as a scaffold for generating the high-quality reference genome sequence within three years. This provides knowledge to link genes with particular diseases, of the influence of genetics and to help discover new treatments.
*TIS

BIRTHS
1730 Charles Messier (26 June 1730 – 12 April 1817) French astronomer who discovered 15 comets. He was the first to compile a systematic catalog of "M objects." The Messier Catalogue (1784), containing 103 star clusters, nebulae, and galaxies. (In Messier's time a nebula was a term used to denote any blurry celestial light source.) He established alphanumeric names for the objects (M1, M2, etc.), which notation continues to be used in astronomy today.

1824 Lord Kelvin (26 June 1824 – 17 December 1907) Born as William Thomson, he became an influential physicist, mathematician and engineer who has been described as a Newton of his era. At Glasgow University, Scotland, he was a professor for over half a century. The name he made for himself was more than just a temperature scale. His activities ranged from being the brains behind the laying of a transatlantic telephone cable, to attempting to calculate the age of the earth from its rate of cooling. In 1892, when raised to the peerage as Baron Kelvin of Largs, he had chosen the name from the Kelvin River, near Glasgow.*TIS

1878 Leopold Löwenheim (26 June 1878 in Krefeld, Germany (also the birthplace of Max Zorn) – 5 May 1957 in Berlin) was a German mathematician who worked on mathematical logic and is best-known for the Löwenheim-Skolem paradox.*SAU

1969 Andrei Yuryevich Okounkov (June 26, 1969 - ) is a Russian mathematician who works on representation theory and its applications to algebraic geometry, mathematical physics, probability theory and special functions. He is currently a professor at Columbia University. In 2006, he received the Fields Medal "for his contributions to bridging probability, representation theory and algebraic geometry." *Wik

DEATHS

1274 Nasir al-Tusi (born 18 February 1201 in Ṭūs, Khorasan – died on 26 June 1274 in al-Kāżimiyyah district of metropolitan Baghdad), was an Islamic astronomer and mathematician who joined the Mongols who conquered Baghdad. He made important contributions to astronomy and wrote many commentaries on Greek texts.*SAU Among the many wonderful antiquities at the Bodleian Library is a 16th century printing of the 13th century Arabic translation by Nasir al-Din al-Tusi of Euclid's Elements. It was part of the collection donated by Thomas Allen.

1796 David Rittenhouse (April 8, 1732 – June 26, 1796) American astronomer, instrument maker and inventor who was an early observer of the atmosphere of Venus. For observations for the transit of Venus on 3 Jun 1769, he constructed a high precision pendulum clock, an astronomical quadrant, an equal altitude instrument, and an astronomical transit. He was the first one in America to put spider web as cross-hairs in the focus of his telescope. He is generally credited with inventing the vernier compass and possibly the automatic needle lifter. He was professor of astronomy at the University of Pennsylvania. Benjamin Franklin consulted him on various occasions. For Thomas Jefferson he standardized the foot by pendulum measurements in a project to establish a decimal system of weights and measures.*TIS

1810 Joseph Montgolfier (26 August 1740 – 26 June 1810) French ballooning pioneer, with his younger brother, Étienne. An initial experiment with a balloon of taffeta filled with hot smoke was given a public demonstration on 5 Jun 1783. This was followed by a flight carrying three animals as passengers on 19 Sep1783, shown in Paris and witnessed by King Louis XVI. On 21 Nov 1783, their balloon carried the first two men on an untethered flight. In the span of one year after releasing their test balloon, the Montgolfier brothers had enabled the first manned balloon flight in the world. *TIS

1951 George Udny Yule (18 February 1871 – 26 June 1951) graduated in Engineering from University College London and then studied in Bonn. He worked with Karl Pearson on the statistics of regression and correlation. He took a post with an examinations board before being appointed to a Cambridge fellowship. He is best known for his book: Introduction to the Theory of Statistics.*SAU

1967 Henry Thomas Herbert Piaggio (2 June 1884–26 June 1967) graduated from Cambridge and then worked at the University of Nottingham. He is best known for his text-book on Differential Equations.("An Elementary Treatise on Differential Equations and their Applications".) *SAU

1990 Joseph Carl Robnett Licklider (March 11, 1915 – June 26, 1990), known simply as J.C.R. or "Lick" was an American computer scientist, considered one of the most important figures in computer science and general computing history. He is particularly remembered for being one of the first to forsee modern-style interactive computing, and its application to all manner of activities; and also as an Internet pioneer, with an early vision of a world-wide computer network long before it was built. He did much to actually initiate all that through his funding of research which led to a great deal of it, including today's canonical graphical user interface, and the ARPANET, the direct predecessor to the Internet.*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

## Sunday, 25 June 2017

### On This Day in Math - June 25

Astronomy was the cradle of the natural sciences and the starting point of geometrical theories.
~Cornelius Lanczos

The 176th day of the year; 176 and its reversal 671 are both divisible by 11. ( Students should confirm that the reverse of  any number that is divisible by 11 will also be divisible by 11.)

176 is a happy number, repeatedly iterating the sum of the squares of the digits will lead to 1, 12 + 72 + 62= 86, 82 + 62 = 100 and 12 + 02 + 02 = 1

The number 15 can be partitioned in 176 ways.

EVENTS

1641 John Pell begins the work of expanding Walter Warner's table of anti-logarithms from 10,000 to 100,000 entries. Warner felt he was too old to complete the laborious task he had set for  himself, and offered Pell 40 GBPounds (appx. worth 5,000 pounds today) to complete the tables and make them ready for printing.  *Thomas Harriot's Doctrine of Triangular Numbers, Beery & Stedall, pg 39

1665 René Descartes died on 11 February 1650 in Stockholm, Sweden, where he had been invited as a teacher for Queen Christina of Sweden. The cause of death was said to be pneumonia—accustomed to working in bed until noon, he may have suffered a detrimental effect on his health due to Christina's demands for early morning study (the lack of sleep could have severely compromised his immune system). Others believe that Descartes may have contracted pneumonia as a result of nursing a French ambassador, Dejion A. Nopeleen, ill with the aforementioned disease, back to health. In his recent book, Der rätselhafte Tod des René Descartes (The Mysterious Death of René Descartes), the German philosopher Theodor Ebert asserts that Descartes died not through natural causes, but from an arsenic-laced communion wafer given to him by a Catholic priest. He believes that Jacques Viogué, a missionary working in Stockholm, administered the poison because he feared Descartes's radical theological ideas would derail an expected conversion to Roman Catholicism by the monarch of Protestant Lutheran Sweden.*Wik

After his death in Stockholm, his body was returned to Paris, arriving on 25 Jun 1665 , though the coffin had been looted by his followers for relics in Stockholm.  Supposedly, the coffin was shipped overland from Copenhagen to avoid piracy by English admirers!  The remains were in Ste. Geneviève, then in Lenoir's Museum of French Monuments, and then finally moved to St‑Germain-des-Prés in 1819. His headstone (or gravestone) is in St‑Germain‑des‑Prés, in the second chapel on the right of the apse.   Stephen Jay Gould says the (purported) skull of Descartes is in the Musée de l'Homme, apparently on display.  Arjen Dijksman recently advised me that the Musee de l'Homme is closed for another year, and there have been efforts to move the skull to the Pantheon.
Église St-Germain-des-Prés, at 3 Place St-Germain-des-Prés, is the oldest church in Paris. Part of it dates to the 6th century, when a Benedictine abbey was founded on the site by King Childebert, son of Clovis. The church was originally built to house a relic of the True Cross brought from Spain in 542. The Normans destroyed the abbey on multiple occasions and only the marble columns in the triforium remain from the original structure. The carved capitals on the pillars are copies of the originals, which are kept in the Musée National du Moyen-Age. The church was enlarged and reconsecrated by Pope Alexander III in 1163. The abbey was completely destroyed during the Revolution, but the church was spared. The present building is a fine example of Romanesque architecture, with gothic interior elements. The square tower dating from the early 11th century, is topped by a landmark spire, which dates to the 19th century. For a time, the abbey served as a pantheon for Merovingian kings. The Chapelle Saint Symphorien, built during the Middle Ages and restored in 1981, served as the necropolis mérovingienne (crypt of the Merovingians). This is the presumed site of first tomb of Saint Germain, Bishop of Paris, who died in 576. Among the others interred here are King Jean-Casimir of Poland

1712 Brook Taylor suggested that if two glass plates which are clamped together into a “V” are placed into a pan of water then capillary action will draw water up into the shape of a rectangular hyperbola with asymptotes the surface of the water and the point of the “V.” This and several similar experiments performed by Francis Hauksbee before the Royal Society caused Newton to rethink his ideas on capillary force. *VFR

1776 Captain Cook sails from Deptford on his third voyage, in the 'Resolution' with the 'Discovery' *Nat. Maritime Museum ‏@NMMGreenwich

1783  Antonie Lavoisier announced to the French Academy of Sciences that water was the product formed by the combination of hydrogen and oxygen. However, this discovery had been made earlier by the English chemist Henry Cavendish *TIS

1795 The Bureau des Longitudes is a French scientific institution, founded by decree of 25 June 1795 and charged with the improvement of nautical navigation, standardization of time-keeping, geodesy and astronomical observation. During the 19th century, it was responsible for synchronizing clocks across the world. It was headed during this time by François Arago and Henri Poincaré. The Bureau now functions as an academy and still meets monthly to discuss topics related to astronomy.
The Bureau was founded by the National Convention after it heard a report drawn up jointly by the Committee of Navy, the Committee of Finances and the Committee of State education. Henri Grégoire had brought to the attention of the National Convention France's failing maritime power and the naval mastery of England, proposing that improvements in navigation would lay the foundations for a renaissance in naval strength. As a result, the Bureau was established with authority over the Paris Observatory and all other astronomical establishments throughout France. The Bureau was charged with taking control of the seas away from the English and improving accuracy when tracking the longitudes of ships through astronomical observations and reliable clocks.
The ten original members of its founding board were:
Geometers:
Joseph-Louis Lagrange;
Pierre-Simon Laplace;
Astronomers:
Joseph Jérôme Lefrançais de Lalande;
Pierre Méchain;
Jean Baptiste Joseph Delambre;
Dominique, comte de Cassini;
Jean-Charles de Borda, who carried out work related to the mechanics of fluids and precursor of Carnot because of his insights on thermodynamics;
Jean-Nicolas Buache, geographer;
Louis Antoine de Bougainville, celebrated navigator; and
Noël Simon Caroché, manufacturer of telescopes.
*Wik

1973 Last total solar eclipse with a maximum duration of totality longer than 7 minutes between year 0 and 4000 was June 30, 1973. The eclipse was visible in Africa. The next total solar eclipse with a duration of totality longer than 7 minutes will be on 25 June 2150 in the Pacific Ocean. Thereafter it will be 5 July 2168 in the Indian Ocean. Ref. More Mathematical AstronomicalMorsels by Jean Meeus; Willmann-Bell, 2002. *NSEC

BIRTHS

1864 Walther Hermann Nernst (25 June 1864 – 18 November 1941) German who was one of the founders of modern physical chemistry. In 1889, he devised his theory of electric potential and conduction of electrolytic solutions (the Nernst Equation) and introduced the solubility product to explain precipitation reactions. In 1906, Nernst showed that it is possible to determine the equilibrium constant for a chemical reaction from thermal data, and in so doing he formulated what he himself called the third law of thermodynamics. This states that the entropy, (a thermodynamic measure of disorder in a system), approaches zero as the temperature goes towards absolute zero. For this, he was awarded the 1920 Nobel Prize in Chemistry. In 1918, he explained the H2-Cl2 explosion on exposure to light as an atom chain reaction. *TIS

1905 Rupert Wildt (/ˈvɪlt/; June 25, 1905 – January 9, 1976) was a German-American astronomer.
He was born in Munich, Germany, and grew up in that country during World War I and its aftermath. In 1927 he was awarded a Ph.D. from the University of Berlin. He joined the University of Göttingen, specializing in the properties of atmospheres.
In 1932 he studied the spectra of Jupiter, and other outer planets, and identified certain absorption bands as belonging to the hydrogen-rich compounds of methane and ammonia. The composition appeared consistent with a composition similar to the sun and other stars.
Assuming that the atmosphere was composed of these gases, during the 1940s and 1950s he constructed a model of the structure of these planets. He believed the core of the planets is solid and composed of a mixture of rock and metal, covered by a thick outer shell of ice, overlaid by a dense atmosphere. His model is still widely accepted.
In 1934 he emigrated to the United States, and became a research assistant at Princeton University from 1937 until 1942. He then became an assistant professor at the University of Virginia until 1947, before joining the faculty of the Yale University.
In 1939 he demonstrated that the major source of optical opacity in the Sun's atmosphere is the H- ion, and thus the main source of visible light for the Sun and stars.
From 1965 until 1968 he was president of the Association of Universities for Research in Astronomy. In the period 1966-1968 he also held the post of the chairman of the department of astronomy at Yale, and from 1973 until his death he was professor emeritus. He died in Orleans, Massachusetts.
His awards include the Eddington Medal in 1966. The Asteroid 1953 Rupertwildt is named after him and the crater Wildt on the Moon is also. *Wik

1928 Alexei Alexeyevich Abrikosov (June 25, 1928; ) is a Soviet and Russian theoretical physicist whose main contributions are in the field of condensed matter physics. He was awarded the Nobel Prize in Physics in 2003.
In two works in 1952 and 1957, Abrikosov explained how magnetic flux can penetrate a class of superconductors. This class of materials is known as type-II superconductors. The accompanying arrangement of magnetic flux lines is called the Abrikosov vortex lattice.
Abrikosov was awarded the Lenin Prize in 1966, the Fritz London Memorial Prize in 1972, and the USSR State Prize in 1982. In 1989 he received the Landau Prize from the Academy of Sciences, Russia. Two years later, in 1991, Abrikosov was awarded the Sony Corporation’s John Bardeen Award. The same year he was elected a Foreign Honorary Member of the American Academy of Arts and Sciences.[1] He is also a member of the Royal Academy of London, a fellow of the American Physical Society, and in 2000 was elected to the prestigious National Academy of Sciences. He was the co-recipient of the 2003 Nobel Prize in Physics, with Vitaly Ginzburg and Anthony James Leggett, for theories about how matter can behave at extremely low temperatures. *Wik

DEATHS

1671 Giovanni Riccioli (17 April 1598 – 25 June 1671) Italian astronomer who was the first to observe (1650) a double star (two stars so close together that they appear to be one) -  Mizar in Ursa Major, the middle star in the handle of the Big Dipper. He also discovered satellite shadows on Jupiter. In 1651, he assigned the majority of the lunar feature names in current use. He named the more prominent features after famous astronomers, scientists and philosophers, while the large dark and smooth areas he called "seas" or "maria". The lunar seas were named after moods (Seas of Tranquillity, Serenity) or terrestrial phenomena (Sea of Rains, Ocean or Storms) His map was published in Almagestum Novum in1651.*TIS
Riccioli studied seventy-seven objections to the Copernican thesis and after studying them Riccioli said that the weight of argument favored a “geo-heliocentric” hypothesis such as that advocated by the great Danish astronomer Tycho Brahe. Riccioli's preference for Tycho's model illustrates something important about how science is done. While today anti-Copernicans are often portrayed as Einstein characterized them (opposed to rational thinking, opposed to science), Riccioli, perhaps the most prominent of the anti-Copernicans, examined the available evidence diligently and rationally. The conclusion he reached was indeed wrong, but wrong because at that time neither the diffraction of light and the Airy disk, nor the details of the Coriolis effect, were understood. Riccioli's anti-Copernican arguments were so solid that they would become subjects of further investigation in physics, long after the Copernican theory had triumphed over the Tychonic theory.*Christopher M. Graney, Teaching Galileo, Physics Teacher V50,1

1879 Sir William Fothergill Cooke (4 May 1806 – 25 June 1879) English inventor who worked with Charles Wheatstone in developing electric telegraphy. Of the pair, Cooke contributed a superior business ability, whereas Wheatstone is generally considered the more important of the two in the history of the telegraph. After Cooke attended a demonstration of the use of wire in transmitting messages, he began his own experiments with telegraphy (1836) and formed a partnership with Wheatstone. Their first patent (1837) was impractical because of cost. They demonstrated their five-needle telegraph on 24 July 1837 when they ran a telegraph line along the railway track from Euston to Camden Town able to transmit and successfully receive a message. In 1845, they patented a single-needle electric telegraph. *TIS

1941 Alfred Pringsheim (2 September 1850 – 25 June 1941). His work in Fourier series, analytic function theory, and continued fractions was a model of the Weierstrassian approach, although he was not a student of Weier­strass. *VFR
In mathematical analysis, Pringsheim studied real and complex functions, following the power-series-approach of the Weierstrass school. Pringsheim published numerous works on the subject of complex analysis, with a focus on the summability theory of infinite series and the boundary behavior of analytic functions.
Pringsheim's theorem concerns the convergence of a power series with non-negative real coefficients. However, Pringsheim's original proof had a flaw (related to uniform convergence), and a correct proof was provided by Ralph P. Boas. Pringsheim's theorem is used in analytic combinatorics and the Perron–Frobenius theory of positive operators on ordered vector spaces.
Besides his research in analysis, Pringsheim also wrote articles for the Encyclopedia of Mathematical Sciences on the fundamentals of arithmetic and on number theory. He published papers in the Annals of Mathematics. As an officer of the Bavarian Academy of Sciences, he recorded the minutes of its scientific meetings.
Pringsheim and Ivan Śleszyński, working separately, proved what is now called the Śleszyński–Pringsheim theorem on convergence of certain continued fractions.*Wik

1960 Walter Baade (24 Mar 1893; 25 Jun 1960 at age 67) German-American astronomer who, with Fritz Zwicky, proposed that supernovae could produce cosmic rays and neutron stars (1934), and Baade made extensive studies of the Crab Nebula and its central star. During WW II blackouts of the Los Angeles area Baade used the 100-inch Hooker telescope to resolve stars in the central region of the Andromeda Galaxy for the first time. This led to his definition of two stellar populations, to the realization that there were two kinds of Cepheid variable stars, and from there to a doubling of the assumed scale of the universe. Baade and Rudolph Minkowski identified and took spectrograms of optical counterparts of many of the first-discovered radio sources, including Cygnus A and Cassiopeia A. *TIS

1974 Cornelius Lanczos (2 Feb 1893 - 25 June 1974) worked on relativity and mathematical physics and invented what is now called the Fast Fourier Transform. *SAU Lanczos served as assistant to Albert Einstein during the period of 1928–29.*Wik

1978 Hsien Chung Wang (April 18, 1918 — June 25, 1978.)worked on algebraic topology and discovered the 'Wang sequence', an exact sequence involving homology groups associated with fibre bundles over spheres. These discoveries were made while he worked with Newman in Manchester. Wang also solved, at that time, an important open problem in determining the closed subgroups of maximal rank in a compact Lie group *SAU

1997 Jacques-Yves Cousteau (11 June 1910 – 25 June 1997) French naval officer, oceanographer, marine biologist and ocean explorer, known for his extensive underseas investigations. He was co-inventor of the aqualung which made SCUBA diving possible (1943). Cousteau developed the Conshelf series of manned habitats, the Diving Saucer, a process of underwater television and numerous other platforms and specialized instruments of ocean science. In 1945 he founded the French Navy's Undersea Research Group. He modified a WWII wooden hull minesweeper into the research vessel Calypso, in 1950. An observation dome added to the foot of Calypso's bow was found to increase the ship's stability, speed and fuel efficiency. *TIS

2006 Irving "Kap" Kaplansky (March 22, 1917, Toronto – June 25, 2006, Los Angeles) was born in Toronto, Ontario, Canada after his parents emigrated from Poland and attended the University of Toronto as an undergraduate. After receiving his Ph.D  from Harvard in 1941 as Saunders Mac Lane's first student, Kaplansky was professor of mathematics at the University of Chicago from 1945 to 1984. He was chair of the department from 1962 to 1967.
"Kap," as his friends and colleagues called him, made major contributions to group theory, ring theory, the theory of operator algebras and field theory. He published over 150 papers with over 20 co-authors. He was a member of the National Academy of Sciences and the American Academy of Arts and Sciences. He was the Director of the Mathematical Sciences Research Institute from 1984 to 1992, and the President of the American Mathematical Society from 1985 to 1986.
Kaplansky also was a noted pianist known to take part in Chicago performances of Gilbert and Sullivan productions. He often composed music based on mathematical themes. One of those compositions, A Song About Pi, is a melody based on assigning notes to the first 14 decimal places of pi.
Kaplansky was the father of singer-songwriter Lucy Kaplansky, who occasionally performs A Song About Pi in her act.
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