Tuesday, 29 June 2021

On This Day in Math - June 29

Jeannie, Happy birthday.

The 180th day of the year; 180 can be formed with the only the first two primes... 180 = 22 x 32 x (2+3) *Prime Curios

180 is the sum of two square numbers: \( 12^2 + 6^2 \). It can also be expressed as either the sum of six consecutive primes: 19 + 23 + 29 + 31 + 37 + 41, or the sum of eight consecutive primes: 11 + 13 + 17 + 19 + 23 + 29 + 31 + 37.

Beautiful trigonometry, arctan1 + arctan2 + arctan3 = pi/2 =180o

More Math Facts for every year day here.


In 3123 BC, a Sumerian astronomer saw a devastating asteroid, perhaps a half-mile wide, according to an interpretation of a clay tablet, made by researchers from Bristol University, reported in The Times on 31 Mar 2008. The ancient date was indicated by a computer recreation of the night sky using symbols on the tablet recording the positions of constellations The Planiform tablet found by Henry Layard at Nineveh, likely a 700 BC copy of the astronomer's notes, described in cuneiform a "white stone bowl approaching" that "vigorously swept along." The asteroid probably crashed into the Austrian Alps, leaving a swath of cataclysmic damage such as, for example, the Genesis destruction of Sodom and Gomorrah.*TIS

1456 According to one story that first appeared in a 1475 posthumous biography and was subsequently embellished and popularized by Pierre-Simon Laplace, Callixtus III excommunicated the 1456 apparition of Halley's Comet, believing it to be an ill omen for the Christian defenders of Belgrade from the besieging armies of the Ottoman Empire. No known primary source supports the authenticity of this account. The 29 June 1456 papal bull of Callixtus III calling for a public prayer for the success of the crusade, makes no mention of the comet. By 6 August, when the Turkish siege was broken the comet had not been visible in either Europe or Turkey for several weeks. *Wik

(John Francis Rigaud, 1785)*Wik
1785 Letitia Ann Sage became the first British woman to fly. From St George's Fields on the south side of the Thames, Vincenzo Lunardi and his partner Biggin, with two invitees, Mrs. Sage and a Colonel Hastings were supposed to make the flight, but the Hydrogen balloon wouldn't take off because of the weight. (Mrs Sage, a actress and model was also a somewhat large woman, rumored to weigh appx 200 pounds.)  Lunardi and Hastings stepped down, and the balloon took off with Biggin and Mrs. Sage. It landed 90 minutes later, near Harrow, where the two aeronauts had to be rescued by a group of boys from Harrow School from the angry farmer whose crops were damaged. *Wik (There were even suggestions that rather more amorous events had occurred in the flight.)

1799 The Royal Charter for the Royal Institute is promised. Ever since its founding year the Royal Institution has maintained close links with the Royal Family. On 29 June 1799, George Finch, Earl of Winchilsea (1752-1826), the President of what had until then had been called simply the “Institution” reported to a meeting of its committee of Managers ‘that he had had the Honour of mentioning this Institution to his Majesty [George III], and that his Majesty was graciously pleased to honour it with His Patronage and to allow it to be called the Royal Institution’. The actual charter was presented on January 13 in 1800. *Royal Institute web page

1803 An open letter to the public, and the Congress of the United States on the topic "Of The Construction of Iron Bridges" is posted by Thomas Paine. Paine had discussed this work with President Jefferson in a letter while he was in England. *The National Intelligencer and Washington Advertiser, (Washington, DC) Wednesday, June 29, 1803; Issue CCCCXIX;

1877 After proving that the points in a square can be put in one-to-one correspondence with the points on a line segment Cantor wrote his friend Dedekind “Je le vois, mais je ne le crois pas.” (I see it, but I don’t believe it.) [Dauben, Georg Cantor, p. 55]*VFR

1927 Gellivara 1073: Minor planet discovered September 14, 1923 by Johann Palisa at Vienna. Named for the small town  Gällivare in Swedish Lapland where in the year 1927 astronomers from several countries observed the Total Solar Eclipse of 1927 Named by the astronomer J. Rheden and endorsed by Anna Palisa.*NSEC
A Poster advertising viewing of Solar Eclipse from London, Midland, and Scotland Railway *GreatAmericanEclipse ‏@AmericanEclipse

In 1954, the Atomic Energy Commission, by a vote of 4 to1 decided against reinstating Dr. J. Robert Oppenheimer's access to classified information. The Atomic Energy Act of 1946 required consideration of  "the character, associations, and loyalty" of the individuals engaged in the work of the Commission. Substantial defects of character and imprudent and dangerous associations, particularly with known subversives who place the interests of foreign powers above those of the United States, were considered reasons for disqualification. The Commission regarded his associations with persons known to him to be Communists exceeded tolerable limits of prudence and self-restraint, and lasted too long to be justified as merely the intermittent and accidental revival of earlier friendships.*TIS

1956 The interstate highway system was signed into law by President Eisenhower. Even (odd) num­bered roads run East–West (North–South) with the numbers increasing from South to North (West to East). Roads with three digit numbers are loops around cities (when the first digit is even) or spurs (first digit odd); In either case the last two digits are the main road number.  *VFR
Eisenhower had seen the speed and efficiency in moving troops and equipment on the four-lane autobahns in Germany during WW II. The idea of federal support of interstate limited-access routes in the U.S. had begun with a study under the Federal-Aid Highway Act of 1938. Little progress was made on building these roads while federal funding was low. When the Federal-Aid Highway Act of 1956 committed federal funds to the States for 90% of the cost, construction began in earnest for the System of Interstate and Defense Highways having at least four lanes with no at-grade railroad crossings. *TIS

2016 - My Jeannie is celebrating her birthday today, and I'm celebrating having her in my life... all the good I ever do is a reflection of a single sun.


1716 Joseph Stepling, (29 June 1716 in Regensburg; 11 July 1778 in Prague) His fields included astronomy, physics and mathematics. At the age of 17 he documented with great accuracy the 1733 lunar eclipse. Later Euler was among his long list of correspondents. He transposed Aristotelian logic into formulas, thus becoming an early precursor of modern logic. already adopted the atomistic conception of matter he radically refused to accept Aristotelian metaphysics and natural philosophy. In 1748, at the request of the Berlin Academy, he carried out an exact observation of a solar and lunar eclipse in order to determine the precise location of Prague. During Stepling's long tenure at Prague, he set up a laboratory for experimental physics and in 1751 built an observatory, the instruments and fittings of which he brought up to the latest scientific standard.
Even though he passed up a professorship in philosophy in favor of a chair in mathematics, Empress Maria Theresa appointed him director of the faculty of philosophy at Prague as part of the reform of higher education. He was very interested in cultivating the exact sciences and founded a society for the study of science modeled on the Royal Society of London. In their monthly sessions. over which he presided until his death, the group carried out research work and investigations in the field of pure mathematics and its appiication to physics and astronomy. A great number of treatises of this academy were published.
Stepling corresponded with the outstanding contemporary mathematicians and astronomers: Christian Wolf. Leonhard Euler. Christopher Maire, Nicolas-Louis de Lacaille, Maximilian Heli, Joseph Franz, Rudjer Boskovic, Heinrich Hiss, and others. Also, Stepling was particularly successful in educating many outstanding scientists, including Johann Wendlingen, Jakob Heinisch, Johannes von Herberstein, Kaspar Sagner, Stephan Schmidt, Johann Korber, and Joseph Bergmann. After his death, Maria Theresia ordered a monument erected in the library of the University of Prague *Joseph MacDonnell, Fairfield Univ web page

1818 Pietro Angelo Secchi (29 June 1818 – 26 February 1878) Italian Jesuit priest and astrophysicist, who made the first survey of the spectra of over 4000 stars and suggested that stars be classified according to their spectral type. He studied the planets, especially Jupiter, which he discovered was composed of gasses. Secchi studied the dark lines which join the two hemispheres of Mars; he called them canals as if they where the works of living beings. (These studies were later continued by Schiaparelli.) Beyond astronomy, his interests ranged from archaeology to geodesy, from geophysics to meteorology. He also invented a meteorograph, an automated device for recording barometric pressure, temperature, wind direction and velocity, and rainfall. *TIS

1868 George Ellery Hale (June 29, 1868 – February 21, 1938) born. American astronomer known for his development of important astronomical instruments. To expand solar observations and promote astrophysical studies he founded Mt. Wilson Observatory (Dec 1904). He discovered that sunspots were regions of relatively low temperatures and high magnetic fields. Hale hired Harlow Shapley and Edwin Hubble as soon as they finished their doctorates, and he encouraged research in galactic and extragalactic astronomy as well as solar and stellar astrophysics. Hale planned and tirelessly raised funds for the 200" reflecting telescope at the Palomar Mountain Observatory completed in 1948, after his death, and named for him - the Hale telescope.*TIS

1893 Prasanta Chandra Mahalanobis FRS[1] (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

1904 Topologist Witold Hurewicz (June 29, 1904 - September 6, 1956) born. Hurewicz is best remembered for two remarkable contributions to mathematics, his discovery of the higher homotopy groups in 1935-36, and his discovery of exact sequences in 1941. His work led to homological algebra. It was during Hurewicz's time as Brouwer's assistant in Amsterdam that he did the work on the higher homotopy groups; "...the idea was not new, but until Hurewicz nobody had pursued it as it should have been. Investigators did not expect much new information from groups, which were obviously commutative...". *Wik He died in 1956 when he fell off a pyramid while attending a conference in Mexico.

1942 K. Jon Barwise (June 29, 1942 – March 5, 2000) an American mathematician, philosopher and logician who proposed some fundamental revisions to the way that logic is understood and used.*Wik


1895 T(homas) H(enry) Huxley (4 May 1825 – 29 June 1895) was an English biologist , known as "Darwin's Bulldog" for his promotion of Darwinism which led him to an advocacy of agnosticism (a word he coined). At the age of 12 he was reading advanced works on geology, and by early adolescence he recorded the results of simple self-conducted experiments. As a ship's assistant surgeon on HMS Rattlesnake he studied marine specimens by microscope. During the 1850's he published papers on animal individuality, the cephalous mollusks (ex. squids), the methods of paleontology, and the methods and principles of science and science education. *TIS

1924 Robert Simpson Woodward (July 21, 1849–June 29, 1924) was an American physicist and mathematician, born at Rochester, Michigan. He graduated C.E. at the University of Michigan in 1872 and was appointed assistant engineer on the United States Lake Survey. In 1882 he became assistant astronomer for the United States Transit of Venus Commission. In 1884 he became astronomer to the United States Geological Survey, serving until 1890, when he became assistant in the United States Coast and Geodetic Survey. In 1893 he was called to Columbia as professor of mechanics and subsequently became professor of mathematical physics as well. He was dean of the faculty of pure science at Columbia from 1895 to 1905, when he became president of the Carnegie Institution of Washington, whose reputation and usefulness as a means of furthering scientific research was widely extended under his direction. He was elected to the National Academy of Sciences in 1896. In 1898-1900 he was president of the American Mathematical Society, and in 1900 president of the American Association for the Advancement of Science. In 1915 he was appointed to the Naval Consulting Board. He died in 1924 in Washington, D.C.*Wik

*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, 28 June 2021

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

More Math Facts for every year date here


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... )


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


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

Sunday, 27 June 2021

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 also has a cube with the same digits as 196:
1783 = 5,639,752
1963 = 7,529,536
*Zoo of Numbers
More Math Facts for each year day here.


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

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."
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

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

Saturday, 26 June 2021

On This Day in Math - June 26

When you measure what you are speaking about and express it in numbers,
you know something about it,
but when you cannot express it in numbers
your knowledge about is of a meagre and unsatisfactory kind
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
 17 & 89 & 71 \\
 113 & 59 & 5 \\
 47 & 29 & 101

An old idea that was new to me, from John Golden@mathhombre and here.  Use two Simple Squares to make a  third, and I just did one with magic sum of 177.
2   3   1
1   2   3
3   1   2 

53  61  57 
61  57  53
57  53  61

Now add the numbers in same location

55  64  58
62  59  56
60  54  63  

More Math Facts for each day here


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.

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


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