**continues to decrease rapidly, but the price of theorem proving continues to hold steady or increase, elementary economics indicates that we ought to spend a larger and larger fraction of our time on calculation.**

John Tukey

**EVENTS**

**1497**Amerigo VESPUCCI (1454-1512) was born in one of the Vespucci houses in Borgo Ognissanti. He is said to have made four voyages to the New World. He reported sighting the South American mainland on 16 Jun 1497, a week before Cabot reached North America, which led to his name being attached to the New World in Martin Waldseemüller's Cosmographiæ Introductio of 1507 – but many authorities doubt that Vespucci ever made this voyage. Waldseemüller realised that he had overrated Vespucci's accomplishments and removed the name from later versions of his map, but it was too late. Simonetta Vespucci, who married his distant cousin was a celebrated beauty, immortalised in Botticelli's paintings – his 'Mars and Venus' in the Uffizi shows little wasps ('vespucci') circling the head of Mars. Florence's airport, in the NW suburb of Peretola, is named Amerigo Vespucci.

**1641**In a letter to Fr. Marin Mersenne, Descartes states that no prime of the form 12n ± 1 will divide a number that is one more than a power of three. He adds that 12n ± 5 will always divide some 3

^{X}+1. He gives a similar rule for five, and states he has one for all primes. (History of the theory of numbers, By Leonard Eugene Dickson)

**1657,**the first pendulum clock was patented by its inventor, Christiaan Huygens. Although others may have worked in this field before him, Huygens made major advances in building a practical clock. He needed time accuracy for his astronomical measurements.*TIS

179

**1799**Gauss awarded his Ph.D. at age 22, the usual requirement of an oral exam being dropped. His dissertation gave the ﬁrst correct proof of the fundamental theorem of algebra. *VFR

**1833**Janos Bolyai was retired as Captain in the cavalry for dueling with thirteen other oﬃcers. He accepted their challenge on the condition that he be allowed to play his violin between duels. [Bonola, Non-Euclidean Geometry, Appendix 1, p. xxix]*VFR

**1854**For the ﬁrst time in more than twenty years, Gauss left Gottingen. He went to see the railway between between Cassel and Gottingen that was under construction. VFR

**1867**A Memorial to Leonardo Bigolli (Fibonacci) was erected in Pisa. The monument includes a 1241 decree by the commune of Pisa that bestowed an annual salary to Leonardo, "In consideration of the honor brought to the city and its citizens and their betterment by the teaching and zealous cooperation of that discrete and learned man." *The Man of Numbers, Keith Devlin

**1885**The first gravity-powered American roller coaster that was commercially successful was put in operation at Coney Island, N.Y., the invention of La Marcus Thompson (patent No. 310,966). Passengers rode a train on undulating tracks over a wooden structure 600-ft long. The train started at a height of 50-ft on one end and ran downhill by gravity until its momentum died. Passengers then left the train and attendants pushed the car over a switch to a higher level. The passengers returned to their sideways facing seats and rode back to the original starting point. Admission on the Thompson Switchback Railway was 5 cents and he grossed an average of $600 / day. Within 4 yrs he had built about 50 more across the U.S. and in Europe.

**1902**Bertrand Russell wrote Gottlob Frege that in his Grundgesetze der Arithmetik “there is just one point where I have encountered a diﬃculty.” The diﬃculty is the Russell Antinomy, a logical contradiction. See 22 June 1902. Russell had found a class of contradictions to Frege's 1879 Begriffsschrift. This contradiction can be stated as "the class of all classes that do not contain themselves as elements".

**1933**FDR signed the Banking Act, which separated commercial banking from investment banking and established the Federal Deposit Insurance Corporation. He also signed the Farm Credit Act, the Emergency Railroad Transportation Act, and the National Industrial Recovery Act (which created the Public Works Administration).

**1963**Valentina Tereshkova became the ﬁrst woman in space. She was aboard the Soviet Union’s Vostok 6. See 18 June 1983.

**1973**Afghanistan issued a postage stamp commemorating the millennium of the birth of Ab'u Rayhan Muhammad ibn Ahmad Al Bırunı (born 4 September 973, died after 1050), author of books on arithmetic, geometry, trigonometry, astronomy and geography. [Scott #881].

**BIRTHS**

**1640 Jacques Ozanam**was born in Sainte-Olive, Ain, France.

All his books sold well and ran to many editions, especially his famous works

*Dictionnaire mathématique*(1691), the five volume work*Cours de mathématiques*(1693) and*Récréations mathématiques et physiques*(1694). It is certainly for this last work on recreational mathematics that Ozanam will be most remembered. The precursor of books to follow for the next 200 years, he published it in four volumes in 1694 and it later went through at least ten editions. Ozanam based his book on earlier works by Bachet, Mydorge, Leurechon, and Schwenter. It was later revised and enlarged by Montucla, then translated into English by Hutton (1803, 1814).Ozanam's original edition contained an early example of a problem about orthogonal Latin squares:-

Arrange the16court cards so that each row and each column contains one of each suit and one of each value.

**1801 Julius Plucke**r born in Elberfeld, Germany. He was a geometer who worked in analytic andprojective geometry, and on the theory of plane curves.*VFR He was a pioneer in the investigations of cathode rays that led eventually to the discovery of the electron. He also vastly extended the study of Lamé curves. *VFR (

*Lame curves are curves with equations of the form (x/a)^n + (y/b)^n = 1. He investigated n for both rational and irrational values*.

*Piet Hein's "super-ellipse" is an example of a Lame curve.*)

**1830 Alfred Enneper**born. He worked on elliptic functions and diﬀerential geometry. *VFR

**1839**

**Julius Petersen**was a Danish mathematician who worked on geometry and graph theory. He is best remembered for the

*Petersen graph*.

In the mathematical field of graph theory, the

**Petersen graph**is an undirected graph with 10 vertices and 15 edges. It is a small graph that serves as a useful example and counterexample for many problems in graph theory. The Petersen graph is named for Julius Petersen, who in 1898 constructed it to be the smallest bridgeless cubic graph with no three-edge-coloring.

^{}Although the graph is generally credited to Petersen, it had in fact first appeared 12 years earlier, in a paper by A. B. Kempe (1886).

Donald Knuth states that the Petersen graph is "a remarkable configuration that serves as a counterexample to many optimistic predictions about what might be true for graphs in general. *Wik

**1888 Alexander Alexandrovich Friedmann**Russian mathematician who was the first to work out a mathematical analysis of an expanding universe consistent with general relativity, yet without Einstein's cosmological constant. In 1922, he developed solutions to the field equations, one of which clearly described a universe that began from a point singularity, and expanded thereafter. In his article

*On the Curvature of Space*received by the journal

*Zeitschrift für Physik*on 29 Jun 1922, he showed that the radius of curvature of the universe can be either an increasing or a periodic function of time. In Jul 1925, he made a record-breaking 7400-m balloon ascent to make meteorological and medical observations. A few weeks later he fell ill and died of typhus. *TIS (

*His date of birth is often given as 29 June. However this is an error which came about in converting the "Old Style" Russian date to the "New Style" date, which requires an addition of 12 days.*)

**1915 John Wilder Tukey**(June 16, 1915 – July 26, 2000) was an American statistician. He was awarded the IEEE Medal of Honor in 1982 "For his contributions to the spectral analysis of random processes and the fast Fourier transform (FFT) algorithm."

Tukey retired in 1985. He died in New Brunswick, New Jersey Tukey coined many statistical terms that have become part of common usage, but the two most famous coinages attributed to him were related to computer science.

While working with John von Neumann on early computer designs, Tukey introduced the word "bit" as a contraction of "binary digit". The term "bit" was first used in an article by Claude Shannon in 1948.

The term "software", which Paul Niquette claims he coined in 1953, was first used in print by Tukey in a 1958 article in American Mathematical Monthly, and thus some attribute the term to him; He also is credited with the terms ANOVA, and boxplot. *Wik

**DEATHS**

**1910 Julius Weingartnen**died. He worked on diﬀerential geometry.*VFR

**1948**

**Marcel Brillouin**worked on topics ranging from history of science to the physics of the earth and the atom. *SAU

**1970 Sydney Chapman**English mathematician and physicist noted for his research in geophysics. After graduation (1910) he worked at the Greenwich Observatory, but returned to Cambridge upon the outbreak of WW I. Between 1915 and 1917 he completed a series of important papers on thermal diffusion and the fundamentals of gas dynamics. He developed systematic approximations to the Maxwell-Boltzmann formulation for the velocity distribution function for interacting particles under general force laws. During WW II he worked on military operational research and incendiary bomb problems. Chapman's main area of research was geomagnetism, beginning in 1913 and extending to terrestrial and interplanetary magnetism, the ionosphere and the aurora borealis.*TIS

1977 Wernher Magnus Maximilian von Braun (23 Mar 1912; 16 Jun 1977 at age 65) was a German-American rocket engineer who was one of the most important developers of rockets and their evolution to applications in space exploration. His interest began as a teenager in Germany, and during WW II he led the development of the deadly V–2 ballistic missile for the Nazis (which role remains controversial). After war, he was taken to use his knowledge to produce rockets for the U.S. Army. In 1960, he transferred to the newly formed NASA and became director of Marshall Space Flight Center and chief architect of the Saturn V launch vehicle used to put men on the moon. His contributions include the Explorer satellites; Jupiter, Pershing, Redstone and Saturn rockets, and Skylab. *TIS

Credits:

*VFR = V Frederick Rickey, USMA

*TIS= Today in Science History

*Wik = Wikipedia

*SAU=St Andrews Univ. Math History