France.... work was never this hectic.

On Holiday in France and the internet is difficult and so daily posts are at a premium... Did get a chance to visit Lisieux but not the cathedral St Pierre where Nicole Oresme was Bishop.  Hope to stop in this week... but the grand kids are pushing for the beach at every opportunity.  Then to Paris for the weekend, and hopefully a chance to catch up on the postings... else "On this day in math" will become "last month in math"   or some such name....your patience is appreciated as I dally in the sunshine.  Summertime.... and the living is ...easy...

On This Day in Math - June 21

I had this rare privilege of being able to pursue in my adult life, 

what had been my childhood dream.

~Andrew Wiles


EVENTS


1667 Louis XIV, The Sun King of France, attends the ceremony of inauguration of the Observatoire de Paris, the oldest working observatory in the world. *Amir D. Aczel, Pendulum, pg 66

1798 Cavendish reads a paper to the Royal Society of London describing experiments to measure the density of the earth, and hence its weight, with results that it is 5.48 times the density of water. (the figures seem to include at least one calculating error) *Philosophical Transactions, 1798, Part II, pgs 469-526

---

1808  on 30 June,Humphry Davy announced he had separated the element boron. However, working independently, French chemist, Joseph Louis Gay-Lussac had announced* the same accomplishment nine days ealier, on 21 Jun 1808*TIS

---

In 1886, the foundation stone of the Tower Bridge in London, England was laid (over a time capsule) by the Prince of Wales. The need to cross the River Thames at this point had become increasingly urgent for many years, and finally the necessary Act was passed in 1885. The bridge, designed by Mr. Wolfe Barry, CB, was completed at a cost of about £1,000,000. To permit the passage of tall ships between the towers, two bascule spans, each of 100-ft length, are raised. The side spans to the towers are of the more familiar suspension type. Pedestrians can traverse a high-level footway nearly at the top of the towers, even when the bridge is raised. It was officially opened 30 Jun 1894, by the Prince of Wales, later Edward VII, on behalf of Queen *TIS

---

In 1893, the first Ferris wheel premiered at Chicago's Columbian Exposition, America's third world's fair. It was invented by George Washington Ferris, a Pittsburgh bridge builder, for the purpose of creating an attraction like the Eiffel Tower in Paris. Each of the 36 cars carried 60 passengers, making a full passenger load of 150 tons. Ferris didn't use rigid spokes: instead, he used a web of taut cables, like a bicycle wheel. Supported by two 140 foot steel towers, its 45 foot axle was the largest single piece of forged steel at the time in the world. The highest point of the wheel was 264 feet. The wheel and cars weighed 2100 tons, with another 2200 tons of associated levers and machinery. Ferris died just four years later, at the age of only 38. *TIS

---

1929 Kazimierz Kuratowski (1896–1980) at a meeting of the Warsaw Section of the Polish Mathemat­ical Society, announced that a graph is planar iff it does not contain a subgraph homeomorphic to either K–5, the complete graph on 5 points, or K–3–3, the complete bipartite graph on two sets of three points. See HM 12, 258, for a discussion of the early history of this theorem which is now the most cited result in graph theory. *VFR (See June 18) 

 "A finite graph is planar if and only if it does not contain a subgraph that is a subdivision of K₅ (the complete graph on five vertices) or K_3,3 (complete bipartite graph on six vertices, three of which connect to each of the other three)." *Wik 
 (in more simple, but less exact terms,  "it can be drawn in such a way that no edges cross each other."  The well-known recreational problem of connecting three houses to three utilities is not possible to draw because it is K_3,3 (below).  The utility problem posits three houses and three utility companies--say, gas, electric, and water--and asks if each utility can be connected to each house without having any of the gas/water/electric lines/pipes pass over any other. (1913 Dudeney: first publication of Gas, Water and Electricity Problem. according to David Singmaster, Gardner says 1917)

---

1948 the first stored-program computer, the Small-Scale Experimental Machine, SSEM, ran its first program. Written by Professor Tom Kilburn, it took 52 minutes to run. The tiny experimental computer had no keyboard or printer, but it successfully tested a memory system developed at Manchester University in England. The system, based on a cathode-ray tube, could store programs. Previous electronic computers had to be rewired to execute each new problem. The Manchester computer proved theories set forth by John von Neumann in a report that proposed modifications to ENIAC, the electronic computer built at the University of Pennsylvania in the mid-1940s. The report also proposed the use of binary instead of digital numbers. *TIS

---

1976 Kenneth Appel and Wolfgang Haken announced that with the aid of a computer that they had proved the four color problem. Because of the use of the computer the solution was not quickly accepted by all, but today most mathematicians accept the proof as correct. However, no simple proof is known as yet. *VFR  {A really nice article on the four color theorem and its history}

---

1993   Andrew Wiles  begins the three days of lectures leading to a solution of Taniyama-Shimura conjecture, and completing the proof of Fermat’s last theorem.. See (June 23)

---

2011  On non-leap years (until 2039), this day marks the summer solstice in the northern hemisphere and the winter solstice in the southern hemisphere, and this is the day of the year with the longest hours of daylight in the northern hemisphere and the shortest in the southern hemisphere.*Wik

---

BIRTHS
 1781 Siméon-Denis Poisson French mathematician known for his work on definite integrals, advances in Fourier series, electromagnetic theory, and probability. The Poisson distribution (1837) describes the probability that a random event will occur in a time or space interval under the conditions that the probability of the event occurring is very small, but the number of trials is very large so that the event actually occurs a few times. His works included applications to electricity and magnetism, and astronomy. He is also known for the Poisson's integral, Poisson's equation in potential theory, Poisson brackets in differential equations, Poisson's ratio in elasticity, and Poisson's constant in electricity.*TIS   Libri wrote of him: “His only passion has been science: he lived and is dead for it.” *VFR

---

1852 Eduard Weyr born (died 1903). He and his brother, Emil Weyr (1848–1894) were the leading members of the Austrian geometrical school. They worked in descriptive geometry, projective geometry, and then became interested in algebraic and synthetic methods. Eduard found a canonical form for matrices that deserves to be better known (American Mathematical Monthly, December 1999). *VFR

---

1863  Maximilian Franz Joseph Cornelius Wolf was a German astronomer who founded and directed the Königstuhl Observatory. He used wide-field photography to study the Milky Way and used statistical treatment of star counts to prove the existence of clouds of dark matter. He was among the first astronomers to show that the spiral nebulae have absorption spectra typical of stars and thus differ from gaseous nebulae. His most important contribution was the introduction of photography to discover hundreds of asteroids, the first of which he named Brucia in honor of the donor of his 16-inch double telescope, Catherine Wolfe Bruce.*TIS

1918  Tibor Szele. He worked in group theory.  *VFR  Hungarian mathematician, working in combinatorics and abstract algebra. After graduating at the Debrecen University, he became a researcher at the Szeged University in 1946, then he went back at the Debrecen University in 1948 where he became full professor in 1952. He worked especially in the theory of Abelian groups and ring theory. He generalized Hajós's theorem. He founded the Hungarian school of algebra. *Wik

---

DEATHS
1874  Anders Jonas Ångström was a Swedish physicist whose pioneering use of spectroscopy is recognised in the name of the angstrom, a unit of length equal to 10^-10 metre. In 1853, he studied the spectrum of hydrogen for which Balmer derived a formula. He announced in 1862 that analysis of the solar spectrum showed that hydrogen is present in the Sun's atmosphere. In 1867 he was the first to examine the spectrum of aurora borealis (northern lights). He published his extensive research on the solar spectrum in Recherches sur le spectre solaire (1868), with detailed measurements of more than 1000 spectral lines. He also published works on thermal theory and carried out geomagnetical measurements in different places around Sweden.*TIS

---

1913  Gaston Tarry was a French combinatorialist whose best-known work is a method for solving mazes.*SAU  He also was able to confirm Leonhard Euler's conjecture that no 6×6 Graeco-Latin square was possible. 
In mathematics, the Prouhet–Tarry–Escott problem asks for two disjoint sets A and B of n integers each, such that:

for each integer power  i from 1 to a given k.
For example, a solution with n = 6 and k = 5 is the two sets { 0, 5, 6, 16, 17, 22 } and { 1, 2, 10, 12, 20, 21 }, because:

0¹ + 5¹ + 6¹ + 16¹ + 17¹ + 22¹ = 1¹ + 2¹ + 10¹ + 12¹ + 20¹ + 21¹

0² + 5² + 6² + 16² + 17² + 22² = 1² + 2² + 10² + 12² + 20² + 21²

0³ + 5³ + 6³ + 16³ + 17³ + 22³ = 1³ + 2³ + 10³ + 12³ + 20³ + 21³

0⁴ + 5⁴ + 6⁴ + 16⁴ + 17⁴ + 22⁴ = 1⁴ + 2⁴ + 10⁴ + 12⁴ + 20⁴ + 21⁴

0⁵ + 5⁵ + 6⁵ + 16⁵ + 17⁵ + 22⁵ = 1⁵ + 2⁵ + 10⁵ + 12⁵ + 20⁵ + 21⁵.

This problem was named after Eugène Prouhet, who studied it in the early 1850s, and Gaston Tarry and Escott, who studied it in the early 1910s.

---

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

---

1948 D'Arcy Thompson graduated from Cambridge University in Zoology. He was a appointed Professor of Biology at Dundee and later Professor of Natural History at St Andrews. He combined skills in a way that made him unique. He was a Greek scholar, a naturalist and a mathematician. He was the first biomathematician. He became an honorary member of the EMS in 1933. *SAU

---

1957  Johannes Stark German physicist who won the 1919 Nobel Prize for Physics for his discovery in 1913 that an electric field would cause splitting of the lines in the spectrum of light emitted by a luminous substance; the phenomenon is called the Stark effect. *TIS

---

Credits:
*VFR = V Frederick Rickey, USMA
*TIS= Today in Science History
*Wik = Wikipedia
*SAU=St Andrews Univ. Math History

On This Day in Math - June 20

the enormous success of mathematics in the natural
sciences is something bordering on the mysterious and ...
there is no natural explanation for it.

—Eugene Wigner

EVENTS

1686 Halley Writes to Newton that Hooke has protested his "discovery" of the inverse square law should be noted in Principia. Newton will respond On July 14, 1686, with a peace offering; "And now having sincerely told you the case between Mr Hooke and me, I hope I shall be free for the future from the prejudice of his letters. I have considered how best to compose the present dispute, and I think it may be done by the inclosed scholium to the fourth proposition." This scholium was "The inverse law of gravity holds in all the celestial motions, as was discovered also independently by my countrymen Wren, Hooke and Halley."

1688 Newton, in a letter to Edmund Halley, again expresses his exasperation with carping critics. [Thanks to Howard Eves]*VFR

1788; Washington Writes to Nicholas Pike to Thank him for a copy of his "A New and Complete System of Arithmetic" , published in 1786 by Nicholas Pike, a Newburyport schoolmaster. In his letter, sent June 20, 1788, from Mount Vernon, Washington writes: "The handsome manner in which that Work is printed and the elegant manner in which it is bound, are pleasing proofs of the progress which the Arts are making in this Country. Washington's letter to Pike also commended him on his accomplishments and the importance of his work.
Pike had written to  Washington on March 25,1786 requesting permission to dedciate the book to Washington. On June 20 of 1786, Washington had replied that, "I must therefore beg leave to decline the honour which you would do me, as I have before done in two or three cases of a similar kind."
1808 Poisson submitted his first paper on the stability of the planetary system, one day before his twenty-seventh birthday. *VFR

---

1831 János Bolyai's pioneering work, The Absolutely True Science of Space, was published in 1832. This important work was published as an appendix to the first volume of his father,Farkas Bolyai's Tentamen , but its off-print had already been ready the previous year, in April 1831. The latter was the version which, together with a letter, was sent to Gauss by Farkas Bolyai on the 20th of June 1831. Gauss got the letter but János's work was lost on the way. On the 16th of January 1832 Farkas sent the Appendix to his friend again with another letter in which he wrote: ``My son appreciates Your critique more than that of whole Europe and it is the only thing he is waiting for''.
After twenty-three years of silence, Gauss replied to his ``old, unforgettable friend'' on the 6th of March 1832. One of his well-known sentences was: ``if I praised your son's work I would praise myself''. The letter deeply afflicted and upset János Bolyai, although it reflects appreciation, too: ``... I am very glad that it is my old friend's son who so splendidly preceded me'' *Komal Journal

---

1877 Georg Cantor, in a letter to Dedekind, announced a proof that the points inside a square are in one-to-one correspondence with those on a line segment. Three years earlier, Cantor had intimated that this was clearly impossible. *VFR

---

1908 Count Zeppelin made his first flight in his fourth new airship at Friedrichshafen, Germany. The Luftschiff LZ4 had its first flight 20 Jun 1908. Its first extended flight (12 hours) was taken to Switzerland 1 Jul 1908. At the beginning of August, it embarked on an extended flight which had taken it among other places to Basel, Straussberg, and many of the major cities of southern Germany. While moored at Echterdingen on 5 Aug 1908, it was torn from the mast by high winds and destroyed. As interest in the Zeppelins ran high in German, the incident was felt as a national disaster. Spontaneous donations resulted in approximately 5.5 million Marks and made it possible for Zeppelin to continue his work. *TIS

---

BIRTHS
1775 Jacques Frédéric Français In September 1813 Français published a work in which he gave a geometric representation of complex numbers with interesting applications. This was based on Argand's paper which had been sent, without disclosing the name of the author, by Legendre to François Français. Although Wessel had published an account of the geometric representation of complex numbers in 1799, and then Argand had done so again in 1806, the idea was still little known among mathematicians. This changed after Français' paper since a vigorous discussion between Français, Argand and Servois took place in Gergonne's Journal. In this argument Français and Argand believed in the validity of the geometric representation, while Servois argued that complex numbers must be handled using pure algebra. *SAU

---

1838 Theodor Reye worked in Geometry and Projective Geometry.*SAU

---

1873 Alfred Loewy born. He worked in group theory and differential equations. *VFR

---

DEATHS
1800 Abraham Kästner was a German mathematician who compiled encyclopaedias and wrote text-books. He taught Gauss. *SAU

---

1807 Ferdinand Berthoud Outstanding Swiss horologist and author of extensive treatises on timekeeping who became involved in the attempt to solve the problem of determining longitude at sea. His major achievement was his further development of an accurate and practical marine clock, or chronometer. (Such an instrument had previously been constructed in expensive and delicate prototypes by Pierre Leroy of France and John Harrison of England.) He made his first chronometer in 1754, which was sent for trial in 1761. Berthoud's improvements to the chronometer have been largely retained in present-day designs. *TIS

---

1966 Georges (Henri) Lemaître was a Belgian astronomer and cosmologist, born in Charleroi, Belgium. He was also a civil engineer, army officer, and ordained priest. He did research on cosmic rays and the three-body problem. Lemaître formulated (1927) the modern big-bang theory. He reasoned that if the universe was expanding now, then the further you go in the past, the universe’s contents must have been closer together. He envisioned that at some point in the distant past, all the matter in the universe was in an exceedingly dense state, crushed into a single object he called the "primeval super-atom" which exploded, with all its constituent parts rushing away. This theory was later developed by Gamow and others.*TIS

---

2003 I. Bernard Cohen (1 March 1914 – 20 June 2003) was the Victor S. Thomas Professor of the history of science at Harvard University and the author of many books on the history of science and, in particular, Isaac Newton.
Cohen was the first American to receive a Ph.D. in history of science, was a Harvard undergraduate ('37) and then a Ph.D. student and protégé of George Sarton who was the founder of Isis and the History of Science Society. Cohen taught at Harvard from 1942 until his death, and his tenure was marked by the development of Harvard's program in the history of science. *Wik

---

Credits:
*VFR = V Frederick Rickey, USMA
*TIS= Today in Science History
*Wik = Wikipedia
*SAU=St Andrews Univ. Math History

On This Day in Math - June 19

The more I see of men, the better I like my dog.

Blaise Pascal (over 350 years before Carrie Underwood)


EVENTS
240  In 240 BC, Eratosthenes, a Greek astronomer and mathematician, estimated the circumference of the earth. As the director of the great library of Alexandria, he read in a papyrus book that in Syene, approaching noon on the summer solstice, the longest day of the year, shadows of temple columns grew shorter. At noon, they were gone. The sun was directly overhead. However, a stick in Alexandria, far to the north, could cast a pronounced shadow. Thus, he realized that the surface of the Earth could not be flat. It must be curved. Not only that, but the greater the curvature, the greater the difference in the shadow lengths. By measurement on the ground and application of geometry, he calculated the circumference of the earth. *TIS

325 The early Christian church opened the council of Nicaea, which decided the rules for computing the date of Easter: The first Sunday after the first full moon on or after the vernal equinox *VFR 

In 1963, Soviet cosmonaut Valentina Tereshkova returned to Earth after spending nearly three days as the first woman in space. She had been interested in parachute jumping when she was young, and that expertise was one of the reasons she was picked for the cosmonaut program. She became the first person to be recruited without experience as a test pilot. On 16 Jun 1963, Tereshkova was launched into space aboard Vostok 6, and became the first woman to travel in space. Her radio name was "Chaika," Russian for "seagull." Her flight made 48 orbits of Earth. Tereshkova never made a second trip into space. She became an important member of the Communist Party and a representative of the Soviet government.*TIS

BIRTHS

1623 Blaise Pascal born in Ferrand, Auvergne, France.  He laid the foundation for the modern theory of probabilities. In hydrodynamics he formulated what came to be known as Pascal's law of pressure, and invented the syringe and hydraulic press. Pascal invented the first digital calculator to help his father with his work collecting taxes. He worked on it for three years (1642-45). The device, called the Pascaline, resembled a mechanical calculator of the 1940s. This, almost certainly, makes Pascal the second person to invent a mechanical calculator for Schickard had manufactured one in 1624. He died at the young age of 39 having been sickly and physically weak through life. Autopsy showed he had been born with a deformed skull.*TIS

1669 Leonty Magnitsky was a Russian teacher who wrote the first guide to mathematics published in Russia.*SAU

1771 Joseph Gergonne born. He came under the influence of Gaspard Monge, the Director of the new École Polytechnique in Paris. In 1810, in response to difficulties he encountered in trying to publish his work, Gergonne founded his own mathematics journal, officially named the Annales de mathématiques pures et appliquées but generally referred to as the Annales de Gergonne. The most common subject of articles in his journal was geometry, Gergonne's specialty. Over a period of 22 years, the Annales de Gergonne published about 200 articles by Gergonne himself, and other articles by many distinguished mathematicians, including Poncelet, Servois, Bobillier, Steiner, Plücker, Chasles, Brianchon, Dupin, Lamé, even Galois.
Gergonne was appointed to the chair of astronomy at the University of Montpellier in 1816. In 1830, he was appointed Rector of the University of Montpellier, at which time he ceased publishing his journal. He retired in 1844.
Gergonne was the first mathematician to employ the word polar. In a series of papers beginning in 1810, he discovered the principle of duality in projective geometry, by noticing that every theorem in the plane connecting points and lines corresponds to another theorem in which points and lines are interchanged, provided that the theorem embodied no metrical notions. In 1816, he devised an elegant solution to the problem of Apollonius: find a circle which touches three given circles.
In 1813, Gergonne wrote the prize-winning essay for the Bordeaux Academy, Methods of synthesis and analysis in mathematics, unpublished to this day and known only via a summary. The essay is very revealing of Gergonne's philosophical ideas. He called for the abandonment of the words analysis and synthesis, claiming they lacked clear meanings. Surprisingly for a geometer, he suggested that algebra is more important than geometry, at a time when algebra consisted almost entirely of the elementary algebra of the real field. He predicted that one day quasi-mechanical methods would be used to discover new results.
In 1815, Gergonne wrote the first paper on the optimal design of experiments for polynomial regression. According to S. M. Stigler, Gergonne is the pioneer of optimal design as well as response surface methodology.

1846 Antonio Abetti (19 Jun 1846, 20 Feb 1928 at age 81) Italian astronomer who was an authority on minor planets. At first a civil engineer, he became an astronomer at the University of Padua (1868-93), with an interest in positional astronomy and made many observations of small planets, comets and star occultations. In 1874, Abetti went to Muddapur, Bengal, to observe the transit of Venus across the sun's disk where his use of a spectroscope was the first use of this kind. Later, he became director at the Arcetri Observatory and Professor of astronomy at the University of Florence (1894-1921). The observatory had been founded by G. B. Donati in 1872, and Abetti equipped it with a new telescope that he had built in the workshops at Padua. He was active after retirement, until his death, and was followed by his son Giorgio.*TIS

---

1851 Silvanus P. Thomson born. In 1910 he published Calculus Made Easy, which was published anonymously until after his death in 1916. It is still in print. *VFR  He was a noted physicist and engineer, and a celebrated teacher and writer on electricity and magnetism. He also wrote popular biographies of Faraday and Lord Kelvin. At his death he was professor at City and Guilds Technical College at Finsbury (London). Thompson’s particular gift was in his ability to communicate difficult scientific concepts in a clear and interesting manner. He attended and lectured at the Royal Institution giving the Christmas lectures in 1896 on Light, Visible and Invisible with an account of Röntgen Light. He was an impressive lecturer and the radiologist AE Barclay said that: “None who heard him could forget the vividness of the word-pictures he placed before them.”

---

DEATHS

1945 Stefan Mazurkiewicz, one of the founders of Fundamenta Mathematicae, died.

Credits:
*VFR = V Frederick Rickey, USMA
*TIS= Today in Science History
*Wik = Wikipedia
*SAU=St Andrews Univ. Math History