Monday 20 May 2024

On This Day in Math - May 20


Mathematicians are like Frenchmen:
whatever you say to them
they translate into their own language
and forthwith it is something entirely different.

-- Johann Wolfgang von Goethe (Maxims and Reflexions, 1829)

The 140th day of the year; 140 is the sum of the squares of the first seven positive integers. 12 + 22 + 32 + 42 + 52 + 62 + 72 = 140. *Prime Curios

140 is a repdigit in bases 13 (aa), 19(7,7), 27(5,5), 34(4,4), 69(2,2), and 139(1,1). (students should become aware that every number n is a repunit in the base n-1.

There are 140 x 1021 (140 followed by 21 zeroes) different configurations of the Rubik's Cube. *Cliff Pickover@pickover (Would anyone notice if he was one off???)

140 is the character limit on Twitter (or was)

A. J. Meyl proved in 1878 that only three tetrahedral numbers are also perfect squares, The largest of these is T(48) =1402 = 19600:

T1 = 1² = 1
T2 = 2² = 4
T48 = 140² = 19600.

140 is the magic constant of this 5x5 square by *Srinivasa Raghave K  Can you see how to easily make one for day 135, or 145? Jeff Miller's Web site on the Earliest Use of Math Words says that Frenicle de Bessy used the term magic in the title to his book, Des quarrez ou tables magiques, published posthumously in 1693, twenty years after his death. The first use in English was the same year in "A New Historical Relation of the Kingdom of Siam."  Appropriate to have de Bessey mentioned here, as he first noted the cubic relation of the Taxi-cab number, 1729 and Srinivasa is a big fan, I believe, of Ramanujan.


1570 Cartographer Abraham Ortelius issues Theatrum Orbis Terrarum, the first modern atlas. *RMAT

The publication of his atlas in 1570 is often considered as the official beginning of the Golden Age of Netherlandish cartography. He was the first person proposing that the continents were joined before drifting to their present positions.

* National Maritime Museum

1608 In a letter to Christopher Clavius, Croation mathematician Marino Ghetaldi says that with his latest parabolic mirror:-
... the sun melts not only lead, but silver.
Ghetaldi had traveled extensively throughout Europe visiting and studying with many of the great science minds, including Viete and Galileo. From Galileo he learned optics and produced a 66cm diameter parabolic mirror which is at the National Maritime Museum in London.

1663 Robert Hooke was one of 98 persons who were declared members at a meeting of the Royal Society. He was admitted to society on 3 Jun 1663, and was peculiarly exempted of all payments. Before the Royal Society had been establish in 1660, Hooke was already distinguished for the invention of various astronomical instruments, and the air-pump he contrived for Charles Boyle (whom he had assisted for several years with chemical experiments at the Philosophical Society, Oxford). He invented a balance or pendulum spring (1656-58), one of the greatest improvements in the construction of timepieces. By 1662, he had been appointed curator of experiments to the Royal Society, and on 11 Jan 1664, awarded a salary of £30 per annum for life for that position.*TIS

1665 Newton's earliest use of dots, "pricked letters," to indicate velocities or fluxions is found on a leaf dated May 20, 1665; no facsimile reproduction of it has ever been made.' The earliest printed account of Newton's fluxional notation appeared from his pen in the Latin edition of Wallis' Algebra [Cajori, History of Mathematical Notations, vol. 2, p. 197] *VFR

1716 In a letter written to Leibniz, May 20, 1716, John Bernoulli discussed the equation : d2y/dx2 = 2y/x2
where the general solution when written in the form
y = x2/a + b2/3x
involves three cases: When b approaches zero the curves are parabolas; when a approaches infinity, they are hyperbolas; otherwise, they are of the third order.   *John E. Sasser, HISTORY OF ORDINARY DIFFERENTIAL EQUATIONS THE FIRST HUNDRED YEARS

Johann Bernoulli

1875 The International Bureau of Weights and Measures established by the International Metric Convention, Sevres, France. The bureau is the repository for the “International Prototype Meter” and the “International Prototype Kilogram.” *SAU= St. Andrews Univ

From 1960 to 1983 the definition used "1,650,763.73 wavelengths of light from a specified transition in krypton-86 ", using the lamp in the image below.

In 1983, the Length was defined as the length of the path traveled by light in a vacuum in 1299,792,458 of a second 


And for your (in case you thought that 3D movie technology was new, file)
In 1901, Claude Grivolas, one of Pathe's main shareholders in Paris, France, invented a projector that produced three-dimensional pictures.*TIS  (The glasses in the image are from somewhat later in time.)

1927 At 7:40 a.m., Charles Lindbergh took off from Roosevelt Field in Long Island, N.Y., aboard the "Spirit of St. Louis" monoplane on his historic first solo flight across the Atlantic Ocean. He arrived in France thirty-three and one-half hours later. *TIS

1930 The Institute for Advanced Study incorporated. Two and a half years later Albert Einstein and Oswald Veblen were appointed the first professors. [Goldstein, The Computer from Pascal to von Neumann, p. 77]*VFR

In 1956, the first hydrogen fusion bomb (H-bomb) to be dropped from an airplane exploded over Namu Atoll at the northwest edge of the Bikini Atoll. The fireball was four miles in diameter. It was designated as "Cherokee," as part of "Operation Redwing."*TIS

1961 France issued a stamp honoring Charles Coulomb (1736–1806) [Scott #B 352].

1964   American radio astronomers Robert Wilson and Arno Penzias discovered the cosmic microwave background radiation (CMB), the ancient light that began saturating the universe 380,000 years after its creation. And they did so pretty much by accident. It is ironic, too, that many researchers -- both theoretical and experimental -- had stumbled on this phenomenon before, but either discounted it or never put it all together. This was partly because, as Steven Weinberg wrote, "in the 1950s, the study of the early universe was widely regarded as not the sort of thing to which a respectable scientist would devote his time." 

Bell Labs' Holmdale Horn Antenna in New Jersey picked up an odd buzzing sound that came from all parts of the sky at all times. The noise puzzled Wilson and Penzias, who did their best to eliminate all possible sources of interference, even removing some pigeons that were nesting in the antenna.


1968 A team of six high school students from Upstate New York went to London to participate in the Fourth British Mathematical Olympiad. This was the first time a team from the U.S. participated in an international mathematical competition. [The College Mathematics Journal, 16 (1985), p. 331] *VFR

Would love a picture of the contestants. surely some proud family took a shot.  

1975 Norway issued a stamp for the centenary of the International Meter Convention in Paris. It pictures Ole Jacob Broch (1818– 1889), the first director of the International Bureau of Weights and Measures. [Scott #655] *VFR At least ten other countries issued stamps to commemorate the same event, including Bulgaria, Romania, France, the Soviet Union..... but not the USA. (see 1975 below for another)

1975 Sweden issued a stamp picturing a metric tape measure to honor the centenary of the International Meter Convention in Paris. [Scott #1121] *VFR

1990 the Hubble Space Telescope sent its first photograph from space, an image of a double star 1,260 light years away. *TIS  

Hubble First Light, *NASA

2012 Solar Eclipse, A total of 154 U.S. national parks will provide views of the eclipse, from partial to full annularity. Many western parks will offer solar observing as a ranger-led program or host a solar party with the help of local amateur astronomy clubs.

Poster advertising viewing the eclipse from Glen Canyon National Recreation Area. Poster © Tyler Nordgren.

2063 99 year old Johnny Depp rolls down red-carpet in wheel-chair for opening of Pirates of the Caribbean sequel #42, “Sun City Pirates”.


1825 George Phillips Bond ((May 20, 1825 {sometimes given 1826} – February 17, 1865) Astronomer who made the first photograph of a double star, discovered a number of comets, and with his father discovered Hyperion, the eight moon of Saturn.*TIS

His early interest was in nature and birds, but after his elder brother William Cranch Bond Jr. died, he felt obliged to follow his father into the field of astronomy. He succeeded his father as director of Harvard College Observatory from 1859 until his death. His cousin was Edward Singleton Holden, first director of Lick Observatory. 

Bond took the first photograph of a star in 1850 (Vega) and of a double star in 1857 (Mizar); suggested photography could be used to measure a star's magnitude; and discovered numerous comets and calculated their orbits.*Wik

In searching for the first imag of Vega, I came across this which disputes credit to George Bond, " The first telescope of the Harvard College Observatory (HCO), "The Great Refractor" was installed in 1847. That telescope was the largest in the United States from its installation until 1867. With it, the first daguerreotype ever made of a star, the bright Vega, was taken by John A. Whipple working under W.C. Bond, following several years of experiments using smaller telescopes."

1861 Henry Seely White (May 20, 1861 - May 20, 1943) worked on invariant theory, the geometry of curves and surfaces, algebraic curves and twisted curves. *SAU He matriculated at Wesleyan University in Connecticut and graduated with honors in 1882 at the age of twenty-one. White excelled at Wesleyan in astronomy, ethics, Latin, logic, mathematics, and philosophy. At the university, John Monroe Van Vleck taught White mathematics and astronomy. Later, Van Vleck persuaded White to continue to study mathematics at the graduate level.[1] Subsequently, White studied at the University of Göttingen under Klein, and received his doctorate in 1891.
White was Mathematics Department Chair at Northwestern University. He left Northwestern to be near his ill mother and became Chairman of the Mathematics Department at Vassar College. He "attributed his interest in geometry both to his work at Wesleyan and Goettingen and to summers spent working on his grandfather’s farm."[2] His particular interests were in the fields of the geometry of curves and surfaces (Curves, Differential geometry of surfaces), algebraic planes and twisted curves (Algebraic Geometry, Algebraic curves, Twisted curves), homeomorphic sets of lines in a plane (line coordinates), the theory of invariants, relativity in mechanics, and correspondences.
In 1915 Seely was elected a Fellow of the United States National Academy of Sciences. Northwestern conferred upon him an LL.D. in the same year. At the time of its 100th anniversary in 1932, Wesleyan conferred upon him an D.Sc. *Wik
Died on his birthday in 1943

1870  Robert Fernand Bernard, Viscount de Montessus de Ballore (20 May 1870, in Villeurbanne – 26 January 1937, in Arcachon) was a French mathematician, known for his work on continued fractions and Padé approximants.

In 1886, Robert obtained his bachelor of science degree. From 1887 to 1889, he attended preparatory classes at l'École des mines de Saint-Étienne. On 8 May 1905, at the Sorbonne, he successfully defended his thesis on continued fractions, written under the supervision of Paul Appell.

Montessus was an editor of the Journal de mathématiques pures et appliquées and the author of numerous mathematical publications. He was a member of the Société mathématique de France and a member of the Société des arts, sciences, belles-lettres et d'agriculture de l'Académie de Mâcon.

1874 Friedrich Moritz Hartogs (20 May 1874, Brussels–18 August 1943, Munich) was a German-Jewish mathematician, known for work on set theory and foundational results on several complex variables. 

Hartogs' main work was in several complex variables where he is known for Hartogs's theorem, Hartogs's lemma (also known as Hartogs's principle or Hartogs's extension theorem) and the concepts of holomorphic hull and domain of holomorphy.

In set theory, he contributed to the theory of well-orders and proved what is also known as Hartogs's theorem: for every set x there is a well-ordered set that cannot be injectively embedded in x. The smallest such set is known as the Hartogs number or Hartogs Aleph of x.*Wik

1901 Machgielis (Max) Euwe (last name is pronounced [ˈøːwə]) (May 20, 1901 – November 26, 1981) was a Dutch chess Grandmaster, mathematician, and author. He was the fifth player to become World Chess Champion (1935–37). Euwe also served as President of FIDE, the World Chess Federation, from 1970 to 1978. 

He studied mathematics at the University of Amsterdam under the founder of intuitionistic logic, L.E.J. Brouwer (who later became his friend and for whom he held a funeral oration), and earned his doctorate in 1926 under Roland Weitzenböck. He taught mathematics, first in Rotterdam, and later at a girls' Lyceum in Amsterdam. After World War II, Euwe became interested in computer programming and was appointed professor in this subject at the universities of Rotterdam and Tilburg, retiring from Tilburg University in 1971. He published a mathematical analysis of the game of chess from an intuitionistic point of view, in which he showed, using the Thue–Morse sequence, that the then-official rules (in 1929) did not exclude the possibility of infinite games.*Wik

1901 Hannes Olof Gösta Alfvén (born 30 May 1908 in Norrköping, Sweden; died 2 April 1995 in Djursholm, Sweden) was a Swedish electrical engineer, plasma physicist and winner of the 1970 Nobel Prize in Physics for his work on magnetohydrodynamics (MHD). He described the class of MHD waves now known as Alfvén waves. He was originally trained as an electrical power engineer and later moved to research and teaching in the fields of plasma physics and electrical engineering. Alfvén made many contributions to plasma physics, including theories describing the behavior of aurorae, the Van Allen radiation belts, the effect of magnetic storms on the Earth's magnetic field, the terrestrial magnetosphere, and the dynamics of plasmas in the Milky Way galaxy.*Wik

1913 William Redington Hewlett (20 May 1913; Ann Arbor, Michigan - 12 Jan 2001 at age 87) was an American electrical engineer who co-founded the Hewlett-Packard Company, a leading manufacturer computers, computer printers, and analytic and measuring equipment. In 1939, he formed a partnership known as Hewlett-Packard Company with David Packard, a friend and Stanford classmate. (The order of their names was determined by a coin toss.) HP's first product was an audio oscillator based on a design developed by Hewlett when he was in graduate school. Eight were sold to Walt Disney for Fantasia. Lesser-known early products were: bowling alley foul-line indicator, automatic urinal flusher, weight-loss shock machine. The company began with $538 intial capital, and its first production facility was a small garage in Palo Alto. *TIS

"In the beginning..."

1946 George Lusztig (born Gheorghe Lusztig; May 20, 1946) is a Romanian-born American mathematician and Abdun Nur Professor at the Massachusetts Institute of Technology (MIT). He was a Norbert Wiener Professor in the Department of Mathematics from 1999 to 2009.
He is known for his work on representation theory, in particular for the objects closely related to algebraic groups, such as finite reductive groups, Hecke algebras, p-adic groups, quantum groups, and Weyl groups. He essentially paved the way for modern representation theory. This has included fundamental new concepts, including the character sheaves, the Deligne–Lusztig varieties, and the Kazhdan–Lusztig polynomials.
In 1983, Lusztig was elected as a fellow of the Royal Society. In 1985 Lusztig won the Cole Prize (Algebra). He was elected to the National Academy of Sciences in 1992. He received the Brouwer Medal in 1999, the National Order of Faithful Service in 2003 and the Leroy P. Steele Prize for Lifetime Achievement in Mathematics in 2008. In 2012, he became a fellow of the American Mathematical Society and in 2014 he received the Shaw Prize in Mathematics. In 2022, he received the Wolf Prize in Mathematics. *Wik


1677 John Kersey the elder (Bap. 23 November, 1616–20 May,1677) was an English mathematician, as well as a textbook writer.

Kersey obtained a wide reputation as a teacher of mathematics. At one time he was tutor to the sons of Sir Alexander Denton of Hillesden House, Buckinghamshire. They were both future public figures (Sir Edmund Denton, 1st Baronet as a Member of Parliament for Buckingham, as his father had been, and Alexander Denton as a judge, as well as MP for Buckingham after Edmund).

He was acquainted with John Collins, who persuaded him to write his work on algebra. He was a friend of Edmund Wingate, and edited the second edition of his Arithmetic in 1650, and subsequent issues till 1683.

To his pupils Edmund and Alexander Denton he dedicated his first and principal original work, The Elements of that Mathematical Art, commonly called Algebra, in two folio volumes, dated respectively 1673 and 1674. Both John Wallis and Collins expected much of this work and on its publication it became a standard authority. It was mentioned in the Philosophical Transactions, and was commended by Charles Hutton. Kersey's method of algebra was employed in Cocker's Arithmetick, edition of 1703. The eighth edition of Wingate was edited by Kersey in 1683; in the tenth, published in 1699, he is spoken of as 'late teacher of the Mathematicks'.

Kersey (1673, p.200) is the earliest known reference to the "aliquot formula" which gives the number of divisors of a positive integer as the product of the powers (plus one) of the primes in the prime decomposition of that number. *Wik

1782 William Emerson (14 May 1701 – 20 May 1782), English mathematician, was born at Hurworth, near Darlington, where his father, Dudley Emerson, also a mathematician, taught a school. William himself had a small estate in Weardale called Castle Gate situated not far from Eastgate where he would repair to work throughout the Summer on projects as disparate as stonemasonry and watchmaking. Unsuccessful as a teacher, he devoted himself entirely to studious retirement. Possessed of remarkable energy and forthrightness of speech, Emerson published many works which are singularly free from errata.
He was early influence in the life of Jeremiah Fenwicke Dixon, of Mason-Dixon fame.

In The Principles of Mechanics (1754) he shows a wind-powered vehicle in which the vertically mounted propeller gives direct power to the front wheels via a system of cogs. In mechanics he never advanced a proposition which he had not previously tested in practice, nor published an invention without first proving its effects by a model. He was skilled in the science of music, the theory of sounds, and the ancient and modern scales; but he never attained any excellence as a performer. He died on 20 May 1782 at his native village, where his gravestone bears epitaphs in Latin and Hebrew.

Emerson dressed in old clothes and his manners were uncouth. He wore his shirt back to front and his legs wrapped in sacking so as not to scorch them as he sat over the fire. He declined an offer to become FRS because it would cost too much after all the expense of farthing candles he had been put to in the course of his life of study. Emerson rode regularly into Darlington on a horse like Don Quixote's, led by a hired small boy. In old age, plagued by the stone, he would alternately pray and curse, wishing his soul 'could shake off the rags of mortality without such a clitter-me-clatter.' *Wik

1798 Erland Bring (19 August 1736 – 20 May 1798) was a Swedish mathemaician who made contributions to the algebraic solution of equations.*SAU

At Lund he wrote eight volumes of mathematical work in the fields of algebra, geometry, analysis and astronomy, including Meletemata quaedam mathematematica circa transformationem aequationum algebraicarum (1786). This work describes Bring's contribution to the algebraic solution of equations. *Wik

1943 Henry Seely White, died on his birthday. (see 1861 above)

1947 Philipp Eduard Anton von Lenard (7 June 1862 – 20 May 1947), was a German physicist and the winner of the Nobel Prize for Physics in 1905 for his research on cathode rays and the discovery of many of their properties. He was a nationalist and anti-Semite; as an active proponent of the Nazi ideology, he had supported Adolf Hitler in the 1920s and was an important role model for the "Deutsche Physik" movement during the Nazi period.
Lenard is remembered today as a strong German nationalist who despised "English physics", which he considered to have stolen its ideas from Germany. He joined the National Socialist Party before it became politically necessary or popular to do so. During the Nazi regime, he was the outspoken proponent of the idea that Germany should rely on "Deutsche Physik" and ignore what he considered the fallacious and deliberately misleading ideas of "Jewish physics", by which he meant chiefly the theories of Albert Einstein, including "the Jewish fraud" of relativity. An advisor to Adolf Hitler, Lenard became Chief of Aryan physics under the Nazis. *Wik

1975 Luiz Henrique Jacy Monteiro (6 November, 1918 - 20 May, 1975) was a Brazilian mathematician who played a major role in the development of Brazilian mathematics in the middle of the 20th century. He did much to introduce modern mathematics to Brazilian school teachers as well as to university students. *SAU

1982  Merle Anthony Tuve (June 27, 1901 – May 20, 1982) was an American geophysicist who was the Chairman of the Office of Scientific Research and Development's Section T, which was created in August 1940. He was founding director of the Johns Hopkins University Applied Physics Laboratory, the main laboratory of Section T during the war from 1942 onward. He was a pioneer in the use of pulsed radio waves whose discoveries opened the way to the development of radar and nuclear energy.

Tuve was born in Canton, South Dakota. He and physicist Ernest Lawrence were childhood friends. 

In 1925, with physicist Gregory Breit, Tuve used radio waves to measure the height of the ionosphere and probe its interior layers. The observations he made provided the theoretical foundation for the development of radar. He was among the first physicists to use high-voltage accelerators to define the structure of the atom. In 1933 he confirmed the existence of the neutron and was also able to measure the binding forces in atomic nuclei.

Tuve proposed that an electronically activated proximity fuze would make anti-aircraft fire far more effective, and led the team of scientists that developed the device, which proved crucial in the allies' victory in World War II. He led in the development of the proximity fuze first at the Department of Terrestrial Magnetism and then later at the Johns Hopkins University Applied Physics Laboratory and also made contributions to experimental seismology, radio astronomy, and optical astronomy

Tuve was elected to the American Philosophical Society in 1943.[ For his service to the nation during World War II, Tuve received the Presidential Medal for Merit from President Harry S. Truman and was named an Honorary Commander of the Order of the British Empire in 1948. He was elected to the American Academy of Arts and Sciences in 1950. Mount Tuve in Ellsworth Land in Antarctica was named in honor of Merle Anthony Tuve. The Library of Congress holds his papers in more than 400 archival boxes. *Wik

2010 Walter Rudin (May 2, 1921 – May 20, 2010) was an Austrian-American mathematician and professor of Mathematics at the University of Wisconsin–Madison. 

In addition to his contributions to complex and harmonic analysis, Rudin was known for his mathematical analysis textbooks: Principles of Mathematical Analysis, Real and Complex Analysis, and Functional Analysis. Rudin wrote Principles of Mathematical Analysis only two years after obtaining his Ph.D. from Duke University, while he was a C. L. E. Moore Instructor at MIT. Principles, acclaimed for its elegance and clarity, has since become a standard textbook for introductory real analysis courses in the United States.

Rudin's analysis textbooks have also been influential in mathematical education worldwide, having been translated into 13 languages, including Russian, Chinese, and Spanish

They are so common and long lived on Campuses that they have their own nicknames; "Baby Rudin" is used for his  Principles of Mathematical Analysis, an undergraduate text.   "Big Rudin" is  for his Real and Complex Analysis, a graduate level text.

In 1970 Rudin was an Invited Speaker at the International Congress of Mathematicians in Nice. He was awarded the Leroy P. Steele Prize for Mathematical Exposition in 1993 for authorship of the now classic analysis texts, Principles of Mathematical Analysis and Real and Complex Analysis. He received an honorary degree from the University of Vienna in 2006.

In 1953, he married fellow mathematician Mary Ellen Estill, known for her work in set-theoretic topology.  She was appointed as Professor of Mathematics at the University of Wisconsin in 1971.  The two resided in Madison, Wisconsin, in the eponymous Walter Rudin House, a home designed by architect Frank Lloyd Wright. They had four children. *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

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