Tuesday, 16 June 2026

Automorphic Numbers and some history notes

   As far back as the Babylonians, and maybe much before, someone looked at the symbol for five, and the symbol for 25 and noticed that both ended with the same symbol for five.  Even 5 x 25 ended in the same XXV as 25 in Roman numerals.    In Roman numerals V times V = XXV, and V times XXV  =  CXXV.  Even XXV times XXV , written as DCXXV repeats the original factor in its ending.  6^2 = 36 also appears easily in Roman numerals, VI x VI = XXXVI, and 76^2 as well,  76 is LXXVI and its square, after a string of  five M's and DCC, ends with the same LXXVI .

It's hard to imagine that number crunchers like Diophantus didn't recognize some of these repetitive patterns, and if there is earlier mention, would one of those more knowledgeable historians give me a note.  

For at least 200 years, the one digit autonomic numbers, 0, 1, 5, and 6 have been called circular numbers. The earliest mention of the term I can find is An Introduction to the knowledge and variety of Numbers, John Smith (Schoolmaster of Norwich), 1809.  On page 104 he writes, "The numbers 5 and 6 are called circular numbers ; because , like the circle , terminating where it begins , these numbers , multiplied by themselves ever so often , always end in the same number : 5 by 5 make 25 , and that product  multiplied by 5 makes 125, So 6 by 6 makes 36, and 6 times this product make 216, etc."  This term and usage is still preserved in some recreational math books into the 21st Century. 

The expanse of this idea to numbers that repeated the last two, or three, or more digits took on the term automorphic numbers, (formed on oneself).  The first use of the term automorphic in mathematics, seems to be by Arthur Cayley in terms of functions, "... invariant with respect to a group of linear transformations of a certain kind leaving a certain function invariant.  This meaning was superseded by Felix Klein's choice of "a function f(x) is automorphic with respect to a group G, then f(Tₙ(x)) = f(x) for every element Tₙ of G."

The term automorphic number now means an n digit number that when squared has the number appear as the last n digits of the square.  thus 25^2 =625 and 376^2 = 141376.  Many more examples below.

The first instances of the use of autonomic numbers I can find is from the early 1940's.

Mathematical Recreations by Maurice Kraitchik, 1942


He explains the term in a footnote :


He explains that prime numbers will not work except for the trivial n=0 or 1, and illustrates numbers in base 6 and 10, He explains that prime numbers will not work as bases except for the trivial n=0 or 1, and he illustrates numbers in base 6 , And lists numbers that are automorphic in base 6, "which end in 4, 44, or 344 and 3, 13, 213, and so on are automorphic."  

Then he does the same with base 10.


He closes by providing "the last digits may be 3740081787109376 or 6259918212890625."  He nowhere mentions other composite numbers whose bases work, 12, 14, 15.

Early in the same year, a problem in The American Mathematical Monthly, Vol. 49, No. 2 (Feb., 1942), pp. 120-121 (2 pages)  used the term. 

Since this was new to me, I tested it with n=2, 90625^4.  It came out as, 67451572418212890625; the last 11 digits were 18212890625 which is itself automorphic , producing a larger number that ends in these same 11 digits.

The Previous reference is from a question in 1941 that show what are now called trimorphic numbers, by H. S. M. Coxeter, 

These numbers are the 13 six-digit trimorphic numbers,  109375, 109376, 218751, 281249, 390625, 499999, 500001, 609375, 718751, 781249, 890624, 890625, 999999. Two of these are the six digit autonomic numbers 109376 and 890625. Tri-morphic are n-digit numbers whose cubes preserve the original in their last n digits. All automorphic numbers are automatically tri-morphic, but there are others which are not automorphic.


The automorphic numbers in base 10 have two sets (ignoring the trivial 0, 1). The fives are mostly self describing, 5^2 =25, 25^2 = 625, 625^2 presents a glitch, since it produces 390625, there is not a four digit automorphic number in this series, but we extend to the next digit to get 90625 which when squared produces 8212890625, and we get the six digit automorph, 890625.
The six series is a little more complex, 6^2=36, but 36 is not automorphic, instead we use the tens compliment of 3, 7 as the lead digit, and 76 is the two digit automorph. 75^2 = 5776, but 776 is not a 3 digit automorph, but the tens compliment of 7 yields 376 which is the three digit automorph.

there is an interesting combination for the numbers in base ten. Notice that 6+5 = 10+1, and 25 + 76 = 100+1. 625 + 376 = 1000+1, and 90625 + 9376= 10000+1.

***There is a flaw in the notes below due to, I believe, a typo in the spreadsheet that I'm working to correct.
There are also a-automorphic numbers for which ax^2 preserves the n-digits of x, so 2-automorphic would be 2x^2, and contain numbers like 8, 88, 688, 4688, 54688...

The 3-automorphic numbers I have found end in 2, 5, and 7. (still exploring these). 2, 92, 792, ... ; 5, 75, 875,..; 7, 67, 667, 6667...;

I think any of these would be great explorations for even middle school students....or old retired guys like me, so enjoy!
For more ideas about automorphic numbers, see the great book, “Exploring the Beauty of Fascinating Numbers” by Shyam Sunder Gupta. It is a truly wonderful exploration, and even has more about automorphic numbers.









On This Day in Math - June 16

 


In a world in which the price of calculation
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 167th day of the year; 167 is the only prime requiring exactly eight cubes to express it. *Prime Curios (I find it amazing that there is only one such prime number)

167= 2 * 34 + 5

167 is the smallest number whose fourth power begins with four identical digits, 1674=777796321.

167 is an emirp, a prime whose reverse, 761 is also prime. The 167th prime is 991 and it is also an emirp. Wait! the 991st prime, 7841 is also an emirp.


167 x 701 = 117067.  Note that the six digits in the product are the six digits on the factors.  Such numbers were named Vampire numbers by Cliff Pickover in 1995.  This particular is the smallest vampire number with prime factors. it is the 17th vampire number. There are seven four digit Vampire numbers. The next that factors into two primes also has a year day for one factor.


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 Amerigo's distant cousin was a celebrated beauty, immortalized 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.
Posthumous portrait in the Giovio Series at the Uffizi in Florence, attributed to Cristofano dell'Altissimo, c. 1568





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 3X +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












On June 16, 1794, a shower of stones fell from the sky just outside Siena, Italy. The many eye-witnesses agreed that a dark cloud had rapidly approached out of a clear sky, exploded like a battery of fireworks, and ejected the stones, which fell with a hissing sound. At the time, most scientists thought that tales of stones falling from the skies were mere peasant inventions. The German physicist Ernst Chladni, a few months before the Siena fall, had written a book making the case for the extra-terrestrial origins of meteorites, but he found no takers. After the Siena fall, Abbé Ambrogio Soldani, an Italian naturalist, interviewed witnesses and collected 19 of the fallen stones; he also sent one stone to an English chemist working in Italy, William Thomson, who analyzed it. Both Soldani and Thomson agreed that the stones had a fusion crust that must have been produced by extreme heat, and that they contained a great deal of iron, which made them quite unlike the other rocks of the Siena countryside

Later that year, Soldani published a book, Sopra una pioggetta di sassi accaduta nella sera de' 16 Giugno del MDCCXCIV, that presented his arguments and Thomson's evidence that the Siena stones really had come from the heavens. This book, along with Chladni's, launched the science of meteoritics, and nine years later, the great fall of stones at L'Aigle France, and the study of these meteorites by Jean-Baptiste Biot, confirmed all that Soldani and Chladni had suggested. *Linda Hall org






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  
It is It is common in modern textbooks to treat the Fundamental Theorem of Algebra as a consequence of Louiville's Theorem in complex analysis (named after Joseph Liouville (1809–1892)). , Liouville’s Theorem itself wasn’t first proved until nearly 50 years after Gauss’s dissertation (and was named after a man who was not even born when Gauss’s dissertation was published). So not only does the standard presentation of the Fundamental Theorem of  Algebra misrepresent the historical development of the theorem, it also postpones the proof of of such an important theorem until one takes an upper level course in complex analysis.  Gauss himself proved the theorem without any appeal to complex numbers at all! Instead, he used ideas from geometry, trigonometry, and calculus. The ideas present in his dissertation are accessible to any interested student who has completed the calculus sequence. While Gauss himself avoided using complex numbers, he sometimes did so only with great effort. Indeed, at several points Gauss took theorems that are easily proved using basic properties of complex numbers and reproved them using somewhat convoluted trigonometric calculations. *On Gauss’s First Proof of the Fundamental Theorem of Algebra, Soham Basu and Daniel J. Velleman


  

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
It took humans over 100 years to determine and confirm the structure of benzene. Why did it take so long? Why was there such a curiosity? The 1:1 ratio of carbon to hydrogen in the empirical formula and low chemical reactivity of benzene were a paradox to chemists in the early 1800's.

In 1825, Michael Faraday isolated an oily residue of gas lamps. Faraday called this liquid "bicarburet of hydrogen" and measured the boiling point to be 80°C. Additionally, Faraday determined the empirical formula to be CH. About nine years later, Eilhard Mitscherlich synthesized the same compound from benzoic acid and lime (CaO).

During the mid to late 1800's, several possible structures (shown below) were proposed for benzene.



It was not until the 1930's that Kekule's structure was confirmed by X-ray and electron diffraction. During the end of Kekule's career he revealed that the structure came to him in a vision after enjoying a glass or two of wine by the fire in his favorite chair. His inspiration for the structure of benzene was derived from an ouroboros in the flames.




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 in plaxe of modern day parentheses.

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
The Leonardo Fibonacci Statue is currently in the old cemetery called Camposanto Monumentale (or Campo Santo, “Holy Field”). It was built in the 12th century and is absolutely spectacular. There are beautiful statues and frescoes on the walls that date back to the 1300s. The Fibonacci statues itself is in the corner of this humongous ancient building.*All Star Charts




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.
2890625


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".
 Frege responded
"... your discovery of the contradiction caused me the greatest surprise and, I would almost say, consternation, since it has shaken the basis on which I intended to build arithmetic."




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.

1911  the Computing-Tabulating-Recording Company (CTR) was incorporated, a predecessor of IBM (1924). Earlier, in 1890, Dr. Herman Hollerith had constructed an electromechanical machine using perforated cards for use in the U.S. census, and in 1896 he founded the Tabulating Machine Co. to construct sorting machines. In 1911, CTR was the result of the merger of the Tabulating Company (founded by Hollerith), the Computing Scale Company, and the International Time Recording Company)



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.
She orbited the Earth 48 times, spent almost three days in space, is the only woman to have been on a solo space mission and is the last surviving Vostok programme cosmonaut. She was the youngest woman to fly in space until 2023 when Anastatia Mayers flew on Galactic 02 at the age of 18. Since Mayers flew a suborbital mission, Tereshkova remains the youngest woman to fly in Earth orbit.





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 the 16 court 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

One of the remarkable things about the Petersen graph is that is the smallest hypohamiltonian graph -- it has no Hamiltonian cycle, but deleting any vertex makes it Hamiltonian. In less formal terms, it's possible to start at any node and visit all 10 nodes while traveling on line segments alone, but there's no way to close the loop and return to the starting node at the end of the trip; but if you remove one vertex, any of them, then it is possible to connect every node in a complete circuit.  This fact seems to have first been discovered by  René Sousselier in 1963.  

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







1965 Andrea Mia Ghez (born June 16, 1965) is an American astrophysicist, Nobel laureate, and professor in the Department of Physics and Astronomy and the Lauren B. Leichtman & Arthur E. Levine chair in Astrophysics, at the University of California, Los Angeles. Her research focuses on the center of the Milky Way galaxy.
She received a BS in physics from the Massachusetts Institute of Technology in 1987. While there, she was a member of the fraternity of St. Anthony Hall. She received a PhD under the direction of Gerry Neugebauer at the California Institute of Technology in 1992.
In 2020, she became the fourth woman to be awarded the Nobel Prize in Physics, sharing one half of the prize with Reinhard Genzel (the other half being awarded to Roger Penrose). The Nobel Prize was awarded to Ghez and Genzel for their discovery of a supermassive compact object, now generally recognized to be a black hole, in the Milky Way's Galactic Center.
Sagittarius A* imaged by the Event Horizon Telescope in 2017,






DEATHS



*Wik 

1813 John Snow (15 March 1813 – 16 June 1858) was an English physician and a leader in the development of anesthesia and medical hygiene. He is considered one of the founders of modern epidemiology, in part because of his work in tracing the source of a cholera outbreak in Soho, London, in 1854, which he curtailed by removing the handle of a water pump. Snow's findings inspired the adoption of anesthesia as well as fundamental changes in the water and waste systems of London, which led to similar changes in other cities, and a significant improvement in general public health around the world.  

Image, John Snow memorial and public house on Broadwick Street, Soho

The Ghost Map: The Story of London's Most Terrifying Epidemic – and How it Changed Science, Cities and the Modern World is a book by Steven Berlin Johnson.  Highly Recommended




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), 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
During his career he was the author of over 200 experimental and theoretic papers on a wide range of topics which include the kinetic theory of gases, viscosity, thermodynamics, electricity, and the physics of melting conditions. Most notably he:
built a new model of the Eötvös balance,
wrote on Helmholtz flow and the stability of aircraft,
worked on a theory of the tides.
Brillouin died in Paris (16 June 1948). His son Léon Brillouin, also had a prominent career in physics.




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




1981  Jule Gregory Charney(1 Jan 1917; 16 Jun 1981) American meteorologist who, working with John von Neumann, first introduced the electronic computer into weather prediction (1950) and improved understanding of the large-scale circulation of the atmosphere. The entire Oct 1947 issue of the Journal of Meteorology published his Ph.D. dissertation, (UCLA, 1936) Dynamics of long waves in a baroclinic westerly current. It emphasized the influence of "long waves" in the upper atmosphere rather than the existing practice of emphasis on the polar front. It also simplified analysis of perturbations of these waves using mathematically rigorous methods that yielded useful physical interpretation. He helped the U.S. Weather Bureau set up (1954) a numerical weather prediction unit. *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




2022  Ken Knowlton, (June 6, 1931-June 16, 2022) an engineer, computer scientist and artist who helped pioneer the science and art of computer graphics and made many of the first computer-generated pictures, portraits and movies.  
In 1962, after finishing a Ph.D. in electrical engineering, Dr. Knowlton joined Bell Labs in Murray Hill, N.J., a future-focused division of the Bell telephone conglomerate that was among the world’s leading research labs. After learning that the lab had installed a new machine that could print images onto film, he resolved to make movies using computer-generated graphics. Over the next several months, he developed what he believed to be the first computer programming language for computer animation, called BEFLIX (short for “Bell Labs Flicks”). The following year, he used this language to make an animated movie.   Called “A Computer Technique for the Production of Animated Movies,” this 10-minute film described the technology used to make it. He died on June 16 in Sarasota, Florida.




*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, 15 June 2026

On This Day in Math - June 15

 


 A statistician is someone who is good with numbers
but lacks the personality to be an accountant.
~unknown
(my apologies to all the statisticians out there)


The 166th day of the year; the reverse (661) of 166 is a prime. If you rotate it 180o (991) it is also prime. The same is true if you put zeros between each digit (60601).  *Prime Curios  90901, 9091, and 9901 are all prime, 


166, like 164, uses all the Roman digits from 100 down, once each. A difference is that 166 uses them in order of their size, CLXVI

166!-1 is a factorial minus one prime. It has 298 digits.  (For which n is N! -1 or n! + 1 a prime?  hint: there are thirteen year days  (\ n<366 \) for which  n! +1  is prime  

166 is the sum of three consecutive triangular numbers, 166 = T9 + T10 + T11

166 in binary has the same number of 1's and 0's.  There are 35  8-digit numbers with this property

166  is a Smith number, since the sum of its digits (13) coincides with the sum of the digits of its prime factors. 

166 is the 11-th centered triangular number.1, 4, 10, 19, 31, 46, 64, 85, 109, 136, 166, ...



More extended number facts for every math day of the year. 





EVENTS

762 BC An eclipse more than 27 centuries old is regarded as one of the earliest events that can be pinpointed by scholars of the Near East. The June 15, 762 B.C. total solar eclipse is mentioned in Assyrian texts as well as the Book of Amos in the Hebrew Bible. While hotly debated (at least among archeo-astronomical types, who love to debate such things) the mention of this eclipse serves as a valuable reference point between ancient Assyrian and Hebrew chronology.*listosaur.com




1641  In a letter to Bernard Frenicle de Bessy, Fermat called the theorem that every prime of the form 4n+1 is the sum of two squares, the fundamental theorem of right triangles.  He stated that he had a proof that was "irrefutable".  Later he suggested he had a proof by infinite descent.  Euler is credited with the first correct proof of the theorem, still called Fermat's theorem.  Euler, after much effort, found a solution based on infinite descent. He announced it in two letters to Goldbach, on May 6, 1747 and on April 12, 1749; he published the detailed proof in two articles (between 1752 and 1755). Lagrange gave a proof in 1775 that was based on his study of quadratic forms. This proof was simplified by Gauss in his Disquisitiones Arithmeticae.
Fermat Statue,  Beaumont-de-Lomagne *Wik



In 1752, Ben Franklin's kite-flying experiment proved lightning and electricity were related while flying a kite with a key attached. In Sep 1752, he equipped his house with a lightning rod, connecting it to bells that ring when rod is electrified. He explained how to perform a kite experiment in the 19 Oct 1752 issue of the Pennsylvania Gazette. He had earlier proposed use of lightning rods to protect houses in a 2 Mar 1750  letter to Collinson and in the same year, on 29 Jul 1750, he devised an experiment involving a sentry-box with a pointed rod on its roof, to be erected on hilltop or in church steeple, with rod attached to a Leyden jar which would collect the electrical charge, and thus prove lightning to be a form of electricity. *TIS
*HULTON ARCHIVE/GETTY IMAGES



1785 Pilâtre de Rozier became aviation’s first casualty when he died attempting the second aerial crossing of the English Channel. Rozier had piloted the first manned flight in a balloon from Paris in 1783. He and other supporters of Hydrogen balloons had competed with the Montgolfier brothers and supporters of the hot air ballons. Pilatre had reasoned that since both hydrogen and hot-air balloons had their separate advantages a combination of the two would be even better. Rozier was accustomed to living dangerously—one of his favorite chemical lecture-demonstrations consisted of flushing his lungs with hydrogen and then speaking in the resulting high-pitched voice (today we tend to use helium). The final flourish (today we would tend to omit this!) was to light the hydrogen as it issued from his mouth. Such a man was obviously the “Right Stuff” to fly a hybrid hot-air-hydrogen balloon. Alas, his luck ran out, and he and a companion crashed shortly after takeoff from Boulogne. *Derek A. Davenport, How the Right Professor Charles Went Up in the Wrong Kind of Balloon; ChemMatters
December 1983 Page 14, American Chemical Society  (See Deaths below)
A 1786 illustration of the Montgolfier brothers’ hot air balloon, flown by de Rozier and M. le Marquis d’Arlandes, 21 November 1783.
*ThisDayInAviation



1857 The Great Comet that didn't come, but still created panic. Astronomers became convinced of the periodic nature of many comets, and loose speculation began about their possible times of return.
an obscure prediction, apparently originally made by the German (or Belgian) Laensberg in his Liege Almanac, In his entry for the week commencing 15 Jun 1857, Laensberg had warned, “about this time, expect a comet”. Through the vagaries of reporting, this eventually came to be understood to be a specific prediction that not only would the comet appear on that date, but that it would also collide with the Earth, and that this would result in the end of the World.
While this prediction was treated with scorn by many, it was also taken very seriously by large parts of the population. All this was a fertile field for satirists such as the French caricaturist Honoré Daumier. He gently mocked the Parisians’ comet obsession in a series of cartoons published in Le Charivari, and represented the offending German prognosticator as a magician playing a magic trick by releasing a comet-like duck. The joke, of course, was that the French for duck, “canard”, also means “hoax”
More about this and related comet tails here.

1915 The U.S. minted the only octagon-shaped coin in U.S. history. The coin was one of two $50 coins (the other one was round) issued as part of a set of five commemorative gold coins designed for the Panama-Pacific International Exposition held in San Francisco between February and December 1915. One hundred years later the coins trade for over a quarter-million dollars each. *Felicity Nie, Ready for Zero Blog

1949  Jay Forrester recorded a proposal for core memory in his notebook. A professor at MIT at the time, Forrester eventually installed magnetic core memory on the Whirlwind computer. Core memory made computers more reliable, faster, and easier to make. Such a system of storage remained popular until the development of semiconductors in the 1970s. *CHM





2015 Astronomers discovered the most powerful supernova ever seen, a star in a galaxy billions of light-years away that exploded with such force it briefly shone nearly 600 billion times brighter than our Sun and 20 times brighter than all the stars in the Milky Way combined. The explosion released 10 times more energy than the Sun will radiate in 10 billion years.
Discovered by ASAS-SN’s twin 14-centimeter telescopes operating in Cerro Tololo, Chile, the supernova just appeared as a transient dot of light in an image, and wasn’t immediately recognized as particularly special. *scientificamerican
Beijing Planetarium / Jin Ma / Wayne Rosing (artist rendering)


BIRTHS

1640  Bernard Lamy (15 June 1640, in Le Mans, France – 29 January 1715, in Rouen) was a French mathematician who wrote on geometry and mechanics. He developed the idea of a parallelogram of forces at about the same time as Newton and Verignon.  The Law of Sines as applied to three static forces in mechanics is sometimes called Lamy's Rule. 



1765 Henry T. Colebrook (June 15, 1765 – March 10, 1837) Sanscrit Scholar and British civil servant in India who translated "algebra with arithmetic and mensuration, from the sanscrit of Brahmagupta and Bhascara."  *Wik

1765 Johann Gottlieb Friedrich von Bohnenberger (15 June 1765 – 19 April 1831) was born at Simmozheim, Württemberg. He studied at the University of Tübingen. In 1798, he was appointed professor of mathematics and astronomy at the University.
He published: Anleitung zur geographischen Ortsbestimmung, (1795); Astronomie, (1811); and Anfangsgründe der höhern Analysis, (1812).  In 1817, he systematically explained the design and use of a gyroscope apparatus which he called simply a “Machine.” Several examples of the 'Machine' were constructed by Johann Wilhelm Gottlob Buzengeiger of Tübingen. Johann Friedrich Benzenberg had already mentioned Bohnenberger's invention (describing it at length) in several letters beginning in 1810. *Wik




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

1894 Nikolai Tschebotarjow (15 June[O.S. 3 June]1894 – 2 July 1947) or Chebotaryov proved his density theorem generalizing Dirichlet's theorem on primes in an arithmetical progression. *SAU (both spellings are used)
He was a student of Dmitry Grave, a Russian mathematician. Chebotaryov worked on the algebra of polynomials, in particular examining the distribution of the zeros. He also studied Galois theory and wrote a textbook on the subject titled Basic Galois Theory. His ideas were used by Emil Artin to prove the Artin reciprocity law. He worked with his student Anatoly Dorodnov on a generalization of the quadrature of the lune, and proved the conjecture now known as the Chebotaryov theorem on roots of unity.*Wik




1906 (William) Gordon Welchman (June 15, 1906, Bristol, England – October 8, 1985, Newburyport, Massachusetts, USA) was a British mathematician, university professor, World War II codebreaker at Bletchley Park, and author.
Just before World War II, Welchman was invited by Commander Alastair Denniston to join the Government Code & Cypher School at Bletchley Park, in case war broke out. He was one of four early recruits to Bletchley (the others being Alan Turing, Hugh Alexander, and Stuart Milner-Barry), who all made significant contributions at Bletchley, and who became known as 'The Wicked Uncles'. They were also the four signatories to an influential letter, delivered personally to Winston Churchill in October 1941, asking for more resources for the code-breaking work at Bletchley Park. Churchill responded with one of his 'Action This Day' written comments.
Welchman moved to the United States in 1948, and taught the first computer course at MIT in the United States. He followed this by employment with Remington Rand and Ferranti. He became a naturalised American citizen in 1962. In that year, he joined the MITRE Corporation, working on secure communications systems for the US military. He retired in 1971, but was still retained as a consultant. In 1982 his book The Hut Six Story was published by McGraw-Hill in the USA, and by Allen Lane in Britain. The National Security Agency disapproved. The book was not banned, but Welchman lost his security clearance (and therefore his consultancy with MITRE), and was forbidden to discuss with the media either the book or his wartime work. Welchman died in 1985. His final conclusions and corrections to the story of wartime codebreaking were published posthumously in 1986 in the paper 'From Polish Bomba to British Bombe: the birth of Ultra' in Intelligence & National Security, Vol 1, No l. The entire paper was included in the revised edition of The Hut Six Story published in 1997 by M & M Baldwin. *Wik


1916  Herbert Alexander Simon (June 15, 1916 – February 9, 2001) was an American social scientist who was a pioneer of the development of computer artificial intelligence. In 1956, with his long-time colleague Allen Newell, Simon produced the computer program, The Logic Theorist, a computer program that could discover proofs of geometric theorems. It was the first computer program capable of thinking, and marked the beginning of what would become known as artificial intelligence. It proved many of the theorems of symbolic logic in Whitehead and Russell's Principia Mathematica. He is further known for his contributions in fields including psychology, mathematics, statistics, and operations research, all of which he synthesized in a key theory for which he won the 1978 Nobel Prize for economics. *TIS




1933 Moshe Carmeli (June 15, 1933 - Sept 27, 2007) was the Albert Einstein Professor of Theoretical Physics, Ben Gurion University (BGU), Beer Sheva, Israel and President of the Israel Physical Society. He received his D.Sc. from the Technion-Israel Institute of Technology in 1964. He became the first full professor at BGU's new Department of Physics. He did significant theoretical work in the fields of cosmology, astrophysics, general and special relativity, gauge theory, and mathematical physics, authoring 4 books, co-authoring 4 others, and publishing 128 refereed research papers in various journals and forums, plus assorted other publications (146 in all). He is most notable for his work on gauge theory and his development of the theory of cosmological general relativity, which extends Albert Einstein's theory of general relativity from a four-dimensional spacetime to a five-dimensional space-velocity framework.







DEATHS


1734 Giovanni Ceva
 (December 7, 1647 – June 15, 1734) was an Italian mathematician widely known for proving Ceva's theorem in elementary geometry. His brother, Tommaso Ceva was also a well known poet and mathematician. *Wik
Ceva's theorem is a theorem in elementary geometry. Given a triangle ABC, and points DE, and F that lie on lines BCCA, and AB respectively, the theorem states that lines ADBE and CF are concurrent, if and only if,
\frac{AF}{FB}  \cdot \frac{BD}{DC} \cdot \frac{CE}{EA} = 1,
where AF indicates the directed distance between A and F (i.e. distance in one direction along a line is counted as positive, and in the other direction is counted as negative).
There is also an equivalent trigonometric form of Ceva's Theorem, that is, AD,BE,CF concur if and only if
\frac{\sin\angle BAD}{\sin\angle CAD}\times\frac{\sin\angle ACF}{\sin\angle BCF}\times\frac{\sin\angle CBE}{\sin\angle ABE}=1.
The theorem was proved by Giovanni Ceva in his 1678 work De lineis rectis, but it was also proven much earlier by Yusuf Al-Mu'taman ibn Hűd, an eleventh-century king of Zaragoza.
Associated with the figures are several terms derived from Ceva's name: cevian (the lines AD, BE, CF are the cevians of O), cevian triangle (the triangle DEF is the cevian triangle of O); cevian nest, anticevian triangle, Ceva conjugate. (Ceva is pronounced Chay'va; cevian is pronounced chev'ian.)*Wik



1785 Jean-François Pilatre de Rozier (30 March 1754 – 15 June 1785)French physicist and aeronaut who, with Marquis Francois Laurant d'Arlandes, became the first men to fly. Their hot-air balloon, built by the Montgolfier brothers, lifted off from La Muettte, a royal palace in the Bois de Boulogne, Paris. They flew nearly 6 miles in 25 mins, reaching an altitude of around 300-ft. King Louis XVI, who offered to send two prisoners for the test flight, but Rozier wanted to deny criminals the glory of being the first men to go into the atmosphere. Rozier died in attempt to cross English Channel in an apparatus composed of two balloons, one filled with hydrogen and the other with warm air. Thus, he was also the first man to die in an air crash. *TIS

1917 Kristian Olaf Bernhard Birkeland (born 13 December 1867 in Christiania (today's Oslo) – 15 June 1917 in Tokyo, Japan) was a Norwegian scientist, professor of physics at the Royal Fredriks University in Oslo. He is best remembered for his theories of atmospheric electric currents that elucidated the nature of the aurora borealis. In order to fund his research on the aurorae, he invented the electromagnetic cannon and the Birkeland–Eyde process of fixing nitrogen from the air. Birkeland was nominated for the Nobel Prize seven times.

Birkeland organized several expeditions to Norway's high-latitude regions where he established a network of observatories under the auroral regions to collect magnetic field data. The results of the Norwegian Polar Expedition conducted from 1899 to 1900 contained the first determination of the global pattern of electric currents in the polar region from ground magnetic field measurements.

Birkeland proposed in 1908 in his book The Norwegian Aurora Polaris Expedition 1902–1903 that polar electric currents, today referred to as auroral electrojets, were connected to a system of currents that flowed along geomagnetic field lines into and away from the polar region. Such field-aligned currents are known today as Birkeland currents in his honour. He provided a diagram of field-aligned currents in the book. The book on the 1902–1903 expedition contains chapters on magnetic storms on the Earth and their relationship to the Sun, the origin of the Sun itself, Halley's comet, and the rings of Saturn.

Birkeland's vision of what are now known as Birkeland currents became the source of a controversy that continued for over half a century, because their existence could not be confirmed from ground-based measurements alone. His theory was disputed and ridiculed at the time as a fringe theory by mainstream scientists, most notoriously by the eminent British geophysicist and mathematician Sydney Chapman who argued the mainstream view that currents could not cross the vacuum of space and therefore the currents had to be generated by the Earth. Birkeland's theory of the aurora continued to be dismissed by mainstream astrophysicists after his death in 1917.


Proof of Birkeland's theory of the aurora only came in 1967 after a probe was sent into space. The crucial results were obtained from U.S. Navy satellite 1963-38C, launched in 1963 and carrying a magnetometer above the ionosphere. Magnetic disturbances were observed on nearly every pass over the high-latitude regions of the Earth. These were originally interpreted as hydromagnetic waves, but on later analysis it was realized that they were due to field-aligned or Birkeland currents.

Norwegian 200-kroner banknote,


*APS Org


1922 Frederick William Sanderson (13 May 1857 – 15 June 1922) was headmaster of Oundle School from 1892 until his death. He was an education reformer, and both at Oundle, and previously at Dulwich College where he had started as assistant master, he introduced innovative programs of education in engineering. Under his headmastership, Oundle saw a reversal of a decline from which it had been suffering in the middle of the 19th century, with school enrollment rising from 92 at the time of his appointment to 500 when he died.
Sanderson was the inspiration for the progressive headmaster character in H. G. Wells' novel Joan and Peter. Wells had sent his own sons to Oundle, and was friendly with Sanderson. After Sanderson's death, which occurred shortly after delivering an address to Wells and others, Wells initially worked on his official biography, entitled Sanderson of Oundle, but later abandoned it in favor of an unofficial biography, The Story of a Great Schoolmaster. *Wik

1938  Hans Fitting (13 November, 1906  – 15 June, 1938) was a mathematician who worked in group theory. Hans Fitting's father, Prof Dr Friedrich Fitting (1862-1945), was a graduate secondary school teacher and a research mathematician who published over twenty papers.  Friedrich Fitting is best known today for giving a proof, in 1931, that there are exactly 880 magic squares of order 4. These 880 magic squares had been given by Frenicle de Bessy in 1693 but no proof was found until Friedrich Fitting's 1931 paper appeared. He taught his son Hans in school and was thus able to quickly recognize his son's extraordinary mathematical talent. With his father's challenge to his understanding of the subject, Hans soon progressed far beyond what was customary for his age.
From 1925 to 1932 Fitting studied mathematics, physics and philosophy at the Universities of Tübingen and Göttingen, where he was awarded his Ph.D. in 1932 for his work on group theory. His thesis advisor at Göttingen was Emmy Noether. 
Among the many mathematical achievements of Fitting we note that he gave a proof of the Remak-Krull-Schmidt theorem on the uniqueness of the direct product decomposition of groups into indecomposable subgroups, even for groups of operators. He devoted himself to an investigation of the ideal theory of noncommutative rings and also studied the theory of determinant ideals of finitely generated modules  over a commutative ring R
Today,he is known as well as for Fitting's Lemma, he is remembered for the 'Fitting subgroup' which is used in the structure theory of finite groups.




1971 Wendell Meredith Stanley (16 August 1904 – 15 June 1971) was an American biochemist, virologist and Nobel laureate. Stanley was born in Ridgeville, Indiana, and earned a BS in Chemistry at Earlham College in Richmond, Indiana. He then studied at the University of Illinois, gaining an MS in science in 1927 followed by a Ph.D. in chemistry two years later. His later accomplishments include writing the book "Chemistry: A Beautiful Thing" and achieving his high stature as a Pulitzer Prize nominee.
Stanley was awarded the Nobel Prize in Chemistry for 1946. His other notable awards included the Rosenburger Medal, Alder Prize, Scott Award, and the AMA Scientific Achievement Award. He was also awarded honorary degrees by many universities both American and foreign, including Harvard, Yale, Princeton and the University of Paris. Most of the conclusions Stanley had presented in his Nobel-winning research were soon shown to be incorrect (in particular, that the crystals of mosaic virus he had isolated were pure protein, and assembled by autocatalysis)
Stanley married Marian Staples (1905-1984) in 1929 and had three daughters (Marjorie, Dorothy and Janet), and a son, (Wendell M. Junior). Stanley Hall at UC Berkeley (now Stanley Biosciences and Bioengineering Facility) and Stanley Hall at Earlham College are named in his honor. *Win



1995 John Vincent Atanasoff, OCM, (October 4, 1903 – June 15, 1995) was an American physicist and inventor credited with inventing the first electronic digital computer. Built in 1937-42 at Iowa State University by Atanasoff and a graduate student, Clifford Berry, it introduced the ideas of binary arithmetic, regenerative memory, and logic circuits. These ideas were communicated from Atanasoff to John Mauchly, who used them in the design of the better-known ENIAC built and patented several years later. On 19 Oct 1973, a US Federal Judge signed his decision following a lengthy court trial which declared the ENIAC patent invalid and named Atanasoff the original inventor of the electronic digital computer, the Atanasoff- Berry Computer or the ABC.*TiS







2013 Kenneth Geddes "Ken" Wilson (June 8, 1936 – June 15, 2013) was an American physicist who was awarded the 1982 Nobel Prize for Physics for his development of a general procedure for constructing improved theories concerning the transformations of matter called continuous, or second-order, phase transitions. These take place at characteristic temperatures (or pressures), but unlike first-order transitions they occur throughout the entire volume of a material as soon as that temperature (called the critical point) is reached. One example of such a transition is the complete loss of ferromagnetic properties of certain metals when they are heated to their Curie points (about ºC for iron). Wilson's work provided a mathematical strategy for constructing theories that could apply to physical systems near the critical point. *TiS







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