**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

The 168th day of the year; there are 168 prime numbers less than 1000. *Prime Curios

168 is the product of the first two perfect numbers. *jim wilder @wilderlab

\(2^{168} = 374144419156711147060143317175368453031918731001856 \) lacks the digit 2; no larger 2

^{n}exists for \(n \lt 10^{399}\) that is not pandigital.

There are 168 hours in a week.

**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

17

**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

**1825**Faraday’s account of his discovery of bicarburet of hydrogen (later called Benzene) was read to the Royal Society. *Jennifer Wilson, Celebrating Michael Faraday’s Discovery of Benzene, Ambix,Volume 59, Issue 3

**1825**Benjamin Gompartz leter to Francis Baily in which he expounded his law of human mortality. Today the curve is expressed as \( N(t) = N(O) e^{-c(e^{at}-1)} \) *Philosophical Transactions of the Royal Society of London

(For those interested in mathematical notation, this paper makes frequent use of the overbar as a vincula or grouping symbol.

**1854**For the ﬁrst time in more than twenty years, Gauss left Gottingen. He went to see the railway 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.

**1893**Secretary of Agriculture J. Sterling Morton begins his attack on the U. S. Weather Bureau with a letter to Cleveland Abbe, "It seems to me that the disbursements of the Weather Bureau for scientists are altogether too extravagant." Within days he would also cut his salary by 25%. *Isaac's Storm, Erik Larson

**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".

**1902**Albert Einstein formally appointed as Technical Expert at the Swiss Patent Office at Bern at a salary equivalent to about $3,000 a year.

**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].

**1993**The 100th anniversary of Cracker Jack (called America's first junk food) was celebrated at Wrigley Field during the game between the Cubs and the expansion Florida Marlins. Before the game, Sailor Jack, the company's mascot, threw out the ceremonial first pitch. Cracker Jacks have been associated with baseball since the 1908 publication of "Take Me Out to the Ball Game", a song written by lyricist Jack Norworth and composer Albert Von Tilzer, with the line: "Buy me some peanuts and Cracker Jack!"

1993 May have been a premature date for the 100th anniversary. Although rumors exist that a "candy coated popcorn

**"**was sold by the Rueckheim brothers at the World's Columbian Exposition in 1893, there seems to be no supporting evidence of this. The first lot of Cracker Jack was produced and the name was registered in 1896.

The Sailor Jack in the logo was modeled after Robert Rueckheim, nephew of the Rueckheim brothers, who sadly died of pneumonia shortly after his image appeared at the age of 8. The dog in the image, Bingo, was a stray who lived on for another 17 years. *Wik

**BIRTHS**

**1640 Jacques Ozanam**(16 June 1640, Sainte-Olive, Ain - 3 April 1718, Paris) 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.

**1782 Olry Terquem**(16 June 1782 – 6 May 1862) was a French mathematician. He is known for his works in geometry and for founding two scientific journals, one of which was the first journal about the history of mathematics. He was also the pseudonymous author (as Tsarphati) of a sequence of letters advocating radical Reform in Judaism. He was French Jewish.

Terquem translated works concerning artillery, was the author of several textbooks, and became an expert on the history of mathematics. Terquem and Camille-Christophe Gerono were the founding editors of the Nouvelles Annales de Mathématiques in 1842. Terquem also founded another journal in 1855, the Bulletin de Bibliographie, d'Histoire et de Biographie de Mathématiques, which was published as a supplement to the Nouvelles Annales, and he continued editing it until 1861. This was the first journal dedicated to the history of mathematics.

The three marked points that lie on the nine point circle and interior to the triangle were found by Terquem. The point of convergence of the three red lines through the triangle is its orthocenter. He is also known for naming the nine-point circle and fully proving its properties. This is a circle defined from a given triangle that contains nine special points of the triangle. Karl Wilhelm Feuerbach had previously observed that the three feet of the altitudes of a triangle and the three midpoints of its sides all lie on a single circle, but Terquem was the first to prove that this circle also contains the midpoints of the line segments connecting each vertex to the orthocenter of the triangle. He also gave a new proof of Feuerbach's theorem that the nine-point circle is tangent to the incircle and excircles of a triangle.

Terquem's other contributions to mathematics include naming the pedal curve of another curve, and counting the number of perpendicular lines from a point to an algebraic curve as a function of the degree of the curve. He was also the first to observe that the minimum or maximum value of a symmetric function is often obtained by setting all variables equal to each other.

He became an officer of the Legion of Honor in 1852. After he died, his funeral was officiated by Lazare Isidor, the Chief Rabbi of Paris and later of France, and attended by over 12 generals headed by Edmond Le Bœuf.

*Wik

**1801 Julius Plucker**(16 June 1801 – 22 May 1868) 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**(June 14, 1830, Barmen - March 24, 1885 Hanover) born. He worked on elliptic functions and diﬀerential geometry. *VFR

**1839**

**Julius Petersen**(16 June 1839, Sorø, West Zealand – 5 August 1910, Copenhagen) 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

**1866 James P. Pierpont**(June 16, 1866, New Have, Connecticut, USA – December 9, 1938) American mathematician. His father Cornelius Pierpont was a wealthy New Haven businessman. He did undergraduate studies at Worcester Polytechnic Institute, initially in mechanical engineering, but turned to mathematics. He went to Europe after graduating in 1886. He studied in Berlin, and later in Vienna. He prepared his PhD at the University of Vienna under Leopold Gegenbauer and Gustav Ritter von Escherich. His thesis, defended in 1894, is entitled Zur Geschichte der Gleichung fünften Grades bis zum Jahre 1858. After his defense, he returned to New Haven and was appointed as a lecturer at Yale University, where he spent most of his career. In 1898, he became professor. Initially, his research dealt with Galois theory of equations. After 1900, he worked in real and complex analysis.

In his textbooks of real analysis, he introduced a definition of the integral analogous to Lebesgue integration. His definition was later criticized by Maurice Fréchet. Finally, in the 1920s, his interest turned to non-Euclidean geometry. *Wik

**1888 Alexander Alexandrovich Friedmann**(June 16 (4 old style) – September 16, 1925, Leningrad, USSR) 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**

**1902 Friedrich Wilhelm Karl Ernst Schröder**(25 November 1841 in Mannheim, Germany -16 June 1902 in Karlsruhe, Germany) Friedrich Wilhelm Karl Ernst Schröder (25 November 1841 in Mannheim, Baden, Germany – 16 June 1902 in Karlsruhe, Germany) was a German mathematician mainly known for his work on algebraic logic. He is a major figure in the history of mathematical logic (a term he may have invented)[citation needed], by virtue of summarizing and extending the work of George Boole, Augustus De Morgan, Hugh MacColl, and especially Charles Peirce. He is best known for his monumental Vorlesungen über die Algebra der Logik (Lectures on the algebra of logic), in 3 volumes, which prepared the way for the emergence of mathematical logic as a separate discipline in the twentieth century by systematizing the various systems of formal logic of the day. *Wik

**1910 Julius Weingartnen**(2 March 1836 in Berlin – 16 June 1910 in Freiburg im Breisgau) He worked on differential geometry. He received his doctorate in 1864 from Martin-Luther-Universität Halle-Wittenberg. He made some important contributions to the differential geometry of surfaces, such as the Weingarten equations *Wik

**1948 Marcel Brillouin**(19 December 1854 – 16 June 1948) worked on topics ranging from history of science to the physics of the earth and the atom. *SAU

**1970 Sydney Chapman**(29 January 1888 – 16 June 1970) 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

**1990 Thomas George Cowling**(17 June 1906 in Hackney, London, England - 16 June 1990 in Leeds, England) Tom Cowling graduated from Oxford and worked at Imperial College London. He lectured at Swansea, Dundee and Manchester and became a professor at Bangor and Leeds. He worked on theoretical astronomy and stellar physics. *SAU

**2001 Alessandro Faedo**(18 November 1913 – 15 June 2001) (also known as Alessandro Carlo Faedo or Sandro Faedo) was an Italian mathematician and politician, born in Chiampo. He is known for his work in numerical analysis, leading to the Faedo–Galerkin method: he was one of the pupils of Leonida Tonelli and, after his death, he succeeded him on the chair of mathematical analysis at the University of Pisa, becoming dean of the faculty of sciences and then rector and exerting a strong positive influence on the development of the university. *Wik

**2004 Herman Heine Goldstine**(September 13, 1913 – June 16, 2004) was a mathematician and computer scientist, who was one of the original developers of ENIAC, the first of the modern electronic digital computers.

Herman Heine Goldstine was born in Chicago in 1913 to Jewish parents. He attended the University of Chicago, where he joined the Phi Beta Kappa fraternity, and graduated with a degree in Mathematics in 1933, a master's degree in 1934, and a PhD in 1936. For three years he was a research assistant under Gilbert Ames Bliss, an authority on the mathematical theory of external ballistics. In 1939 Goldstine began a teaching career at the University of Michigan, until the United States' entry into World War II, when he joined the U. S. Army. In 1941 he married Adele Katz, who was an ENIAC programmer and who wrote the technical description for ENIAC. He had a daughter and a son with Adele, who died in 1964. Two years later he married secondly Ellen Watson.

In retirement Goldstine became executive director of the American Philosophical Society in Philadelphia between 1985 and 1997, in which capacity he was able to attract many prestigious visitors and speakers.

Goldstine died on June 16, 2004 at his home in Bryn Mawr, Pennsylvania, after a long struggle with Parkinson's disease. His death was announced by the Thomas J. Watson Research Center in Yorktown Heights, New York, where a post-doctoral fellowship was renamed in his honor. *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