Saturday 1 June 2024

On This Day in Math - June 1


There are certainly people who regard √2
as something perfectly obvious but jib at √-1.
This is because they think they can visualise 
the former as something in physical space 
but not the latter. 
Actually √-1 is a much simpler concept
~Edward Titchmarsh

The 152nd day of the year; the eighth prime number is 19, and 8 x 19 = 152.... 152 is also the largest known even number that can be expressed as the sum of two primes in exactly four ways. (Students should find all four ways. And how many ways can 152 be expressed as the sum of two odd numbers only one of which is prime?)

152 is a refactorable number since it is divisible by the total number of divisors (8) it has, and in base 10 it is divisible by the sum of its digits(8), making it a Niven number.

There are 152  mm tick marks on a six-inch ruler.

152 is the smallest number you can make as the sum of two distinct odd primes cubed.

152 is the sum of four consecutive primes, starting with 31.

the digits 152 occur beginning at the digit of e, that is the 152nd prime number (881).


1495 – A monk, John Cor, records the first known batch of Scotch whisky. *@eventsonthisday 
("Can I get an Amen?")

1631 Pierre de Fermat married Louise de Long (his mother’s cousin), who gave him three sons. *VFR One of them (Samuel) edited and published his father’s mathematical letters and papers in 1679. It was in these publications that Samuel revealed the marginal note in his father's copy of Diophantus's Arithmetica which became known to the world as Fermat’s Last Theorem.

1639 At the request of his dying mentor, the acclaimed mathematician, astronomer, and polymath Peter Krüger, Johannes Hevelius meticulously observed the solar eclipse, then decided to dedicate the rest of his life to understanding the cosmos. *Maria Popova at
Crüger's Azimuthal Quadrant, completed by Johannes Hevelius 1644 (the observer is Hevelius) *Wik

1658 Pascal posed six questions related to the cycloid as challenge problems. They dealt with area, volume of solids of revolution, and center of gravity. See Scripta Mathematica, 26(1963), 297– 298 for a list of the problems.*VFR
Pascal used the pseudonym Amos Dettonville, which is an anagram of the name Louis de Montalt, under which he wrote his “letters provinciales”. Wren, Huygens, and de Sleuse gave partial solutions.
The famous toothache had occurred earlier that year and caused him to return to mathematics and to study the cycloid. 
In 1654, late in the evening Pascal experienced a religious ecstasy that called him to give up his intermittent interest in mathematics and to devote his time to religious contemplation. For years he devoted no time to mathematics. Then one night, unable to sleep because of an abscessed tooth, Pascal began to think about some problems about the cycloid. His pain disappeared and he interpreted this as a sign that God was pleased by his mathematical studies. In a brief time he completed the investigation of the cycloid. Then he established a contest about the cycloid with himself and Roberval as the judges
 Pascal answered all six questions in publications the next year under the same pseudonym. (The Early Mathematical Manuscripts of Leibniz By Gottfried Wilhelm Leibniz, J. M. Child)
There is a famous statue by Pajou in the Louvre of Pascal in which he is contemplating the Roulette (cycloid). (And in this photo, I am contemplating Pascal contemplating the roulette)

1709 The Rev. John Colson becomes the first headmaster of Sir Joseph Williamson's Free Mathematical School. He held the position until he was elected Lucasian Professor on March 1, of 1739(1740 NS). *Correspondence of Sir Isaac Newton and Professor Cotes, pg 2

1761 The existence of an atmosphere on Venus was concluded by Rusian Polymath Mikhail Lomonosov on the basis of his observation of the transit of Venus of 1761 from the Imperial Academy of Sciences of St. Petersburg. He used a two-lens achromat refractor and a weak solar filter (smoked glass) and reported seeing a bump or bulge of light ("Lomonosov's arc") off the solar disc as Venus began to exit the Sun. Lomonosov attributed that effect to refraction of solar rays through an atmosphere; he also reported the appearance of a sliver around the part of Venus that had just entered the Sun's disk during the initial phase of transit. *Wik

1809 The word Tangram emerged in American vocabulary about this time. According to various dictionaries, the word may be derived from a Chinese word tang, or it may be derived from the obsolete English word trangam, meaning a trinket or a gimcrack. Merriam-Webster says the word is of unknown origin.

Trangam is found in a 1658 dictionary.

On June 1, 1809, the American Citizen reported, “Vast numbers of those ‘tangrams and gimcracks’ are piled up in the office, of every shape and size, making it a great toy shop. [Joel S. Berson]

A classified advertisement in the Franklin Gazette of Feb. 24, 1818, offers “Chinese Tangrams,” which were probably puzzles [Bill Mullins].

According to Wikipedia and this web page, the word tangram was coined by Dr. Thomas Hill in 1848 for his book Geometrical Puzzles for the Young. [Perhaps this is the first use of the word with its modern meaning.] According to the same web page, the device was invented between 1796 and 1802 in China by Yang-cho-chu-shih, who published the book Ch'i ch'iao t'u (Pictures using seven clever pieces). * Jeff Miller

In 1869, Thomas Edison of Boston, Mass., received his first patent. It was for an "electrographic vote recorder." The device was the first of its kind, and would enable a legislator to register a vote either for or against an issue by turning a switch to the right or left. His application was executed on 13 Nov 1868 and submitted to the U.S. Patent Office on 28 Nov 1868 (No. 90646).   Edison's invention stirred little interest and was never manufactured.

1889 Charles P. Steinmetz arrived in New York City, having fled Breslau because of his socialist views. He went to work for the Eickenmeyer Dynamo Machine Company, later General Electric, as an electrical engineer. In spite of a natural inclination to mathematics, circumstances forced him to become the most distinguished and highest paid electrical engineer in the world. [A Century of Mathematics in America, Part I, p. 14]. *VFR

Steinmetz is the very short man in the center.
Einstein to his right.

1890 The first census compiled by machine was started. The previous census took nearly a decade to compute. The 1890 census recorded the U.S. population at 62,979,766. See 8 January 1889. [Kane, p. 169] *VFR ... The 2010 census reported the population of the USA as 308,745,538.  (*****NOTE... 
 gives this date as the first use of "Hollerith's tabulating machine to count census returns." Wikipedia says the census for 1990 BEGAN on June 2, 1990, and took six years to complete.This last fact is confirmed by "Report of the Commissioner of Labor in Charge of The Eleventh Census to the Secretary of the Interior for the Fiscal Year Ending June 30, 1895"  saying the census would end "during the present calendar year. ... " )

After using census data in many years of teaching AP stats, I had a chance to actually work on the 20202 census as an enumerator. All I can say is quote from Billy Currington's country song, " Beer is Good, God is Great, and people are crazy!"

1890 Hollerith census card with fields coded

1912 The famous problem of the division of coconuts with leftovers going to a monkey seems to have first been printed in English around this date, in School Science and Mathematics by N. Anning. The problem is known to have existed back to the 8th century when Mahavira wrote the recreational math book: Ganita-sara-sangraha. *Singmaster
 In 1926 Saturday Evening Post prints "Coconuts" story by Ben Ames Williams with problem of five men and a monkey and a pile of coconuts. In the following week 2000 letters to the Post demand to know the answer. Editor-in-chief Horace Latimore sent Williams an emphatic telegram, "FOR THE LOVE OF MIKE, HOW MANY COCONUTS? HELL POPPING AROUND HERE."
For those who seek the problem:  see this date 

1936 Einstein first, and perhaps only, paper ever subjected to peer review. It would be rejected, with good reason, and he would not take it well. The Physical Review received Einstein’s submission on 1 June 1936, according to the journal’s logbook. Tate returned the manuscript to Einstein on 23 July with a critical review and the mild request that he “would be glad to have [Einstein’s] reaction to the various comments and criticisms the referee has made.” Einstein wrote back on 27 July in high dudgeon, withdrawing the paper and dismissing out of hand the referee’s comments. In the paper it seems Einstein thought he had a proof that gravity waves, something of his own creation, could not exist. *Physics Today

1944 First COLOSSUS Mark II works.
The Colossus machines were electronic computing devices used by British codebreakers to help read encrypted German messages during World War II. They used vacuum tubes (thermionic valves) to perform the calculations.
Colossus was designed by engineer Tommy Flowers with input from Harry Fensom, Allen Coombs, Sid Broadhurst and Bill Chandler at the Post Office Research Station, Dollis Hill to solve a problem posed by mathematician Max Newman at Bletchley Park. The prototype, Colossus Mark 1, was shown to be working in December 1943 and was operational at Bletchley Park by February 1944. An improved Colossus Mark 2 first worked on 1 June 1944, just in time for the Normandy Landings. Ten Colossi were in use by the end of the war.   The Colossus was used to find possible key combinations for the Lorenz machines – rather than decrypting an intercepted message in its entirety.
In spite of the destruction of the Colossus hardware and blueprints as part of the effort to maintain a project secrecy that was kept up into the 1970s—a secrecy that deprived some of the Colossus creators of credit for their pioneering advancements in electronic digital computing during their lifetimes—a functional replica of a Colossus computer was completed in 2007. *Wik

In 1947, the Doomsday Clock appeared for the first time, as the fourth quadrant of a clock face with its hands at 7 min.  to midnight. It was the background image on the cover of the June issue of the Bulletin of the Atomic Scientists. From then to the present, the Doomsday Clock image has been on the cover of the Bulletin, though the hands over the years have been shown moving forward or back to conveyy how close humanity is to catastrophic destruction. Midnight represents Doomsday. The closest approach, two minutes to midnight began on the Sep 1953 cover. Russia's first hydrogen bomb test the previous month (12 Aug 1953) within nine months of an American H-bomb test (1 Nov 1952). In  Dec 1991, the clock was set at 17 min. to midnight marking the Strategic Arms Reduction Treaty.
The Bulletin has reset the minute hand on the Doomsday Clock 25 times since its debut in 1947, most recently in 2023 when we moved it from 100 seconds to midnight to 90 seconds to midnight. 

1957 The June issue of Mad Magazine carried, among several other unusual features, the first published work of 19 year old Case Western Reserve Freshman, Donald Knuth. His article developed the "Potrzebie System of Weights and Measures". The base of this new revolutionary system is the potrzebie, which equals the thickness of Mad issue 26, or 2.263348517438173216473 mm.  Google's calculator and Wolfram Alpha can perform conversions between potrzebies and other units.*Wik

In 1965, A. Penzias and R. Wilson detected a 3 degree kelvin primordial background radiation using a horn reflector antenna built for radio astronomy. The Big Bang description of the origin of the universe took place 15 to 20 billion years ago in an explosion from a hot dense state. The high energy radiation produced when the universe was very young and very hot would have been absorbed and degraded as the universe expanded and cooled. The microwave background radiation first observed by Penzias and Wilson is thought to be a relic of this very early state, when the universe was only about a million years old. The uniformity of microwave background indicates that the universe was homogeneous until it was a few million years old.*TIS

1966 Surveyor I was launched. It was the first American spacecraft to make a soft landing on the Moon. Curiously, the word “spaceship” was defined by the 1958 edition of Webster’s New Collegiate Dictionary as “An imaginary aircraft of the future for interplanetary travel outside the earth’s atmosphere.” *VFR

2003  Jean-Pierre Serre became the first recipient of the Abel Prize. The ceremony was held at the Abel Monument in Slottsparken, Oslo.


1796 Nicolas-Leonard Sadi Carnot(1 June 1796 — 24 August 1832) was a French physicist. He became a captain of engineers in the army, and spent much of his life investigating the design of steam engines. His book Reflections on the Motive Power of Heat (1824) contained a theorem which says that a maximum efficiency of heat engine can be obtained by a reversible engine, and that efficiency depends only on the temperatures of the hot and the cool sources of the engine. This theorem played an essential role for the subsequent development of thermodynamics. It was written to promote the construction of steam engines and other heat engines in France, whose industrial development was lagging behind England's. *TIS The name Carnot is listed among the seventy-two names of French scientists, engineers and other notable people On the Eiffel Tower, however it honors the father of Sadi Carnot, Lazare Nicholas Marguerite Carnot.

1843 Henry Faulds (1 Jun 1843, 19 Mar 1930 at age 86) Scottish physician who, from 1873, became a missionary in Japan, where he worked as a surgeon superintendent at a Tokyo hospital, taught at the local univeristy, and founded the Tokyo Institute for the Blind. In the late 1870s, his attention was drawn to fingerprints of ancient potters remaining on their work that he helped unearth at an archaeological dig site in Japan. He commenced a study of fingerprints, and became convinced that each individual had a unique pattern. He corresponded on the subject with Charles Darwin, and published a paper about his ideas in Nature (28 Oct 1880). When he returned to Britain in 1886, he unsuccessfully offered his fingerprinting identification scheme for forensic uses to Scotland Yard. Undeserved confusion on priority for the discovery with Francis Galton and Sir William J. Herschel lasted until 1917. *TIS

1866 Charles Benedict Davenport (1 Jun 1866, 18 Feb 1944 at age 77) American zoologist who contributed substantially to the study of eugenics (the improvement of populations through breeding) and heredity and who pioneered the use of statistical techniques in biological research. Partly as a result of breeding experiments with chickens and canaries, he was one of the first, soon after 1902, to recognize the validity of the newly discovered Mendelian theory of heredity. In Heredity in Relation to Eugenics (1911), he compiled evidence concerning the inheritance of human traits, on the basis of which he argued that the application of genetic principles would improve the human race. These data were at the heart of his lifelong promotion of eugenics, though he muddled science with social philosophy. *TIS

1868  Annie Louise MacKinnon Fitch (June 1, 1868 – September 12, 1940) was a Canadian-born American mathematician who worked with Felix Klein and became a professor of mathematics at Wells College. She was the third woman to earn a mathematics doctorate at an American university.
She graduated in 1889, and remained at the University of Kansas for graduate study in mathematics, becoming the third mathematics graduate student at the university and the first woman. She earned a master's degree in 1891, remaining one more year at the university to work there with Henry Byron Newson.

In 1892, MacKinnon transferred to Cornell University. She finished her doctorate there in 1894, supported as an Erastus Brooks fellow. Her dissertation, Concomitant Binary Forms in Terms of the Roots, was supervised by James Edward Oliver, and also thanked James McMahon as a faculty mentor. This made her the third woman to earn a mathematics doctorate at an American university, following Winifred Edgerton Merrill in 1886 at Columbia University in 1886 and Ida Martha Metcalf at Cornell in 1893.

MacKinnon taught high school mathematics in Lawrence, Kansas from 1890 to 1892. After her return from Europe in 1896, she became professor of mathematics at Wells College, a women's college in Aurora, New York; she was the only mathematician on the faculty. She also served as registrar for the college for 1900–1901.

In 1901, MacKinnon married Edward Fitch, an American classics scholar who had been at Göttingen at roughly the same time as MacKinnon, and later taught at Hamilton College. After marrying, she gave up her mathematical career.[2]

She died on September 12, 1940, in Clinton, New York. A scholarship in mathematics at Hamilton College was established in her name by her husband.

1899 Edward Charles Titchmarsh (1 June 1899 in Newbury, -  died 18 January 1963 at Oxford) English mathematician whose contributions to analysis placed him in the forefront of his profession. His contributions helped resolve the differences between the general theory of quantum mechanics and the methods used to solve particular problems in quantum theory. All Titchmarsh's work is in analysis. His early studies were on Fourier series, Fourier integrals, functions of a complex variable, integral equations and the Riemann zeta function. From 1939, Titchmarsh concentrated on the theory of series expansions of eigenfunctions of differential equations, work which helped to resolve problems in quantum mechanics. His work on this topic occupied him for the last 25 years of his life. *TIS


1815  James Gillray, a British caricaturist and etcher, died June 1, 1815, at age 58.  In the opinion of many modern political cartoonists, Gillray was the father of their craft,  outdistancing other worthy candidates such as William Hogarth and George Cruickshank by his composition, his satirical wit, and his skill at portraiture.  His primary targets were the Royal family (that of King George III), political figures, the excesses of the British peerage, and Napoleon, who crowned himself Emperor when Gillray was at the height of his powers. *Linda Hall Org
Image:  Detail of the laughing gas demonstration depicted in the fifth image, caricaturing (right to left) Benjamin Thompson, Count Rumford; Humphry Davy; Thomas Garnett or James Watt; and James Coxe Hippisley (

1861 Kurt Hensel  (29 December 1861 – 1 June 1941) He is best known for his work on p-adic numbers. *VFR  First described by Kurt Hensel in 1897, the p-adic numbers were motivated primarily by an attempt to bring the ideas and techniques of power series methods into number theory. Their influence now extends far beyond this. For example, the field of p-adic analysis essentially provides an alternative form of calculus.

1867 Karl George Christian von Staudt (January 24, 1798 – June 1, 1867) German mathematician who developed the first complete theory of imaginary points, lines, and planes in projective geometry. His early work was on determining the orbit of a comet and, based on this work, he received his doctorate. He showed how to construct a regular inscribed polygon of 17 sides using only compasses. He turned to projective geometry and Bernoulli numbers. An important work on projective geometry, Geometrie der Lage was published in 1847. It was the first work to completely free projective geometry from any metrical basis. He also gave a geometric solution to quadratic equations.*TIS

1918 Eduardo Torroja Caballe (February 1, 1847 – June 1, 1918) was a Spaniard mathematician born in the city of Tarragona, Spain. His father was Juan Torroja, a Professor of Geography and History. He continued his studies at Complutense University, where he obtained the degrees of Bachelor of Science (1864), Masters of Science (1866), Architect (1869) and Doctor of Science (1873) in Mathematics.
Very early in his studies he became a disciple of Karl Georg Christian von Staudt (who also died on this same date), whose ideas of Geometry he embraced and promoted among his fellow mathematicians for the rest of his life. The strong presence of Geometry in Spain's mathematical curriculum, even to this day, can be traced back to Torroja's influence. *Wik

1997  Robert Serber (March 14, 1909 – June 1, 1997) was an American physicist who participated in the Manhattan Project. He gave lectures (5-14 Apr 1943) at Los Alamos, on the design and construction of atomic bombs as background for the Manhattan Project. Notes were typed and mimeographed as The Los Alamos Primer, technical report LA-1, given to scientists newly arriving at the top-secret laboratory. Serber coined the code-names of the three bomb designs: “Little Boy” (uranium gun), “Thin Man” (plutonium gun), and “Fat Man” (plutonium implosion). He helped assemble atomic bombs on Tinian Island that were dropped on Japan. He was part of the first American team visiting to assess their damage at Hiroshima and Nagasaki. After WW II, he returned to academia, and by 1951 was a professor of physics at Columbia University. *TIS

2006 Shokichi Iyanaga (April 2, 1906 – June 1, 2006) was a Japanese mathematician. Iyanaga published many papers which arose through several courses such as algebraic topology, functional analysis, and geometry, which he taught. He became Professor at the University of Tokyo in 1942. It was during World War II. Towards the end of the war, many Japanese cities were bombarded and he had to find refuge in the countryside. He was busy in editing textbooks from primary and secondary schools and he continued to give courses and organise seminars.*Wik

*CHM=Computer History Museum
*FFF=Kane, Famous First Facts
*NSEC= NASA Solar Eclipse Calendar
*RMAT= The Renaissance Mathematicus, Thony Christie
*SAU=St Andrews Univ. Math History
*TIA = Today in Astronomy
*TIS= Today in Science History
*VFR = V Frederick Rickey, USMA
*Wik = Wikipedia
*WM = Women of Mathematics, Grinstein & Campbell

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