Tuesday, 5 July 2022

On This Day in Math - July 5

There is no smallest among the small and no largest among the large,
But always something still smaller and something still larger.

Quoted in E Maor, To Infinity and Beyond: a Cultural History of the Infinite

The 186th day of the year;  186 is the product of the first four primes less; the product of the first four positive integers (7 x 5 x 3 x 2 - 4 x 3 x 2 x 1 = 186) . *Prime Curios

186 is the sum of consecutive primes, 186 = = 89 + 97,

186 is a sphenic (wedge) number, product of 3 distinct primes: 186 = 2*3*31

More Math Facts for every year date here


In 1643, an exceptionally strong wind occurred in Essex County, Mass. The description by Governor John Winthrop is the first record suggestive of a tornado in the U.S.: "There arose a sudden gust so violent for one-half hour as it blew down multitudes of trees. It lifted up their meeting house at Newbury, the people being in it. It darkened the air with dust, yet through God’s great mercy it did no hurt, but only killed one Indian with the fall of a tree." However, no tornado-like funnel shape - so likely to be noted, if seen - was not included in his log. So, it was likely not a tornado, in fact, but a severe straight-line squall with strong downburst winds. Reverend Increase Mather cited a likely tornado in Jul 1680 storm at Cambridge, Mass*TIS

1687 Halley wrote to Newton that his Principia was finally published. [Westfall, p. 468] *VFR 1687 – ushering in a tidal wave of changes in thought that would significantly accelerate the already ongoing scientific revolution by giving it tools that produced technologically valuable results, which had theretofore been otherwise unobtainable. (Thony Christie has pointed out that the use of "published" may give a false impression to the modern reader, even though this is the date printed on the title page of the document. The actual words, used by Halley were, "I have at length brought your Book to an end, and hope it will please you. the last errata came just in time to be inserted. I will present from you the books you desire to...." )

1698 Johann Bernoulli, in a letter to Leibniz, defined the notion of a function. The term “function” is due to Leibniz. [Cajori, Historical Introduction to the Mathematical Literature, p. 96]*VFR

1766 Ben Franklin writes from England to Rev Ezra Stiles, "I have lately propos’d our ingenious and learned Contriman Mr: Winthorp, as a Member of the Royal Society." On Feb 20, 1766. John Winthrop Esqr. Hollisian Professor of Mathematics and Natural Philosophy was unanimously elected Fellow of the Royal Society in London. *Franklin Papers, Natl Archives

1951 – William Shockley invents the junction transistor. *Wik

2012  Gresham College  announces the appointment of Raymond Flood, Fellow of Kellogg College, Oxford, as Professor of Geometry and Other Mathematical Sciences. The Geometry chair at Gresham College is the oldest in England, dating back to the College’s founding in 1597. Gresham College was the first higher education institution in England besides the Universities of Oxford and Cambridge, and it was created with the guiding principle of providing free education to the traders and people of London so that England could maintain a position at the forefront of a global economy. Gresham College’s central position in science and mathematics has seen the Royal Society formed within the College, and past luminaries including Henry Briggs, Sir Christopher Wren, Robert Hooke, Sir Christopher Zeeman and Sir Roger Penrose. *Gresham Press Release

2022  Maryna Viazovska became the second woman to be awarded the Fields Medal.  The Ukrainian mathematician accepted her Fields Medal at the International Congress of Mathematicians in Helsinki, Finland.   The IMU cited Viazovska’s many mathematical accomplishments, in particular her proof that an arrangement called the E8 lattice is the densest packing of spheres in eight dimensions.


1820 William John Macquorn Rankine, (5 July 1820 – 24 December 1872) Scottish engineer and physicist and one of the founders of the science of thermodynamics, particularly in reference to steam-engine theory. As the chair (1855) of civil engineering and mechanics at Glasgow, he developed methods to solve the force distribution in frame structures. Rankine also wrote on fatigue in the metal of railway axles, on Earth pressures in soil mechanics and the stability of walls. He was elected a Fellow of the Royal Society in 1853. Among his most important works are Manual of Applied Mechanics (1858), Manual of the Steam Engine and Other Prime Movers (1859) and On the Thermodynamic Theory of Waves of Finite Longitudinal Disturbance. *TIS While many students never encounter it, there is a temperature scale named after Rankine. It is the Fahrenheit scale equivalent of the Kelvin scale for Celsius.

1867 Andrew Ellicott Douglass (July 5, 1867, Windsor, Vermont – March 20, 1962, Tucson, Arizona) American astronomer and archaeologist who coined the name dendrochronology for tree-ring dating, a field he originated while working at the Lowell Observatory, Flagstaff, Ariz. (1894-1901). He showed how tree rings could be used to date and interpret past events. Douglass also sought a connection between sunspot activity and the terrestrial climate and vegetation. The width of tree rings is a record of the rainfall, with implications on the local food supply in dry years. Archaeologist Clark Wissler collaborated in this work by furnishing sections of wooden beams from Aztec Ruin and Pueblo Bonito so Douglass could cross-date the famous sites. Thus the study of tree rings enables archaeologists to date prehistoric remains. *TIS

1888 Louise Freeland Jenkins (July 5, 1888 – May 9, 1970) was an American astronomer.
She was born in Fitchburg, Massachusetts. In 1911 she graduated from Mount Holyoke College, then she received a Master's degree in astronomy in 1917 from the same institution. From 1913 to 1915 she worked at the Allegheny Observatory in Pittsburgh.
About 1921 she moved to Japan, becoming a teacher at the Women's Christian College, a missionary school. She returned to the United States in 1925 after her father died. A year later she returned to teach at a school in Himeji. (Hinomoto Gakuen girl's high school.)
In 1932 she returned to the US and became a staff member at Yale University Observatory. She was co-editor of the Astronomical Journal starting in 1942, and continued in this post until 1958. She would return to visit Japan later in her life.
She was noted for her research into the trigonometric parallax of nearby stars. She also studied variable stars.
The crater Jenkins on the Moon is named in her honor. *Today in Astronomy

1946 Gerardus (Gerard) 't Hooft (July 5, 1946 - ) is a Dutch theoretical physicist and professor at Utrecht University, the Netherlands. He shared the 1999 Nobel Prize in Physics with his thesis advisor Martinus J. G. Veltman "for elucidating the quantum structure of electroweak interactions".
His work concentrates on gauge theory, black holes, quantum gravity and fundamental aspects of quantum mechanics. His contributions to physics include a proof that gauge theories are renormalizable, dimensional regularization, and the holographic principle. *Wik


1865 Oskar Bolza died (12 May 1857–5 July 1942). Bolza was a German mathematician, and student of Felix Klein. He was born in Bad Bergzabern, Bolza published The elliptic s-functions considered as a special case of the hyperelliptic s-functions in 1900 which related to work he had been studying for his doctorate under Klein. However, he worked on the calculus of variations from 1901. Papers which appeared in the Transactions of the American Mathematical Society over the next few years were: New proof of a theorem of Osgood's in the calculus of variations (1901); Proof of the sufficiency of Jacobi's condition for a permanent sign of the second variation in the so-called isoperimetric problems (1902); Weierstrass' theorem and Kneser's theorem on transversals for the most general case of an extremum of a simple definite integral (1906); and Existence proof for a field of extremals tangent to a given curve (1907). His text Lectures on the Calculus of Variations published by the University of Chicago Press in 1904,[3] became a classic in its field and was republished in 1961 and 2005.[4] After the death of his friend Maschke in 1908, Bolza became unhappy in the United States and, in 1910, he and his wife returned to Freiburg in Germany where he was appointed as an honorary professor. Chicago gave him the title of 'non-resident professor of mathematics' which he retained for the rest of his life.*Wik He returned to Germany in 1910, where he researched function theory, integral equations and the calculus of variations. In 1913, he published a paper presenting a new type of variational problem now called "the problem of Bolza." The next year, he wrote about variations for an integral problem involving inequalities, which later become important in control theory. Bolza ceased his mathematical research work at the outbreak of WW I in 1914.*TIS

1911 George Johnstone Stoney (15 February 1826 – 5 July 1911) Irish physicist who introduced the term electron for the fundamental unit of electricity. At the Belfast meeting of the British Association in Aug 1874, in a paper: On the Physical Units of Nature, Stoney called attention to a minimum quantity of electricity. He wrote, "I shall express 'Faraday's Law' in the following terms ... For each chemical bond which is ruptured within an electrolyte a certain quantity of electricity traverses the electrolyte which is the same in all cases." Stoney offered the name electron for this minimum electric charge. When J.J. Thomson identified cathode rays as streams of negative particles, each carrying probably Stoney's minimum quantity of charge, the name was applied to the particle rather than the quantity of charge.*TIS

1926 Peter Scott Lang graduated from Edinburgh University and after a period as assistant in Edinburgh he became Regius Professor of Mathematics at St Andrews. He held this position for 42 years. *SAU

1932 Rene Louis Baire died (21 January 1874 – 5 July 1932) a French mathematician most famous for his Baire category theorem, which helped to generalize and prove future theorems. His theory was published originally in his dissertation Sur les fonctions de variable réelles ("On the Functions of Real Variables") in 1899.*Wik French mathematician whose study of irrational numbers and whose concept to divide the notion of continuity into upper and lower semi-continuity greatly influenced the French School of Mathematics. His doctoral thesis led to the solution of the problem of the characteristic property of limited functions of continuous functions and helped establish the theory of functions of real variables.*TIS

1977 Henry Scheffé (New York City, USA, 11 April 1907 – Berkeley, California, USA, 5 July 1977) worked in several different areas of Statistics, including linear models, analysis of variance and nonparametrics.*SAU He is known for the Lehmann–Scheffé theorem and Scheffé's method.

*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

Monday, 4 July 2022

On This Day in Math - July 4

Things that people learn purely out of curiosity
can have a revolutionary effect on human affairs

~Frederick Seitz - born 100+ years ago today

The 185th day of the year; the decimal expansion of the first 185 digits of Euler's constant is prime. *Prime Curios

185 is the sum of two square numbers in two different ways: \( 13^2+ 4^2 \) and \(11^2 + 8^2 \)  I'm not sure it is commonly known that this implies that these pairs can be used as the opposite sides of a quadrilateral forcing the diagonals to be perpendicular(if the sides of a quadrilateral are 13, 11, 4, 8; then the quadrilateral has perpendicular diagonals.)

Like all odd numbers, 185 is the difference of the squares of consecutive integers, 93^2 - 92^2 = 185, because it ends in five, it is the difference of two squares of integers that are five apart; 21^2 - 16^2 = 185

and from Jim Wilder @wilderlab An equation for July 4th: 7⁴ = 2401 = (2 + 4 + 0 + 1)⁴   And a followup from World Observer@WKryst2011 points out that there are only two other such year dates. (student's should find both)

See more Math Facts for every year date here.


1054 The Crab Nebula supernova is recorded in China and Japan. *VFR The Crab Nebula (catalogue designations M1, NGC 1952, Taurus A) is a supernova remnant and pulsar wind nebula in the constellation of Taurus. Corresponding to a bright supernova recorded by Chinese astronomers in 1054, the nebula was observed later by John Bevis in 1731. *Wik

1826 Thomas Jefferson , principal author of the Declaration of Independence dies on U.S. Independence day. (See Date under Deaths)  He was buried at his home, Monticello. He wrote his own epitaph: “Here was buried Thomas Jefferson, author of the Declaration of Independence, of the statute of Virginia for religious freedom, and father of the University of Virginia.” *VFR I find it striking that when he lists his accomplishments, being President of the US did not make his top three.

1662 “By and by comes Mr. Cooper ... of whom I entend to learn Mathematiques; and so begin with him today ... . After an hour’s being with him at Arithmetique, my first attempt being to learn the Multiplication table, then we parted till tomorrow.” Samuel Pepys, in his diary....At the time he was something like a modern Secretary of the Navy. *VFR

1744 Euler wrote Christian Goldbach that he has finished his book Introductio in analysin infinitorum (Lausanne 1748). In this work the trigonometric and logarithmic functions were first treated in their modern form. *VFR

1802 The United States Military Academy at West Point established by act of congress earlier in the year opened on July 4. This school was the first engineering school in the U.S. Charles Davies, a noted textbook writer, taught there.*VFR Before 1812 it was conducted as an apprentice school for military engineers and, in effect, as the first U.S. school of engineering.

1819 William Herschel writes to his sister, Caroline, "Lina, there is a great comet. I want you to come and assist me. Come to dine and spend the day here.... we shall have time to prepare maps and telescopes. I saw it's situation last night, it has a long tail." He was eighty years old at the time, and he was still at work when he died, two years later. *Timothy Ferris, Coming of Age in the Milky Way

1843 Liouville began an address to the Academy of Sciences with the words: “I hope to interest the Academy in announcing [that in] the papers of Evariste Galois I have found a solution, as precise as it is profound, of this beautiful problem: whether or not it [the general equation of fifth degree] is solvable by radicals.” This work of Galois was published in 1846. *VFR

1862 Charles Lutwidge Dodgson, mathematics teacher at Oxford, went boating on the Isis, a tributary of the Thames, with the three daughters of Henry George Liddell, dean of Christ Church, Oxford. He was especially fond of Alice Liddell, then ten, and it was mainly for her that he began the story of another Alice’s tumble down a rabbit hole. The work was published exactly three years later as Alice’s Adventures under Ground under the pseudonym Lewis Carroll, with the famous illustrations by John Tenniel (see note). This work is a favorite of mathematicians, so if you haven’t read it recently, you should. See 26 November 1864. [Note: "When Charles Dodgson – more widely known as Lewis Carroll – made drawings in the early 1960s for his book Alice’s Adventures in Wonderland, he was disappointed with the results. He employed cartoonist John Tenniel to create the now-famous illustrations, while his original ideas were consigned to the archive of Christ Church College, Oxford, where he worked as a lecturer in mathematics until his death in 1898. TATE ETC. sent a cultural historian to view Dodgson’s rarely seen drawings which feature in Tate Liverpool’s ‘Alice in Wonderland’ exhibition. " *Tate ETC] From Nov 2011 to Jan 2012 the Tate Liverpool was showing these original works as part of the "Alice in Wonderland" exhibit. You can see some of them at the web page where I found the notes above.)

1934 Leo Szilard patented the chain-reaction design for the atomic bomb.

1943The 1943 Gibraltar Liberator AL523 crash was an aircraft crash that resulted in the death of General Władysław Sikorski, the commander-in-chief of the Polish Army and Prime Minister of the Polish government-in-exile. Sikorski's Liberator II crashed off Gibraltar almost immediately after takeoff on 4 July 1943. An estimated sixteen people died, including many other senior Polish military leaders. The plane's pilot was the only survivor. Included in the casulties was Zofia Lesniowka, the first commandant of the Polish Women's Auxiliary Service, the General's Daughter. 
The crash was ruled to have been an accident, but Sikorski's death remains an unsolved mystery. The crash marked a turning point for Polish influence on their Anglo-American allies in World War II.

*Wik, *Jenny Grant@SilenceinPolish 

1963 The San Francisco Chronicle carried a report entitled, “A Milestone in Math—Professor’s New Concept,” by David Perlman. This popular account of Paul J. Cohen’s proof of the independence of the axiom of choice was probably the first published. *VFR

1971 Michael S. Hart posts the first e-book, a copy of the United States Declaration of Independence, on the University of Illinois at Urbana–Champaign's mainframe computer, the origin of Project Gutenberg. *wik

1994 Replica of Hubble space telescope is dedicated in his hometown, on the west side of the Webster County Courthouse in Marshfield, Mo.

1997 Mars Pathfinder lands on the surface of Mars. Launched on December 4, 1996 by NASA aboard a Delta II booster a month after the Mars Global Surveyor was launched, it landed on July 4, 1997 on Mars's Ares Vallis, in a region called Chryse Planitia in the Oxia Palus quadrangle. The lander then opened, exposing the rover which conducted many experiments on the Martian surface. *Wik

2014 U S Independence day occurs on Friday. In what year will it next appear on a Friday? And the time after that?

1790 Sir George Everest, (4 July 1790 – 1 December 1866) British military engineer and geodesist, born in Gwernvale, Powys, Wales, UK. He worked on the trigonometrical survey of India (1818-43), providing the accurate mapping of the subcontinent. For more than twenty-five years and despite numerous hardships, he surveyed the longest arc of the meridian ever accomplished at the time. Everest was relentless in his pursuit of accuracy. He made countless adaptations to the surveying equipment, methods, and mathematics in order to minimize problems specific to the Great Survey: immense size and scope, the terrain, weather conditions, and the desired accuracy. Mount Everest, formerly called Peak XV, was renamed in his honour in 1865. *TIS Mathematically, he was the uncle of Mary Everest Boole, the wife of George Boole, and a mathematician in her own right who is remembered for
encouraging children to explore mathematics through playful activities such as 'curve stitching'. (string-art) *Wik The Preparation of the Child for Science

1868 Henrietta Swan Leavitt (July 4, 1868 – December 12, 1921) American astronomer known for her discovery of the relationship between period and luminosity in Cepheid variables, pulsating stars that vary regularly in brightness in periods ranging from a few days to several months. Leavitt's greatest discovery came from her study of 1777 variable stars in the Magellanic Clouds. She determined the periods of 25 Cepheid variables and in 1912 announced what has since become known as the famous Period-Luminosity relation: "since the variables are probably nearly the same distance from the earth, their periods are apparently associated with their actual emission of light, as determined by their mass, density, and surface brightness." Today the Period-Luminosity relation is used to calculate the distances of galaxies.*TIS

1906 Dan Rutherford (4 July 1906 in Stirling, Scotland - 9 Nov 1966 in St Andrews, Fife, Scotland)studied at St Andrews and Amsterdam. He spent most of his career in St Andrews becoming Gregory Professor of Applied Mathematics. In spite of this title most of his research was in pure mathematics and in particular in algebra. He became President of the EMS in 1940 and 1963. *SAU

1911 Frederick Seitz (July 4, 1911 – March 2, 2008) American physicist who made fundamental contributions to the theory of solids, nuclear physics, fluorescence, and crystals. As Eugene Wigner's first doctoral student, late in 1932, Seitz developed the cellular method of deriving solid-state wave functions. The widespread application of this Wigner-Seitz method to the understanding of metals is regarded as the catalyst for the formation of the field of solid-state physics in the U.S. His subsequent research focused on the theory and properties of crystals. He studied dislocations and imperfections in crystal structures, the effect of irradiation on crystals, and the process of diffusion (the movement of atoms or particles caused by random collision) in crystalline materials.*TIS

1936 Birthday of Guy Otttewel, writer of the eclipse book Understanding Eclipses and many other astronomical publications. *NSEC

1945 John Allen Paulos (July 4, 1945 - )born in Denver, Colorado. Currently a professor at Temple University, he is the author of the popular book Innumeracy. *VFR American mathematician and author of books encouraging people to make sense of the statistics and figures that inform their lives. He represents that mathematics as a subject that is easy to learn and understand. Paulos argues that ignorance of basic mathematical concepts discourages critical thinking and results in costly mistakes and misguided decisions by both political leaders and ordinary people in their everyday lives.*TIS

1742 Guido Grandi died. He corresponded with Leibniz on the sum of the series 1−1+1−1+1−•••. *VFR Luigi Guido Grandi (October 1, 1671 – July 4, 1742) was an Italian priest, philosopher, mathematician, and engineer born in Cremona. He was Jesuit-educated and became a member of the Camaldolese order. He became a professor of philosophy at the Camaldolese monastery in Florence in 1700 and a professor of mathematics in 1714.
In mathematics Grandi is best known for studying the rose curve, a curve which has the shape of a petalled flower, and for Grandi's series. He named the rose curve rhodonea. He also contributed to Note on the Treatise of Galileo Concerning Natural Motion in the first Florentine edition of Galileo Galilei's works and helped introduce Gottfried Leibniz's ideas on calculus to Italy. He also worked as an engineer, being superintendent of water at Tuscany, and in that capacity he was involved in the drainage of the Chiana Valley. In 1709 he visited England where he was elected a Fellow of the Royal Society.*Wik

1826 Thomas Jefferson (13 Apr 1743, 4 Jul 1826 at age 83) U.S. president who was throughout his lifetime an extraordinarily learned man, including interests in mathematics and natural sciences. He corresponded with such men as Joseph Priestley, and sometimes contributed time and money to progress in these fields. He collected and classified fossils. He was interested in the experiments being made in ballons and submarines. While visiting Europe, he sent home various mechanical and scientific gadgets produced including a polygraph and phosphorus matches. At his Monticello estate, he practiced scientific farming, and was always on the lookout for a significant new plant or seed. Jefferson died shortly before 1pm. His old friend, John Adams, died a few hours later.*TIS

1901 Peter Guthrie Tait (28 April 1831 – 4 July 1901) Scottish physicist and mathematician who helped develop quaternions, an advanced algebra that gave rise to vector analysis and was instrumental in the development of modern mathematical physics.*TIS Tait was a fellow-pupil of Maxwell at Edinburgh Academy and both of them went on to study at Edinburgh University and Cambridge. Tait became Professor of Mathematics at Queen's College Belfast and then moved to the Chair of Natural Philosophy at Edinburgh which he occupied for more than 40 years. With his collaborations with Maxwell, Thomson (Lord Kelvin) and Hamilton he made important contributions in both mathematics and physics. He became one of the first honorary members of the EMS in 1883. *SAU

1910 Giovanni Virginio Schiaparelli, (14 March 1835 - 4 July 1910) Italian astronomer who is remembered for his observations of Mars over seven oppositions and named the "seas" and "continents". In 1877, he saw on the surface of the planet Mars the markings that he called canali (channels), later misinterpreted as "canals." He made extensive studies, both observational and theoretical, of comets, determining from the shapes of their tails that there was a repulsive force from the sun. He showed that meteor swarms travel through space in cometary orbits. He explained the regular meteor showers as the result of the dissolution of comets and proved it for the Perseids. He suggested that Mercury and Venus rotate on their axes, discovered the asteroid Hesperia (1861) and was a major observer of double stars.*TIS

1934 Marie Marja Sklodowska Curie (7 November 1867 – 4 July 1934) was a Polish-born French chemist and physicist. In 1898, her celebrated experiments on uranium minerals led to discovery of two new elements. First she separated polonium, and then radium a few months later. The quantity of radon in radioactive equilibrium with a gram of radium was named a curie (subsequently redefined as the emission of 3.7 x 1010 alpha particles per sec.) With Henri Becquerel and her husband, Pierre Curie, she was awarded the 1903 Nobel Prize for Physics. She was then sole winner of a second Nobel Prize in 1911, this time in Chemistry. Her family won five Nobel awards in two generations. She died of radiation poisoning from her pioneering work before the need for protection was known.*TIS

1962 Thomas Jefferson Jackson See (19 Feb 1866 in Montgomery City, Missouri - 4 July 1962 in Oakland, California, USA) was an U S astronomer who studied in the University of Missouri and in Berlin. He fell out with his astronomical colleagues and was eventually banned from publishing. He spend the last part of his life arguing against Einstein's Theory of Relativity. *SAU

1986 Oscar Zariski's work was on foundations of algebraic geometry using algebraic methods. He worked on the theory of normal varieties, local uniformisation and the reduction of singularities of algebraic varieties.*SAU

1987 Bengt Strömgren (21 Jan 1908; 4 Jul 1987) Bengt (Georg Daniel) Strömgren was a Danish astrophysicist who pioneered the present-day knowledge of the gas clouds in space. Researching for his theory of the ionized gas clouds around hot stars, he found relations between the gas density, the luminosity of the star, and the size of the "Strömgren sphere" of ionized hydrogen around it. He surveyed such H II regions in the Galaxy, and he also did important work on stellar atmospheres and ionization in stars. *TIS

2002 Laurent-Moïse Schwartz (5 March 1915 in Paris – 4 July 2002 in Paris) was a French mathematician. He pioneered the theory of distributions, which gives a well-defined meaning to objects such as the Dirac delta function. He was awarded the Fields medal in 1950 for his work (developing the theory of distributions, a new notion of generalized functions motivated by the Dirac delta-function of theoretical physics). He was the first French mathematician to receive the Fields medal. For a long time he taught at the École polytechnique. *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

Sunday, 3 July 2022

On This Day in Math - July 3


Music is the pleasure the human mind experiences from counting
without being aware that it is counting. 
 ~Gottfried Leibniz

The 184th day of the year; 184 = 23 * 23 (concatenation of the first two primes).

The smallest number that can be written as q * pq + r * p r, where p, q and r are distinct primes (184 = 3 * 23 + 5 * 25). *Prime Curios

25^2-21^2 = 184, and the sum of three squares 12^2 + 6^2 + 2^2 and of four squares, 10^2 + 8^2+4^2 + 2^2
The concatenation of 183 and 184, 183184 is a perfect square. There are no smaller numbers for which the concatenation of two consecutive numbers is square. (Students might seek the next such pair of numbers. They are small enough to be year dates)

1822 Charles Babbage described his ideas for a “difference engine” to the Royal Society. *VFR

1841, John Couch Adams decided to determine the position of an unknown planet by the irregularities it causes in the motion of Uranus. He entered in his journal; "Formed a design in the beginning of this week in investigating, as soon as possible after taking my degree, the irregularities in the motion of Uranus... in orderto find out whether they may be attributed to the action of an undiscovered planet beyond it..." In Sep 1845 he gave James Challis, director of the Cambridge Observatory, accurate information on where the new planet, as yet unobserved, could be found; but unfortunately the planet was not recognized at Cambridge until much later, after its discovery at the Berlin Observatory on 23 Sep 1846. *TIS
1886 Karl Benz officially unveils the Benz Patent-Motorwagen, the first purpose-built automobile. *
the painter flynn

2011  Astronomers using the Hubble Space Telescope discovered a fourth moon orbiting the icy dwarf planet Pluto. The tiny, new satellite – temporarily designated P4 -- was uncovered in a Hubble survey searching for rings around the dwarf planet.

Two labeled Hubble WFC3/UVIS images of the Pluto system with new moon P4 circled. Left side image taken on June 28, 2011. Right side image taken on July 3, 2011.
Two labeled images of the Pluto system taken by the Hubble Space Telescope's Wide Field Camera 3 ultraviolet visible instrument with newly discovered fourth moon P4 circled. The image on the left was taken on June 28, 2011. The image of the right was taken on July 3, 2011. Credit: NASA, ESA, and M. Showalter (SETI institute)

1820 Ernest de Jonquières (3 July 1820 Carpentras, France – 12 Aug 1901 Mousans-Sartoux, France) was a French naval officer who discovered many results in geometry. After his introduction to advanced mathematics by Chasles it is not surprising that his main interests were geometry throughout his life. He made many contributions many of them extending the work of Poncelet and Chasles. An early work, the treatise Mélanges de géométrie pure (1856) contains: an amplifications of Chasles' ideas on the geometric properties of an infinitely small movement of a free body in space; a commentary on Chasles' work on conic sections; the principle of homographic correspondence; and constructions relating to curves of the third order. In a final section de Jonquières presented a French translation of Maclaurin's work on curves. *SAU

1849 Prosper-René Blondlot (3 July 1849 – 24 November 1930) was a French physicist, best remembered for his mistaken "discovery" of N rays, a phenomenon that subsequently proved to be illusory.
In order to demonstrate that a Kerr cell responds to an applied electric field in a few tens of microseconds, Blondlot, in collaboration with Ernest Bichat, adapted the rotating-mirror method that Léon Foucault had applied to measure the speed of light. He further developed the rotating mirror to measure the speed of electricity in a conductor, photographing the sparks emitted from two conductors, one 1.8 km longer than the other and measuring the relative displacement of their images. He thus established that the speed of electricity in a conductor is very close to that of light.
In 1891, he made the first measurement of the speed of radio waves, by measuring the wavelength using Lecher lines. He used 13 different frequencies between 10 and 30 MHz and obtained an average value of 297,600 km/s, which is within 1% of the current value for the speed of light. This was an important confirmation of James Clerk Maxwell's theory that light was an electromagnetic wave like radio waves.
In 1903, Blondlot announced that he had discovered N rays, a new species of radiation. The "discovery" attracted much attention over the following year until Robert W. Wood showed that the phenomena were purely subjective with no physical origin. The French Academy of Sciences awarded the Prix Leconte (₣50,000) for 1904 to Blondot, although they hedged on the reason, citing the totality of his work rather than the discovery of N-rays.
Little is known about Blondlot's later years. William Seabrook stated in his Wood biography Doctor Wood, that Blondlot went insane and died, supposedly as a result of the exposure of the N ray debacle: "This tragic exposure eventually led to Blondlot's madness and death." Using an almost identical wording this statement was repeated later by Martin Gardner, possibly without having investigated into the subject: "Wood's exposure led to Blondlot's madness and death." However, Blondlot continued to work as a university professor in Nancy until his early retirement in 1910. He died at the age of 81; at the time of the N-ray affair he was nearly 60 years old. *Wik

1866 Henry Frederick Baker FRS (3 July 1866 – 17 March 1956) was a British mathematician, working mainly in algebraic geometry, but also remembered for contributions to partial differential equations (related to what would become known as solitons), and Lie groups.
Baker was born in Cambridge, England and educated at The Perse School before winning a scholarship to St John's College, Cambridge in October 1884. Baker graduated as Senior Wrangler in 1887, bracketed with 3 others.
Baker was elected Fellow of St John's in 1888 where he remained for 68 years.
In June, 1898 he was elected a Fellow of the Royal Society. In 1911, he gave the presidential address to the London Mathematical Society.
In January 1914 he was appointed Lowndean Professor of Astronomy. *Wik
In the 1930s before the war Baker's graduate students would meet at what they called Professor Baker’s "Tea Party", who met once a week to discuss the areas of research in which we were all interested. It was to one of these meetings that a young Donald Coxeter brought his "Aunt Alice", the 69 year old Alicia Boole to co-present on the subject of Polytopes in higher dimensions.

1897 Jesse Douglas (3 July 1897 – 7 September 1965) born in New York City. He did important work on Plateau’s problem, which asks for the minimal surface connecting a given boundary. For this work he received a Fields medal in 1936, the first time that they were given. *VFR ..the Plateau problem... had first been posed by the Italian-French mathematician Joseph-Louis Lagrange in 1760. The Plateau problem is one of finding the surface with minimal area determined by a fixed boundary. Experiments (1849) by the Belgian physicist Joseph Plateau demonstrated that the minimal surface can be obtained by immersing a wire frame, representing the boundaries, into soapy water. Douglas developed what is now called the Douglas functional, so that by minimizing this functional he could prove the existence of the solution to the Plateau problem. Douglas later developed an interest in group theory.*TIS

1933 Frederick Justin Almgren,(July 3, 1933, Birmingham, Alabama–February 5, 1997, Princeton, New Jersey) Almost certainly Almgren's most impressive and important result was only published in 2000, three years after his death. Why was this? The paper was just too long to be accepted by any journal. Brian Cabell White explains the background in a review of the book published in 2000 containing the result:-
By the early 1970s, geometric analysts had made spectacular discoveries about the regularity of mass-minimizing hypersurfaces. (Mass is area counting multiplicity, so that if k sheets of a surface overlap, the overlap region is counted k times.) In particular, the singular set of an m-dimensional mass-minimizing hypersurface was known to have dimension at most m - 7. By contrast, for an m-dimensional mass-minimizing surface of codimension greater than one, the singular set was not even known to have m-measure 0. Around 1974, Almgren started on what would become his most massive project, culminating ten years later in a three-volume, 1700-page preprint containing a proof that the singular set not only has m-dimensional measure 0, but in fact has dimension at most (m - 2). This dimension is optimal, since by an earlier result of H Federer there are examples for which the dimension of the singular set is exactly (m - 2). ... Now, thanks to the efforts of editors Jean Taylor and Vladimir Scheffer, Almgren's three-volume, 1700-page typed preprint has been published as a single, attractively typeset volume of less than 1000 pages.*SAU

1933 William (Bill) Parry FRS (3 July 1934–20 August 2006) was an English mathematician. During his research career, he was highly active in the study of dynamical systems, and, in particular, ergodic theory, and made significant contributions to these fields. He is considered to have been at the forefront of the introduction of ergodic theory to the United Kingdom. He played a founding role in the study of subshifts of finite type, and his work on nilflows was highly regarded.*Wik

1945 Saharon Shelah (July 3, 1945 - ) is an Israeli mathematician. He is a professor of mathematics at the Hebrew University of Jerusalem and Rutgers University in New Jersey. Shelah is one of the most prolific contemporary mathematicians. As of 2009, he has published nearly 900 mathematical papers (together with over 200 co-authors). His main interests lie in mathematical logic, model theory in particular, and in axiomatic set theory.*Wik

1749 William Jones, FRS (1675 – 3 July 1749) was a Welsh mathematician, most noted for his proposal for the use of the symbol π (the Greek letter pi) to represent the ratio of the circumference of a circle to its diameter. He was a close friend of Sir Isaac Newton and Sir Edmund Halley. In November, 1711 he became a Fellow of the Royal Society, and was later its Vice-President.*Wik

1789 Jakob Bernoulli II died. *VFR    Born in Basel in 1759 (17 October), the son of Johann (II).  assistant to Daniel in experimental physics
He graduated in Jurisprudence in 1778 but also studied Maths and Physics. In 1782, he applied for Daniel's former chair but was unsuccessful.
He became secretary to an imperial representative in Venice
In 1786 he went to Petersburg, to the Academy of Science (Fuss recommended him to Dashkoff) and in 1788 became ordentlich academy member for mathematics.
He married one of Euler's granddaughters, Charlotte.
At thirty years of age, he drowned in the Neva.  *Brian Daugherty

1991 Ernst Witt (June 26, 1911-July 3, 1991) was a German mathematician born on the island of Als (German: Alsen). Shortly after his birth, he and his parents moved to China, and he did not return to Europe until he was nine.
Witt's work was mainly concerned with the theory of quadratic forms and related subjects such as algebraic function fields.*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

Saturday, 2 July 2022

On This Day in Math - July 2


Heavier-than-air flying machines are impossible.
I have not the smallest molecule of faith in aerial navigation other than ballooning,
or of the expectation of good results from any of the trials we hear of. 1895
And in a Letter to Baden-Powell (1896) Radio has no future.
William Thomson, Lord Kelvin

The 183rd day of the year; the concatenation of 183 and 184, 183184 is a perfect square. There are no smaller numbers for which the concatenation of two consecutive numbers is square. (Students might seek the next such pair of numbers. They are small enough to be year dates)

The sum of the first 183 primes minus 183 is prime.

183 is the eighth of the 12 year-days which are perfect totient numbers.  (There are only 57 such numbers under 103).  A list of the perfect totient numbers seems to suggest that all of them are multiples of three, but then you get to 4375, the smallest perfect totient number that is not divisible by 3.[a perfect totient number is a number that is the sum of it's iterated totients, that is, the number of integers smaller than, and relatively prime to 183 + the number smaller than and less than that result, + ... down to one, "For example, start with 327. Then φ(327) = 216, φ(216) = 72, φ(72) = 24, φ(24) = 8, φ(8) = 4, φ(4) = 2, φ(2) = 1, and 216 + 72 + 24 + 8 + 4 + 2 + 1 = 327 " *Wik
Get more Math Facts for every year date here


1133 First trade security agreement between Pisans and Alibibn Yusof of Morocco.Under such an agreement, Guilielmo, father of Leonardo brought his young son (who would much later be called Fibonacci) to Bugia, where he would learn of the Arabic calculation system that he would introduce to his  homeland in his Liber Abbaci in 1202. *Devlin, The Man of Numbers

In 1698 Thomas Savery was issued British Letters Patent No.356 for what he called "The Miner's Friend; or an engine to raise water by fire" which was the first application of steam power for pumping water. The steam powered pump had no piston. Two years earlier Savery was issued British Letters Patent No.347 for his invention for "Navigation improved; or the art of rowing ships of all rates in calms with a more easy, swift, and steady motion than oars can." ( which involved paddle-wheels driven by a capstan and which was dismissed by the Admiralty following a negative report by the Surveyor of the Navy,Edmund Dummer.)*TIS*Wik

1779 One of the earliest mentions of blackboards in Colonial America was in a letter from John Taylor, a tutor at Queens College (to become Rutgers University)to a graduate student, John Bogart, that he was asking to take over his classes while Taylor was away on military duties. "I have spoken to Mr. Briton to make a blackboard.." *Kidwell, Hastings, & Roberts; Tools of American Mathematics Teaching.

1832 Legendre writes to Nathanial Bowditch regarding his translation of LaPlace's "Mecanique Celeste" ,"Your work is not merely a translation with a commentary; I regard it as a new edition, augmented and improved, and such a one as might have come from the hands of the author himself, ... if he had been solicitously studious of being clear."   LaPlace's classic is a very difficult book, and Biot, who helped him prepare it for printing said that Laplace himself would frequently get lost in following his own line of reasoning  and insert, "il est aise a voir" (It is easy to see). *The Teaching and History of Mathematics in the United States, F. Cajori

1850 Stokes’s theorem made its first appearance as a postscript to a letter from Sir William Thompson (Lord Kelvin) to Stokes. It first appeared publicly as question 8 on the Smith’s Prize exam for 1854. Stokes drew up this competitive exam, which was taken by the best mathematics students at Cambridge University. By the time Stokes died the theorem was universally known as “Stokes’s theorem.” [Spivak, Calculus on Manifolds, p. viii].

1865 Sylvia Ann Howland died in 1865, leaving roughly half her fortune of some 2 million dollars (equivalent to $31,291,000 in 2016) to various legatees, with the residue to be held in trust for the benefit of Hetty Robinson, Howland's niece. The remaining principal was to be distributed to various beneficiaries on Robinson's death.

Robinson produced an earlier will, leaving her the whole estate outright. To the will was attached a second and separate page, putatively seeking to invalidate any subsequent wills. Howland's executor, Thomas Mandell, rejected Robinson's claim, insisting that the second page was a forgery, and Robinson sued.

In the ensuing case of Robinson v. Mandell, Charles Sanders Peirce testified that he had made pairwise comparisons of 42 examples of Howland's signature, overlaying them and counting the number of downstrokes that overlapped. Each signature featured 30 downstrokes and he concluded that, on average, 6 of the 30 overlapped, 1 in 5. Benjamin Peirce showed that the number of overlapping downstrokes between two signatures also closely followed the binomial distribution, the expected distribution if each downstroke was an independent event. When the admittedly genuine signature on the first page of the contested will was compared with that on the second, all 30 downstrokes coincided, suggesting that the second signature was a tracing of the first.

Benjamin Peirce, Charles' father, then took the stand and asserted that, given the independence of each downstroke, the probability that all 30 downstrokes should coincide in two genuine signatures was \frac {1}{2.666* 10^{21}} *wik

1866 Alfred Russell Wallace writes to Darwin with to suggest a name change for his basic principal of Evolution:
I wish.. to suggest ... adopting Spencer's term, (which he generally uses in preference to Natural Selection, viz, "Survival of the Fittest"
*Mario Livio, Brilliant Blunders, pg 29

1883 Helmholtz writes to Heinrich Hertz to congratulate him on his investigations. "I have read with the greatest interest your investigation on the cathode ray discharge, and cannot refrain from writing to say Bravo!" Hemholtz was not given to token praise, and was the opinion that was most valued by Hertz. *Hertz Miscellaneous Papers

1897 – Italian scientist Guglielmo Marconi obtains a patent for radio in London.*Wik

1982 Science (p. 39) reported that Steven Smale had proved that the average-case behavior of the simplex algorithm for linear programming is far better than the worse-case behavior, which is exponential. [Mathematics Magazine 56 (1983), p. 55]. *VFR

1944 Grace Hopper meets Howard Aiken for the first time. Here is her description of the meeting:
Until 1944, I had been a thoroughly respectable mathematician. I had never met a digit, and I wanted nothing to do with digits. I came into the computer business in a unique fashion. I was ordered to the Navy Liaison Officer at Harvard. I left Midshipmen School on Friday, and on Monday morning, 2nd July 1944, I reported to the Navy Liaison Officer, Harvard. He took me by the hand, and led me over to an underground laboratory. I had just acquired one-and-a-half stripes. There stood a large object, with three stripes, who took one look at me and said: "Where the hell have you been?" I spluttered, and said that I had had two days' travel time. He said: "For the last three months." I said: "Midshipmen's School", and he said he had told them it was not necessary. By this time I was practically cowering, of course, but with one-and-a-half stripes, I would stand up straight and listen to three stripes. He waved his hand and said: "That's a computing machine." I said, "Yes, Sir." What else could I say? He said he would like to have me compute the coefficients of the arc tangent series, for Thursday. Again, what could I say? "Yes, Sir." I did not know what on earth was happening, but that was my meeting with Howard Hathaway Aiken. In the long run, he taught me one very important thing. One can always make a mistake once, but it must not be made a second time. That was a very good thing to learn. He also flatly informed me that he had told the Bureau of Naval Personnel not to send him a female. At this point, and over the next few months, I learned another lesson. I could have taken the attitude of showing him, and making him take that back. Instead, I decided it would be far better to learn to work with him. This is a lesson we all need to learn: of not showing people, but learning to work with people. It certainly made a difference in getting things done in the computer field.

1992 On July 2, fearing for the impact that a park service removal of homeowners around Elkmont, Tennessee in the Great Smokey Mountain Natl Park would have on a variety of local fireflys, Lynn Faust wrote a letter to Professor Steven Stogratz, who had recently written a paper in Science Magazine about synchronized flashing of the firelies (lightning bugs) known to exist in Southeast Asia. Ms. Faust's letter would, in Strogatz's words, "shatter a (scientific) myth that had lasted for decades."
The letter, in Ms. Faust's own hand, can be read here. (My thanks to both Professor Strogatz and Ms. Faust for their cooperation in sharing this letter.)

2011 Simon Chua, 58, received Australia's B. H. Neumann Award for pioneering efforts in training and honing the talent of young Filipino mathematicians for the past 15 years.
The Australian Mathematics Trust (AMT) bestowed the award to Chua on July 2, 2011. The B. H. Neumann Awards are presented annually for "important contributions over many years to the enrichment of mathematics learning in Australia and its region," according to the AMT.
The award is named in honor of Bernhard H. Neumann, the so-called father of Australian mathematics, who “provided outstanding leadership, support and encouragement for mathematics and the teaching of mathematics at all levels."
Chua, who is president and co-founder of the Mathematics Trainers Guild-Philippines (MTG), is the first Asian to receive the award.
Through the MTG, Filipino students have won numerous medals in math competitions abroad including in China, United States, Singapore, Thailand, Hong Kong and Indonesia.
In 2006, Chua became the first Filipino to win the Paul Erdos Award from the World Federation of National Mathematics Competitions. *MathDL


1622 Rene-Francoise de Sluse (2 July 1622 – 19 March 1685) Sluse contributed to the development of calculus and this work focuses upon spirals, tangents, turning points and points of inflection. He and Johannes Hudde found algebraic algorithms for finding tangents, minima and maxima that were later utilized by Isaac Newton. These algorithms greatly improved upon the complicated algebraic methods of Pierre de Fermat and René Descartes, who themselves had improved upon Roberval's kinematic, but geometric, non-algorithmic methods of determining tangents. Augustus De Morgan has the following to say about de Sluse's contribution to Newton's method of fluxions in his discussion of the Leibniz–Newton calculus controversy.
When they state that Collins had been four years in circulating the letter in which the method of fluxions was sufficiently described to any intelligent person, they suppress two facts: first, that the letter itself was in consequence of Newton's learning that Sluse had a method of tangents; secondly, that it revealed no more than Sluse had done. ...this method of Sluse is never allowed to appear ...Sluse wrote an account of the method which he had previously signified to Collins, for the Royal Society, for whom it was printed. The rule is precisely that of Newton... To have given this would have shown the world that the grand communication which was asserted to have been sent to Leibniz in June 1676 might have been seen in print, and learned from Sluse, at any time in the previous years: accordingly it was buried under reference. ...Leibniz had seen Hudde at Amsterdam, and had found that Hudde was in possession of even more than Sluse
He corresponded with the mathematicians and intellectuals of the day; his correspondents included Blaise Pascal, Christiaan Huygens, John Wallis, and Michelangelo Ricci. He was appointed Chancellor of Liege and Counsellor and Chancellor to Prince Maximilian-Henry of Bavaria. He was elected a Fellow of the Royal Society in 1674. *Wik

1842 George Thom (2 July 1842 in Forgue near Huntly, Scotland - 20 Dec 1916 in Aberdeen, Scotland) graduated from Aberdeen and then became Principal of Doveton College in Madras, India. He returned to Scotland as Vice-Principal of Chanonry School Aberdeen and then became Rector of Dollar Institution (later to become Dollar Academy). He held this post for 24 years. He was a founder member of the EMS and became the fifth President in 1886. *SAU

1847 Andrew Gray graduated from Glasgow University and was appointed assistant and secretary to Lord Kelvin. He became Professor of Physics at University College Bangor and then returned to Glasgow as Kelvin's successor. He produced many books and papers in both mathematics and physics.*SAU

1852 Birthdate of William Burnside, whose Theory of Groups (1897, 1911) is now a classic. His suspicion that every group of odd order is solvable was proved in 1962 by Walter Feit and John G. Thompson. *VFR He is known mostly as an early contributor to the theory of finite groups. In 1897 Burnside's classic work Theory of Groups of Finite Order was published. The second edition (published in 1911) was for many decades the standard work in the field. A major difference between the editions was the inclusion of character theory in the second.
Burnside is also remembered for the formulation of Burnside's problem (which concerns the question of bounding the size of a group if there are fixed bounds both on the order of all of its elements and the number of elements needed to generate it) and for Burnside's lemma (a formula relating the number of orbits of a permutation group acting on a set with the number of fixed points of each of its elements) though the latter had been discovered earlier and independently by Frobenius and Cauchy.

1862 Sir William Henry Bragg (2 July 1862 – 10 March 1942) was a pioneer British scientist in solid-state physics who was a joint winner (with his son Sir Lawrence Bragg) of the Nobel Prize for Physics in 1915 for research on the determination of crystal structures. During the WW I, Bragg was put in charge of research on the detection and measurement of underwater sounds in connection with the location of submarines. He also constructed an X-ray spectrometer for measuring the wavelengths of X-rays. In the 1920s, while director of the Royal Institution in London, he initiated X-ray diffraction studies of organic molecules. Bragg was knighted in 1920. *TIS

1885 Émile Henriot (2 July 1885 - 1 February 1961) was a French chemist notable for being the first to show definitely that potassium and rubidium are naturally radioactive.
He investigated methods to generate extremely high angular velocities, and found that suitably placed air-jets can be used to spin tops at very high speeds - this technique was later used to construct ultracentrifuges.
He was a pioneer in the study of the electron microscope. He also studied birefringence and molecular vibrations.
He obtained his DSc in physics in 1912 the Sorbonne, Paris, under Marie Curie. *Wik

1906 Hans Bethe, (July 2, 1906 – March 6, 2005) German-born American theoretical physicist who helped to shape classical physics into quantum physics and increased the understanding of the atomic processes responsible for the properties of matter and of the forces governing the structures of atomic nuclei. Bethe did work relating to armour penetration and the theory of shock waves of a projectile moving through air. He studied nuclear reactions and reaction cross sections (1935-38). In 1943, Oppenheimer asked Bethe to be the head of the Theoretical Division at Los Alamos on the Manhattan Project. After returning to Cornell University in 1946, Bethe became a leader promoting the social responsibility of science. He received the Nobel Prize for Physics (1967) for his work on the production of energy in stars. *TIS


1566 Nostradamus, French astrologer died on this day (b. 1503). I wonder if he predicted THIS in his prophacies.

1591 Vincenzo Galilei ( c. 1520 – 2 July 1591) Italian, music theorist, lutenist and composer, who as the father of Galileo Galilei, adopted experimentation to prove aspects of acoustics, and may thus have influenced his son, Galileo, away from pure, abstract mathematics and towards making experiments and investigation. Vincenzo's discoveries in acoustics included some of the physics of vibrating strings and columns of air. In particular he was the first to show that the ratio of an interval was proportional to string lengths but varied as the square of the tension applied to the strings and as the cubes of volumes of air. He recognized the superiority of equal tempered tuning and compiled a codex of pieces illustrating the use of all 24 major and minor keys as early as 1584.*TIS

1613 Bartholomeo Pitiscus (August 24, 1561 – July 2, 1613) was a Polish theologian who first coined the word Trigonometry. *SAU Pitiscus achieved fame with his influential work written in Latin, called Trigonometria: sive de solutione triangulorum tractatus brevis et perspicuus (1595, first edition printed in Heidelberg), which introduced the word "trigonometry" to the English and French languages, translations of which had appeared in 1614 and 1619, respectively. It consists of five books on plane and spherical trigonometry. Pitiscus is sometimes credited with inventing the decimal point, the symbol separating integers from decimal fractions, which appears in his trigonometrical tables and was subsequently accepted by John Napier in his logarithmic papers (1614 and 1619).*Wik

1621 Thomas Harriot (Oxford, c. 1560 – London, 2 July 1621) died of a cancerous ulcer on his left nostril. While in America in 1586 he learned to “drink” tobacco smoke from the Indians. This probably makes him the earliest recorded tobacco fatality. He is best known for his contributions to algebra, including the invention of the symbol for less than, \( \lt \) and greater than, \( \gt \) . He might have adopted this symbol from a decoration on an Indian’s back. See C. L. Smith, “On the origin of ‘<’ and ‘>’,” The Mathematics Teacher, 57(1964), 479–481 for a picture of this Indian.*VFR
He also is credited with the mathematical symbol for "therefore" \(\therefore \) His executors posthumously published his Artis Analyticae Praxis on algebra in 1631; Nathaniel Torporley was the intended executor of Harriot's wishes, but Walter Warner in the end pulled the book into shape. It may be a compendium of some of his works but does not represent all that he left unpublished (more than 400 sheets of annotated writing). It isn't directed in a way that follows the manuscripts and it fails to give the full significance of Harriot's writings.*Wik He introduced a simplified notation for algebra and his fundamental research on the theory of equations was far ahead of its time. He was able to solve equations, even with negative or complex roots. However, he published no mathematical work in his lifetime. (Artes analyticae praxis, posthumous, 1631). Especially early in his career, he worked on navigation for his patron Walter Raleigh. Harriot carried out extensive telescopic observations of the satellites of Jupiter and of sunspots. When investigating optics, he discovered the sine law and measured the refractive indices of 13 different substances. He investigated free motion and motion resisted in air, and ballistic curves.*TIS Thomas Harriot was an English mathematician who did outstanding work on the solution of equations, recognising negative roots and complex roots in a way that makes his solutions look almost like a present day solution.*SAU
The solution of quadratic equations by the method of factoring was often referred to as Harriot's method because of his introduction of the method in his writing.
It is not possible today to find Harriot's grave. Although he was buried near the altar of St Christopher le Stocks in London,the church was destroyed in the great fire of 1666. There is a plaque in the entrance hall of the Bank of England, which is close to the site of Harriot's grave. It reproduces the original Latin wording of his epitaph.(p474) An English translation would read:
Stay, traveler, lightly tread;
Near this spot lies all that was mortal
Of that most celebrated man Thomas Harriot.
He was that most learned Harriot . . .
Who cultivated all the sciences and excelled in all . . .
A most studious searcher after truth . . .

1644 William Gascoigne (1612 – 2 July 1644) was an English astronomer, mathematician and maker of scientific instruments from Middleton, Leeds who invented the micrometer. He was one of "nos Keplari" a group of astronomers in the north of England who followed the astronomy of Johannes Kepler which included, Jeremiah Horrocks and William Crabtree. Gascoigne's micrometer is shown at right from a drawing by Hooke. Gascoigne, was working on a Keplerian optical arrangement when a thread from a spider’s web happened to become caught at exactly the combined optical focal points of the two lenses. When he looked through the arrangement Gascoigne saw the web bright and sharp within the field of view. He realized that he could more accurately point the telescope using the line as a guide, and went on to invent the telescopic sight by placing crossed wires at the focal point to define the centre of the field of view. Gascoigne died at the Battle of Marston Moor, Yorkshire, *Wik

1874 Gouverneur Emerson American physician, statistician and agriculturalist who prepared a series of tables of deaths and causes in Philadelphia, during thirty years from 1807. These showed, for example, the excessive mortality of males during childhood. He began practice in Philadelphia on 4 Aug 1820, where yellow fever broke out a few weeks later, with 73 deaths by that fall. Emerson recorded cases, dates, locations, and outcomes. He concluded no current medical treatments was especially effective. When smallpox reappeared there, with 325 deaths in 1824, Emerson drafted a bill for control measures. There were only 6 cases of smallpox in the city in 1825, and 3 in 1826. In retirement, he turned to peach culture, and studied phosphate and guano fertilizers. *TIS

1947 Nikolai Grigorievich Chebotaryov (15 June [O.S. 3 June] 1894 – 2 July 1947) proved his density theorem generalising Dirichlet's theorem on primes in an arithmetical progression*SAU

1963 Seth Barnes Nicholson (November 12, 1891 – July 2, 1963) was an American astronomer best known for discovering four satellites of Jupiter. As a graduate student at the University of California, while photographing the recently- discovered 8th moon of Jupiter with the 36-inch Crossley reflector, he discovered a 9th (1914). During his life career at Mt.Wilson Observatory, he discovered two more Jovian satellites (1938) and the 12th (1951), as well as a Trojan asteroid, and computed orbits of several comets and of Pluto. His main assignment at Mt. Wilson was observing the sun with the 150-foot solar tower telescope, and he produced annual reports on sunspot activity and magnetism for decades. With Edison Pettit, he measured the temperatures of the moon, planets, sunspots, and stars in the early 1920s. *TIS

2002 Daniel Chonghan Hong (3 Mar 1956; 2 Jul 2002 at age 46) Korean theoretical physicist specializing in statistical physics and nonlinear dynamic physics, who with colleague Hugo Caram, originated the void diffusing-void model of granular flow, which is recognized as an effective theoretical treatment for a broad range of dynamical phenomena in granular media. In general, his work ranged from percolation network, viscous fingering, granular flows to traffic equations. He studied and taught in America from 1981, and wrote articles for popular magazines on various topics. He died at the young age of 46 of cardiac arrest. *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

Friday, 1 July 2022

On This Day in Math - July 1


Mathematics, rightly viewed, possesses not only truth, but supreme beauty
a beauty cold and austere, like that of sculpture, 
without appeal to any part of our weaker nature,
without the gorgeous trappings of painting or music, 
yet sublimely pure, and capable of a stern perfection such as only the greatest art can show. 
 The true spirit of delight, the exaltation, 
the sense of being more than Man, 
which is the touchstone of the highest excellence, 
is to be found in mathematics as surely as in poetry.

The 182nd day of the year; there are 182 connected bipartite graphs with 8 vertices. *What's So Special About This Number

The 182nd prime (1091) is the smaller of a pair of twin primes (the 40th pair, actually) *Math Year-Round ‏@MathYearRound(Students might convince themselves that it was not necessary to say it was the smaller of the pair.)

Language time:
182 is called a pronic, promic, or heteromecic and even an oblong number. Pronic Numbers are numbers that are the product of two consecutive integers; 2, 6, 12, 20, ..(doubles of triangular numbers).  Pronic seems to be a misspelling of promic, from the Greek promekes, for rectangular, oblate or oblong. Neither pronic nor promic seems to appear in most modern dictionaries. Richard Guy pointed out to the Hyacinthos newsgroup that pronic had been used by Euler in series one, volume fifteen of his Opera, so the mathematical use of the "n" form has a long history.

Oblong is from the Latin ob (excessive) + longus (long). The word oblong is also commonly used as an alternate name for a rectangle. In his translation of Euclid's "Elements", Sir Thomas Heath translates the Greek word eteromhkes[hetero mekes - literally "different lengths"] in Book one, Definition 22 as oblong. . "Of Quadrilateral figures, a square is that which is both equilateral and right-angled; an oblong that which is right angled but not equilateral...". (note that with this definition, a square is not a subset of rectangles.)

More Math Facts for every year date here.


1349 Sometimes, a little astronomical knowledge can be a dangerous thing, even to those who possess it. A tale from medieval England is passed down from the chronicles of the scholar Thomas Bradwardine of a witch who attempted to force her will on the people through knowledge of an impending eclipse. Bradwardine, who had studied astronomical predictions of Arabian astronomers, saw through the ruse, and matched the prediction of the July 01, 1349 A.D. lunar eclipse with a more precise one of his own. No word survives as to the fate of the accused, but one can only suspect banishment or worse.*listosaur.com

1694 Opening of the University of Halle in Germany. Georg Cantor later taught there. *VFR

1770 – Lexell's Comet passed closer to the Earth than any other comet in recorded history, approaching to a distance of 0.0146 a.u. *OnThisDay & Facts ‏@NotableHistory discovered by astronomer Charles Messier

1798 Napoleon’s fleet reached Alexandria, bearing Monge and Fourier.*VFR

1819 William George Horner’s (1786–1837) method of solving equations is presented to the Royal Society.*VFR In numerical analysis, the Horner scheme (also known as Horner algorithm), named after William George Horner, is an algorithm for the efficient evaluation of polynomials in monomial form. Horner's method describes a manual process by which one may approximate the roots of a polynomial equation. The Horner scheme can also be viewed as a fast algorithm for dividing a polynomial by a linear polynomial with Ruffini's rule. Student's often learn this process as synthetic division.  *Wik

1847 The United States issued its first two postage stamps. They pictured Benjamin Franklin and George Washington respectively [Scott #1-2]. *VFR

1852 Dirichlet delivers a memorial lecture at the Berlin Academy in honor of his close friend Jacobi, calling him the greatest member of the Academy since Lagrange. *VFR

1856 Weierstrass appointed Professor of Mathematics at the Royal Polytechnic School in Berlin. *VFR

In 1858, the Wallace-Darwin theory of evolution was first published at the Linnaean Society in London*. The previous month Charles Darwin received a letter from Alfred Wallace, who was collecting specimens in the East Indies. Wallace had independently developed a theory of natural selection - which was almost identical to Darwin's. The letter asked Darwin to evaluate the theory, and if worthy of publication, to forward the manuscript to Charles Lyell. Darwin did so, almost giving up his clear priority for he had not yet published his masterwork The Origin of Species. Neither Darwin nor Wallace were present for the oral presentation at the Linnaean Society, where geologist Charles Lyell and botanist Joseph Hooker presented both Wallace's paper and excerpts from Darwin's unpublished 1844 essay.*TIS
In his annual report the following May, society president Thomas Bell wrote, “The year which has passed has not, indeed, been marked by any of those striking discoveries which at once revolutionize, so to speak, the department of science on which they bear.” *Futility Closet

1873 From a letter dated July 1, 1873, in the Coast Survey files in the National Archives in Washington. Peirce writes, "Newcomb, in a paper .... says he finds that pendulums hung by springs twist and untwist as they oscillate and says this will affect the time of oscillation."The Charles S. Peirce-Simon Newcomb Correspondence by Carolyn Eisele.

1894 The New York Mathematical Society changed its name to the American Mathematical Society to reflect its national charter. [AMS Semicentennial Publications, vol. 1, p. 74]. *VFR

1908 International agreement to use SOS for distress signal signed. An International Radiotelegraphic Convention, ... met in Berlin in 1906. This body signed an international agreement on November 3, 1906, with an effective date of July 1, 1908. An extensive collection of Service Regulations was included to supplement the Convention, and in particular Article XVI adopted Germany's Notzeichen distress signal as the international standard, stating: "Ships in distress shall use the following signal: · · · — — — · · · repeated at brief intervals". *Citizens Compendium

1908  The Chicago Daily News Style Book, dated July 1, 1908, bans the word Scientist.  On the Style Sheet of the Century Magazine it is listed among the "words and phrases to be avoided." It was prohibited by the famous Index Expurgatorius prepared by William Cullen Bryant for the New York Evening Post, and his prohibition is still theoretically in force, but the word is now actually permitted by the Post. * How the term Scientist came to be .

1918 Florian Cajori (1859–1930) appointed professor of the history of mathematics at the University of California, Berkeley, one of the few such chairs in the the world. During the next twelve years he published 159 papers on the history of mathematics. *VFR

1948 The Bell System Technical Journal publishes the first part of Claude Shannon's "A Mathematical Theory of Communication", regarded as a foundation of information theory, introducing the concept of Shannon entropy and adopting the term Bit. *Wik

1964 The New York Times, in a full page ad, announced that Paul Newman and Joanne Woodward would play a game on an elliptical pool table. It had a pocket at one focus so that if the ball passed over the other focus it would bank off the rail into the pocket. [UMAP Journal, 4(1983), p. 176; Recreational Mathematics Magazine, no. 14, January-February 1964] *VFR

1980 A method of trisecting any given acute angle Origami is demonstrated. Hisashi Abe invented this idea and published in July, 1980 edition of the Japanese journal "Suugaku Seminar"(Mathematics Seminar). For this method, and more ways to trisect the angle, see this post.
*Takaya Iwamoto

2001 The last occurrence that there were 3 eclipses in one month, and of which two solar eclipses. For July 2000 being on 1st a partial solar eclipse, 16th a total lunar eclipse, and 31st a partial solar eclipse. The next occurrence with a month with 3 eclipses will be December 2206 with a partial solar eclipse on 1st and 30th and a total lunar eclipse on 16th. Ref. Fred Espenak 06/00 SEML. *NSEC

2010 Grigori Yakovlevich Perelman turned down the Clay Millineum prize of one million dollars, saying that he considers his contribution to proving the Poincaré conjecture to be no greater than that of Richard Hamilton, who introduced the theory of Ricci flow with the aim of attacking the geometrization conjecture. On March 18 It had been announced that he had met the criteria to receive the first Clay Millennium Prize for resolution of the Poincaré conjecture. *Wik

2015 Michael Elmhirst Cates, becomes the 19th Lucasian Professor of Mathematic at the University of Cambridge. Professor Cates is a physicist and Professor of Natural Philosophy and Royal Society Research Professor at the University of Edinburgh. Previous recognitions for Prof. Cates include Maxwell Medal and Prize (1991), the Paul Dirac Medal and Prize (2009), and the Weissenberg Award (2013). He will assume the chair from another Physicist, Michael Green. He follows a line that began with Isaac Barrow and Isaac Newton and includes Charles Babbage, Paul Dirac, and Stephen Hawking


1646 Gottfried Wilhelm Leibniz (July 1, 1646 – November 14, 1716) born in Leipzig, Germany. Leibniz occupies a prominent place in the history of mathematics and the history of philosophy. He developed the infinitesimal calculus independently of Isaac Newton, and Leibniz's mathematical notation has been widely used ever since it was published. He became one of the most prolific inventors in the field of mechanical calculators. While working on adding automatic multiplication and division to Pascal's calculator, he was the first to describe a pinwheel calculator in 1685[4] and invented the Leibniz wheel, used in the arithmometer, the first mass-produced mechanical calculator. He also refined the binary number system, which is at the foundation of virtually all digital computers. In philosophy, Leibniz is mostly noted for his optimism, e.g. his conclusion that our Universe is, in a restricted sense, the best possible one that God could have created. Leibniz, along with René Descartes and Baruch Spinoza, was one of the three great 17th century advocates of rationalism. The work of Leibniz anticipated modern logic and analytic philosophy, but his philosophy also looks back to the scholastic tradition, in which conclusions are produced by applying reason to first principles or a priori definitions rather than to empirical evidence. Leibniz made major contributions to physics and technology, and anticipated notions that surfaced much later in biology, medicine, geology, probability theory, psychology, linguistics, and information science. He wrote works on politics, law, ethics, theology, history, philosophy, and philology. Leibniz's contributions to this vast array of subjects were scattered in various learned journals, in tens of thousands of letters, and in unpublished manuscripts. As of 2010, there is no complete gathering of the writings of Leibniz.*Wik

1779 John Farrar (July 1, 1779 – May 8, 1853) born at Lincoln, Massachusetts. As Hollis professor of mathematics and natural philosophy at Harvard, he was responsible for a sweeping modernization of the science and mathematics curriculum, including the change from Newton’s to Leibniz’s notation for the calculus. *VFR

1788 Jean Victor Poncelet (July 1, 1788 – December 22, 1867) born in Metz, France. He taught engineering and mechanics, but had a hobby of much greater interest—projective geometry. *VFR French mathematician and engineer whose study of the pole and polar lines associated with conic led to the principle of duality. While serving as an engineer in Napoleon's 1812 Russian campaign as an engineer, he was left for dead at Krasnoy, but then captured. During his imprisonment he studied projective geometry and wrote a treatise on analytic geometry. Released in 1814, he returned to France, and in 1822 published Traité des propriétés projectives des figures in which he presented his fundamental ideas of projective geometry such as the cross-ratio, perspective, involution and the circular points at infinity. As a professor of mechanics (1825-35), he applied mechanics to improve waterwheels and was able to double their efficiency.*TIS

1848 Emil Weyr (1 July 1848 in Prague, Bohemia (now Czech Republic) - 25 Jan 1894 in Vienna, Austria) His father Frantisek Weyr, was a professor of mathematics at a realschule (secondary school) in Prague from 1855. Emil was four years older than his brother Eduard Weyr who also became a famous mathematician. Emil attended the realschule in Prague where his father taught, then studied at the Prague Polytechnic from 1865 to 1868 where he was taught geometry by Vilém Fiedler.
He studied in Italy with Cremona and Casorati during the academic year 1870-71 returning to Prague where he continued to teach. In 1872 he was elected to be Head of the Union of Czech Mathematicians and Physicists. In 1875 he was appointed as professor of mathematics at the University of Vienna. He, together with his brother Eduard Weyr, were the main members of the Austrian geometric school. They were interested in descriptive geometry, then in projective geometry and their interests turned towards algebraic and synthetic methods in geometry. Among many works Emil Weyr published were Die Elemente der projectivischen Geometrie and Über die Geometrie der alten Aegypter.
Emil Weyr led the geometry school in Vienna throughout the 1880's up until his death. Together with Gustav von Escherich, Emil Weyr founded the important mathematical journal Monatshefte fuer Mathematik und Physik in 1890. The first volumes of the journal contain papers written by his brother Eduard. In 1891 Emil Weyr became one of the first 19 founder members of the Royal Czech Academy of Sciences. *SAU

1906 Jean Dieudonn´e (1 July 1906 – 29 November 1992) born. *VFR French mathematician and educator known for his writings on abstract algebra, functional analysis, topology, and his theory of Lie groups. Dieudonné was one of the two main contributors to the Bourbaki series of texts. He began his mathematical career working on the analysis of polynomials. He worked in a wide variety of mathematical areas including general topology, topological vector spaces, algebraic geometry, invariant theory and the classical groups. *TIS


1957 Donald McIntosh (Banffshire, 13 January 1868 – Invernesshire, 1 July 1957) graduated from the University of Aberdeen and taught at George Watson's Ladies College in Edinburgh. He was appointed a Director of Education. He became Secretary of the EMS in 1899 and President in 1905. *SAU

1963 Bevan Braithwaite Baker (1890 in Edinburgh, Scotland - 1 July 1963 in Edinburgh, Scotland) graduated from University College London. After service in World War I he became a lecturer at Edinburgh University and was Secretary of the EMS from 1921 to 1923. He left to become Professor at Royal Holloway College London. *SAU

1971 Sir William Lawrence Bragg (31 Mar 1890; 1 Jul 1971 at age 81) was an Australian-English physicist and X-ray crystallographer who at the early age of 25, shared the Nobel Prize for Physics in 1915 (with his father, Sir William Bragg). Lawrence Bragg formulated the Bragg law of X-ray diffraction, which is basic for the determination of crystal structure: nλ = 2dsinθ which relates the wavelength of x-rays, λ, the angle of incidence on a crystal, θ, and the spacing of crystal planes, d, for x-ray diffraction, where n is an integer (1, 2, 3, etc.). Together, the Braggs worked out the crystal structures of a number of substances. Early in this work, they showed that sodium chloride does not have individual molecules in the solid, but is an array of sodium and chloride ions. *TIS

1983 Richard Buckminster Fuller (July 12, 1895 – July 1, 1983) was a U.S. engineer and architect who developed the geodesic dome, the only large dome that can be set directly on the ground as a complete structure, and the only practical kind of building that has no limiting dimensions (i.e., beyond which the structural strength must be insufficient). Fuller also invented a wide range of other paradigm-shifting machines and structural systems. He was especially interested in high-strength-to-weight designs, with a maximum of utility for minimum of material. His designs and engineering philosophy are part of the foundation of contemporary high-tech design aesthetics. He held over 2000 patents.*TIS
This is another one who died within two weeks of his date of birth. I must organize data on this...

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