Friday, 31 July 2026

   


Regarding all these basic topics in infinitesimal calculus which we teach today as canonical requisites ... the question is never raised, "Why so?" or "How does one arrive at them?" Yet all these matters must at one time have been goals of an urgent quest, answers to burning questions, at the time, namely, when they were created. If we were to go back to the origins of these ideas, they would lose that dead appearance of cut-and-dried facts and instead take on fresh and vibrant life again.
Otto Toeplitz - The calculus : A genetic approach (Chicago, 1963)


This is the 213th day of the year; 213 is a square free number as it has no repeated prime factors. How many days of the year are square free?

For 213, the sum of the digits and the product of the digits are equal, and forms a prime when one is added or subtracted.

The average prime factor of 213 is a prime number. [213 = 3*71 and (3+71)/2=37 ]

The square of 213 is a sum of distinct factorials: 2132 = 45369 = 1! + 2! + 3! + 7! + 8!, it is the smallest 3 digit number with this property. (what's next?)



EVENTS


1681, Michelangelo Ricci was made a cardinal by Pope Innocent XI.  Born in Rome in 1619, Ricci was educated in the tradition of rigorous Jesuit schooling, and he showed early promise in mathematics. He became closely associated with prominent mathematicians of the time, especially Evangelista Torricelli (the inventor of the barometer), whose works Ricci helped to preserve and promote after Torricelli’s death. Ricci moved in the same intellectual circles as Galileo Galilei and was involved in the post-Galilean scientific environment in Italy. 

  He studied theology and law in Rome, where he was a contemporary of René-François de Sluse. Sluse contributed to the development of calculus, focusing 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.

Ricci also studied mathematics under Benedetto Castelli who himself had been a student of Galileo Galilei.




1767 “Mason and Dixon finished drawing the world’s longest straight line.” [366 Dumb Days in History, by Tom Koch]

For those not familiar with the names and the line in question, "The Mason–Dixon line is a demarcation line separating four U.S. states, Pennsylvania, Maryland, Delaware and West Virginia. It was surveyed between 1763 and 1767 by Charles Mason and Jeremiah Dixon as part of the resolution of a border dispute involving Maryland, Pennsylvania, and Delaware in the colonial United States."

"Dixie, also known as Dixieland or Dixie's Land, is a nickname for all or part of the Southern United States. While there is no official definition of this region (and the included areas have shifted over the years), or the extent of the area it covers, most definitions include the U.S. states below the Mason–Dixon line that seceded and comprised the Confederate States of America, almost always including the Deep South.[1] The term became popularized throughout the United States by songs that nostalgically referred to the American South."*Wik



In 1774, Joseph Priestley, British Presbyterian minister and chemist, identified a gas which he called "dephlogisticated air" -- later known as oxygen. Priestley found that mercury heated in air became coated with "red rust of mercury," which, when heated separately, was converted back to mercury with "air" given off. Studying this "air" given off, he observed that candles burned very brightly in it. Also, a mouse in a sealed vessel with it could breathe it much longer than ordinary air. A strong believer in the phlogiston theory, Priestley considered it to be "air from which the phlogiston had been removed." Further experiments convinced him that ordinary air is one fifth dephlogisticated air, the rest considered by him to be phlogiston. *TIS  

 Named from the Greek oxys + genes, "acid-former", oxygen was discovered in 1772 by  German-Sweedish chemist Carl Wilhelm Scheele  (although Joseph Priestley published his findings first) and independently by Priestly in 1774. Oxygen was given its name by the French scientist, Antoine Lavoisier.

Joseph Priestley



1786 Caroline Herschel discovered her first comet, Comet Herschel C/1786 P1 and became history's first woman with this distinction **(see below). Her comet came to be known as the "first lady's comet" and brought with it the fame that secured her own place in history books.*The Woman Astronomer
** The Renaissance Mathematicus pointed out in a blog that "Maria Margarethe Kirch (née Winkelmann), the wife of Gottfried Kirch the Astronomer Royal of Berlin, discovered the comet of 1702 (C/1702 H1) that is forty-eight years before Caroline Herschel was born. Unfortunately the discovery was published by her husband and it was he who was incorrectly acknowledged as the discoverer. In 1710 Gottfried admitted the error and publicly acknowledged Maria as the discoverer but she was never official credited with the discovery.
Both Maria Kirch and Caroline Herschel were excellent astronomers with much important work to their credit. However credit where credit is due, Caroline was not the first woman to discover a comet, Maria was."



1814 Almost a month after eloping with Georgiana Whitmore; a marriage of which his father did not approve, Charles Babbage writes to his friend John Herschel, who knew nothing of his secret romance, "I am married and have quarreled with my father." Then after a few lines of self-justification, he explains some theorems he has been working on. Herschel was shocked, and responded on the seventh of the same month.*Anthony Hyman, Charles Babbage: Pioneer of the Computer

Herschel responds six days later, ""I am married and I have quarreled with my father - Good God Babbage - How is it possible for a man to pen those two sentences, then ... pass off to functional expressions?" 


Charles Babbage and his "Engine"



In 1831, New London Bridge opened to traffic. In 1821, a committee was formed by Parliament to consider the poor condition of the existing centuries-old bridge. The arches had been badly damaged by the Great Freeze, so it was decided to build a new bridge. Building commenced under John Rennie in 1825, and completed in 1831, at the expense of the city. The bridge is composed of five arches, and built of Dartmoor granite. It was opened with great splendour by King William the fourth, accompanied by Queen Adelaide, and many of the members of the royal family, August 1st, 1831. In the 1960's it was auctioned and sold for $2,460,000 to Robert McCulloch who moved it to Havasu City, Arizona. The rebuilt London Bridge was completed and dedicated on 10 Oct 1971.*TIS




1861 First use of "weather forecast". From the BBC I read, "Telling people what had happened was useful, but not as useful as telling them what was going to happen. The man who made the first attempt to bridge that gap, and who coined the phrase "weather forecast", was Admiral Robert Fitzroy. Thirty years before, he had been captain of the Beagle voyage that carried Charles Darwin, so he was no stranger to the perils of weather when at sea. In 1854, Fitzroy was given the job of collecting data on weather at sea, leading what later became the Met Office. After a few years, he saw that weather systems could be tracked. He became convinced that predictions were possible and that storm warnings would save many lives. His bosses did not agree that predictions were realistic, but in spite of them Fitzroy started to issue storm warnings in 1861. Then, on the 1st of August 1861 (exactly 151 years ago), Fitzroy issued the first ever weather forecast for the general public, published in The Times. This earned him a slap on the wrist and a huge amount of criticism, because it was considered that the forecasts could not possibly be accurate. After a lot of debate, the public forecasts ended in 1866."   A tweet from @ Rebekah Higgitt corrected this to : weather predictions existed long before (including, but not only, astrological), but Aug 1861 *is* 1st use of term "weather forecast"..




1944 The MARK I computer began operation at Harvard. *VFR

The Harvard Mark I, or IBM Automatic Sequence Controlled Calculator (ASCC), was one of the earliest general-purpose electromechanical computers used in the war effort during the last part of World War II.

One of the first programs to run on the Mark I was initiated on 29 March 1944 by John von Neumann. At that time, von Neumann was working on the Manhattan Project, and needed to determine whether implosion was a viable choice to detonate the atomic bomb that would be used a year later. The Mark I also computed and printed mathematical tables, which had been the initial goal of British inventor Charles Babbage for his analytical engine in 1837. *Wik



1946 President Harry Truman signs the McMahon Act creating the Atomic Energy Commission.

* HT to Ben Gross ‏@bhgross144


1947 The Netherlands issued a postage stamp honoring Jans (Johan) de Witt (1625–1672), who did important early work dealing with analytic geometry. *VFR Besides being a statesman Johan de Witt, also was an accomplished mathematician. In 1659 he wrote "Elementa Curvarum Linearum" as an appendix to his translation of René Descartes' "La Géométrie". In this, De Witt derived the basic properties of quadratic forms, an important step in the field of linear algebra. *Wik


In 1957, the Solar Building (Bridgers and Paxton Office Building), Albuquerque NM, was the first commercial building to be heated by the sun's energy. It was subsequently listed in the National Register of Historic Places for its "exceptional importance," in the area of engineering because it was an early solar-heated commercial building, the equipment for which survived largely intact. It was constructed when active solar-energy systems were still considered experimental. The site is privately owned, at 213 Truman St., NE., Albuquerque, NM. The architectural design was provided by Wright and Stanley.*TIS




1963 Greece issued a postage stamp picturing the “Acropolis at Dawn” by Lord Baden-Powell.*VFR

To commemorate the realization of the 11th World Scout Jamboree in Greece, the Hellenic Post issued a special series of 5 stamps which circulated on August 1st, 1963, on the day the Jamboree officially opened.


1. DENOMINATION : 1 DRACHMA

“Athens at dawn”. A water-colour painted by Lord Baden-Powell of Gilwell in 1872, depicting the Acropolis and surrounding area. 2.5 million stamps of this denomination were circulated.






1967US Navy recalls Hopper to head COBOL effort.  The US Navy recalls Captain Grace Murray Hopper to active duty to help develop the programming language COBOL. With a team drawn from several computer manufacturers and the Pentagon, Hopper -- who had worked on the Mark I and II computers at Harvard in the 1940s -- created the specifications for COBOL (COmmon Business Oriented Language) with business uses in mind. These early COBOL efforts aimed at creating easily-readable computer programs with as much machine independence as possible. Designers hoped a COBOL program would run on any computer for which a compiler existed with only minimal modifications.
Hopper made many major contributions to computer science throughout her very long career, including what is likely the first compiler ever written, "A-0." She appears to have also been the first to coin the word "bug" in the context of computer science, taping into her logbook a moth which had fallen into a relay of the Harvard Mark II computer. She died on January 1, 1992.
The U.S. Navy commissioned their most advanced ship, the U.S.S. Hopper (DDG 70), on September 6, 1997 named in honor of Grace Hopper. *CMH

Log book showing the "bug" found caught in a Mark II relay




1980 Michael Aschbaher wrote Daniel Gorenstein that he had completed the classification of the finite simple groups. This culminated a 20-year effort by some 300 group theorists. The complete proof is about 5000 pages long. [Mathematics Magazine 54 (1981), p. 41



1986   Apple discontinues production of the Macintosh XL, effectively ending the life of the Apple Lisa computer platform. In January of 1985, the Macintosh line of computers was gaining momentum but the Lisa line of computers was not selling well. In order to salvage what they could from the Lisa and offer a more powerful Macintosh computer, Apple created the Macintosh XL model by modifying a Lisa 2/10 computer to run the Macintosh operating system. Apple discontinued the Lisa in April of 1985, but continued production of the hybrid Lisa/Mac Macintosh XL until this date. *This Day in Tech History



1987 The Italian Stronzo Bestiale appeared as a co-author in an erudite physics papers connecting fractal geometry, irreversibility, and the second law of thermodynamics,(Diffusion in a periodic Lorentz gas) along with the U.S. scientists Bill Moran and William G. Hoover. Until Bestiale joined them, the paper had been rejected. But Moran and Hoover had simply made this person up, and named him after hearing two Italian women on an aeroplane constantly referring to someone called “stronzo bestiale,”, which they discovered was not actually a person’s name, but meant “total asshole”. You can even get a T-shirt “I’m friends with Stronzo Bestiale”. *lenfisherscience


2011   Carolin Crawford selected as the Gresham Professor of Astronomy. *Wik

Crawford studied the Mathematical Tripos and received a Bachelor of Arts honours degree in mathematics at Newnham College, Cambridge in 1985. In 1988 she received her PhD[5] for research undertaken at the Institute of Astronomy, Cambridge on cooling flows.

After her PhD, Crawford progressed through a series of postdoctoral and research fellowships at Balliol College, Oxford, the Institute of Astronomy, Trinity Hall, Cambridge and Newnham College, Cambridge.[6] From 1996 to 2007 she held a Royal Society University Research Fellowship.

In 2004 she was appointed a Fellow and College Lecturer at Emmanuel College, Cambridge, where was also the undergraduate admissions tutor for the Physical Sciences. She held this position in conjunction with her role as Public Astronomer at the Institute of Astronomy, which she first took on in 2005.

She served as Gresham Professor of Astronomy at Gresham College from 2011 to 2015, a position in which she delivered free public lectures on astronomy and astrophysics in the City of London.[8]

Crawford's "primary research interests are in combining X-ray, optical and near-infrared observations to study the physical processes occurring around massive galaxies at the core of clusters of galaxies. In particular, she observes the complex interplay between the hot intra-cluster medium, filaments of warm ionized gas, cold molecular clouds, star formation and the radio plasma flowing out from the central supermassive black hole.





BIRTHS



1662  Paul Halcke (also: Halcken or Halke), (1662 in Elmshorn, 1731 in Buxtehude was a German mathematician, writer, computer, and calendar maker.

He was the brother of writer and computer Johann Halcke and founded, in 1690, together with Heinrich Meißner, the Hamburgischen Kunst-Rechnungs lieb- und übenden Societät, today's Hamburg Mathematical Society. Since about 1687 he was writer and calculator at the city school of Buxtehude.

In 1694 he issued a solution's book to a collection of exercises by Heinrich Meißner, and later he published his own collection of 574 exercises from mathematics and astronomy, entitled Mathematischer Sinnen-Confect ("mathematical mind candy"), which was translated in various languages and remained a seminal textbook for more than a century. The exercises were enriched by poems and descriptions of the solving methods. In particular, exercise 289 on page 256 consists in finding the smallest Euler brick, for which Paul Halcke is most well-known today. This cuboid has sides and face diagonals of integer lengths {44, 117, 240} and {125, 244, 267}.

Halcken was also the first (1729) to show that  the product of the aliquot divisors of 24, equals its cube,         \(1*2*3*4*6*8*12 = 13824=24^3\)  and that the same fact is true about 40.

He also edited several popular calendars for the years 1705, 1707, 1715, 1716 and 1725.

An Euler brick, named after Leonhard Euler, is a rectangular cuboid whose edges and face diagonals all have integer lengths. A primitive Euler brick is an Euler brick whose edge lengths are relatively prime. A perfect Euler brick is one whose space diagonal is also an integer, but such a brick has not yet been found.



1817 Sir (Joseph) Henry Gilbert (1 August 1817 - 23 December 1901) English chemist who as co-director with John Bennet Lawes of the Rothamsted Experimental Station, Hertfordshire, for over 50 years established a premier reputation for research at the first organized agricultural experimental station in the world. Their work applied skills in chemistry, meteorology, botany, animal and vegetable physiology, and geology to determine practical improvements for agricultural methods. They studied the nitrogen requirements of plants, how the element was taken up by plants, and the effects of nitrogen fertilizers on grain production and quality. In the 1840s, they initiated the manufacture of superphosphate fertilizer, one of their inventions.*TIS




First Astronomy Class at Vassar College 1866

1818 Maria Mitchell (August 1, 1818 – June 28, 1889) First professional woman astronomer in the United States, born Nantucket, Mass. While pursuing an amateur interest, on 1 Oct 1847, she gained fame from the observation of a comet which she was first to report. She was also the first female member of the American Association of Arts and Scienes.
She became professor of astronomy at Vassar College in 1865, the first person (male or female) appointed to the faculty.  She was also named as Director of the Vassar College Observatory. After teaching there for some time, she learned that despite her reputation and experience, her salary was less than that of many younger male professors. She insisted on a salary increase, and got it. She taught at the college until her retirement in 1888, one year before her death.She died at age 70 in Lynn, Mass. *TIS




1861 Ivar Otto Bendixson (August 1, 1861 – 1935) taught at Stockholm, then from 1913 to 1927 he was rector of Stockholm University. He worked on set theory and differential equations. He is best remembered for the Poincaré - Bendixson theorem. *SAU



1881 Otto Toeplitz (1 August 1881, Breslau – 15 February 1940, Jerusalem) born in Breslau, Germany. In 1905 he received his Ph.D. in algebraic geometry at the university there and then moved to G¨ottingen, where he was deeply influenced by the work of Hilbert. He was also interested in the history of mathematics and held that only a mathematician of stature is qualified to be a historian of mathematics. In 1949 he published an introduction to the calculus on a historical basis. This delightful book is available in English as The Calculus. A Genetic Approach. *VFR



1905 Helen Battles (Sawyer) Hogg (1 Aug 1905, 28 Jan 1993) was a Canadian astronomer who located, cataloged and measured the distances to variable stars in globular clusters (stars with cyclical changes of brightness found within huge, dense conglomerations of stars located in the outer halo of the Milky Way galaxy). Her interest in astronomy was spurred when she witnessed a total eclipse of the sun in 1925. Alongside her career work, she was also foremost in Canada in popularizing astronomy, about which she wrote a column in the Toronto Star for thirty years. She was the first woman to become president of the Royal Canadian Institute. In 1989, the observatory at the National Museum of Science and Technology in Ottawa was dedicated in her name.*TIS



1913 Mischa Cotlar (August 1,1913, Sarny, Russian Empire – January 16, 2007, Buenos Aires, Argentina) was a mathematician who started his scientific career in Uruguay and worked most of his life on it in Argentina and Venezuela.


His contributions to mathematics are in the fields of harmonic analysis, ergodic theory and spectral theory. He introduced the Cotlar–Stein lemma. He was the author or co-author of over 80 articles in refereed journals.

According to Alberto Calderón, Cotlar showed in 1955 "that theorems on singular integrals can be generalized and put in the framework of ergodic theory." According to Krause, Lacey, and Wierdl, Karl E. Petersen in 1983 published an "especially direct proof" of Cotlar's 1955 theorem.

In January 1994 in Caracas, an international conference was held in his honor.*Wik



1924 Georges Charpak (1 August 1924 – 29 September 2010) was a French physicist who was awarded the Nobel Prize in Physics in 1992 "for his invention and development of particle detectors, in particular the multiwire proportional chamber". This was the last time a single person was awarded the physics prize. *Wik



1937 Barry Edward Johnson (1 Aug 1937 Woolwich, London, England – 5 May 2002 Newcastle upon Tyne, England) is well known for his work on Banach algebras and operator algebras, in particular, studying cohomology in these algebras. His mathematical publications started in 1964 with a series of papers on topological algebras, measure algebras and Banach algebras. In these he examined the theory of centralizers and the continuity of transformations. In 1964 he wrote a joint paper with Ringrose Derivations of operator algebras and discrete group algebras and his next papers continued to examine the continuity of homomorphisms, derivations and linear operators. He developed cancer on February 2000 and fought the disease bravely. Despite his deteriorating physical condition, he continued to undertake cutting edge mathematical research. He died of cancer in St Oswald's Hospital in Newcastle upon Tyne aged 64. *SAU



1945 Douglas Dean Osheroff (born August 1, 1945) is an American physicist who shared with David M. Lee and Robert Richardson) was the corecipient of the 1996 Nobel Prize for Physics for their discoveryof superfluidity in the isotope helium-3. As helium is reduced in temperature toward almost absolute zero, a strange phase transition occurs, and the helium takes on the form of a superfluid. The atoms had until that point had moved with random speeds and directions. But as a superfluid, the atoms then move in a co-ordinated manner! *TiS, *Wik



1955 Bernadette Perrin-Riou (August 1, 1955 - ) was awarded the 1999 Ruth Lyttle Satter Prize in recognition of her number theoretical research on p-adic L-functions and Iwasawa theory.

A French number theorist whose parents had both had a scientific education; her mother and father were a physicist and chemist, respectively. She was brought up, along with her sisters, in Neuilly-sur-Seine.

She became maître de conferences at UPMC in 1983, and was then invited to spend a year as a visiting professor at Harvard University; she subsequently became a professor at the same university.

In 1994 she moved to a position at University of Paris-Sud in Orsay. In the same year, she was invited to give an address at the International Congress of Mathematicians, which was held in Zürich, which she gave on "Fonctions L p-adiques" ("p-adic L-functions"). *Wik




1970 Elon Lindenstrauss (August 1, 1970 - ) was the first Israeli to be awarded the Fields Medal, for his results on measure rigidity in ergodic theory, and their applications to number theory.
Since 2004, he has been a professor at Princeton University. In 2009, he was appointed to Professor at the Mathematics Institute at the Hebrew University.
Lindenstrauss is the son of the mathematician Joram Lindenstrauss, the namesake of the Johnson–Lindenstrauss lemma, and computer scientist Naomi Lindenstrauss, both professors at the Hebrew University.
Lindenstrauss was awarded the Erdős Prize and the Fermat Prize in 2009. *Wik





DEATHS

1630 Federico Cesi (13 Mar 1585; 1 Aug 1630 at age 45) Italian scientist who founded the Accademia dei Lincei (1603, Academy of Linceans or Lynxes), often cited as the first modern scientific society, and of which Galileo was the sixth member (1611). Cesi first announced the word telescope for Galileo's instrument. At an early age, while being privately educated, Cesi became interested in natural history and that believed it should be studied directly, not philosophically. The name of the Academy, which he founded at age 18, was taken from Lynceus of Greek mythology, the animal Lynx with sharp sight. He devoted the rest of his life to recording, illustrating and an early classification of nature, especially botany. The Academy was dissolved when its funding by Cesi ceased upon his sudden death(at age 45). *TIS It was revived in its currently well known form of the Pontifical Academy of Sciences, by the Vatican, Pope Pius IX in 1847.




1896 Sir William Robert Grove, (11 July 1811 – 1 August 1896) British physicist and a justice of Britain's high court (from 1880), who first offered proof of the thermal dissociation of atoms within a molecule. He showed that steam in contact with a strongly heated platinum wire is decomposed into hydrogen and oxygen in a reversible reaction. In 1839, Grove mixed hydrogen and oxygen in the presence of an electrolyte, and produced electricity and water. This Grove Cell was the invention of the fuel cell. The technology was not seriously revisited until the1960s. Through the electrochemical process, the energy stored in a fuel is converted - without combusting fuel - directly into DC electricity.*TIS




1920 Bal Gangadhar Tilak (23 July 1856 – 1 August 1920, age 64), scholar, mathematician, philosopher, and militant nationalist who helped lay the foundation for India's independence. He founded (1914) and served as president of the Indian Home Rule League and, in 1916, concluded the Lucknow Pact with Mohammed Ali Jinnah, which provided for Hindu-Muslim unity in the struggle for independence. *TIS




1904 Adolf Lindenbaum (12 June 1904 – ? August 1941) was a Polish-Jewish logician and mathematician best known for Lindenbaum's lemma and Lindenbaum–Tarski algebras.

He was born and brought up in Warsaw. He earned a Ph.D. in 1928 under Wacław Sierpiński and habilitated at the University of Warsaw in 1934. He published works on mathematical logic, set theory, cardinal and ordinal arithmetic, the axiom of choice, the continuum hypothesis, theory of functions, measure theory, point-set topology, geometry and real analysis. He served as an assistant professor at the University of Warsaw from 1935 until the outbreak of war in September 1939. He was Alfred Tarski's closest collaborator of the inter-war period. Around the end of October or beginning of November 1935 he married Janina Hosiasson, a fellow logician of the Lwow–Warsaw school. He and his wife were adherents of logical empiricism, participated in and contributed to the international unity of science movement, and were members of the original Vienna Circle. Sometime before the middle of August 1941 he and his sister Stefanja were shot to death in Naujoji Vilnia (Nowa Wilejka), 7 km east of Vilnius, by the occupying German forces or Lithuanian collaborators



1987 Evelyn Merle Nelson (November 25, 1943 – August 1, 1987), born Evelyn Merle Roden, was a Canadian mathematician. Nelson made contributions to the area of universal algebra with applications to theoretical computer science. Nelson's teaching record was, according to one colleague, "invariably of the highest order". However, before earning a faculty position at McMaster, prejudice against her lead to doubts about her teaching ability. Nelson published over 40 papers during her 20-year career before she died from cancer in 1987.
She, along with Cecilia Krieger, is the namesake of the Krieger–Nelson Prize, awarded by the Canadian Mathematical Society for outstanding research by a female mathematician. *Wik




1992 Leslie Fox (September 1918 Dewsbury, Yorkshire-1 August 1992 Oxford) was a British Mathematician noted for his contribution to numerical analysis.
Fox studied mathematics as a Scholar of Christ Church, Oxford graduating with a First in 1939 and continued to undertake research in the engineering department. While working on his D.Phil. in computational and engineering mathematics under the supervision of Sir Richard Southwell he was also engaged in highly secret war work. He worked on the numerical solution of partial differential equations at a time when numerical linear algebra was performed on a desk calculator. Computational efficiency and accuracy was thus even more important than in the days of electronic computers. Some of this work was published after the end of the Second World War jointly with his supervisor Richard Southwell.
On gaining his doctorate in 1942 Fox joined the Admiralty Computing service. Following the war, in 1945 he went to work in the mathematics division of the National Physical Laboratory. He left the National Physical Laboratory in 1956 and spent a year at the University of California. In 1957 Fox took up an appointment at Oxford University where he set up the Computing Laboratory. In 1963 Fox was appointed as Professor of Numerical Analysis at Oxford and Fellow of Balliol College, Oxford.
Fox's laboratory at Oxford was one of the founding organisations of the Numerical Algorithms Group, and Fox was also a dedicated supporter of the Institute of Mathematics and its Applications (IMA). The Leslie Fox Prize for Numerical Analysis of the IMA is named in his honour.*Wik


1996 Tadeusz Reichstein (20 July 1897 – 1 August 1996) was a Polish-born Swiss chemist, botanist and Nobel laureate.

Reichstein, with Philip S. Hench and Edward C. Kendall, received the Nobel Prize for Physiology or Medicine in 1950 for his discoveries concerning hormones of the adrenal cortex, their structure and biological effects. With his co-workers, Reichstein accomplished the first isolation of four active hormones from the adrenal cortex, the first synthesis of one of them, the proof of the steroid nature of said hormones, and numerous details on the structure and properties of these important bodies. This made synthesis possible, leading to the creation of new medications *TiS *Wik 




1999 Marie Paris Pişmiş de Recillas (30 January 1911 – 1 August 1999) was an Armenian-Mexican astronomer.

Pişmiş was born Mari Sukiasian (Armenian: Մարի Սուքիասեան) in 1911, in Ortaköy, Istanbul. She completed her high school studies at Üsküdar American Academy. In 1937, she became the first woman to get a Ph.D. from the Science Faculty of Istanbul University. Her advisor was Erwin Finlay Freundlich. Later, she went to Harvard University where she met her future husband Félix Recillas, a Mexican mathematician. They settled in Mexico, and she became the first professional astronomer in Mexico. According to Dorrit Hoffleit, "she is the one person most influential in establishing Mexico’s importance in astronomical education and research".

For more than 50 years she worked at UNAM which awarded her a number of prizes including the "Science Teaching Prize". She was a member of the Mexican Academy of Sciences.

Pişmiş studied among others the kinematics of galaxies, H II nebulae, the structure of open star clusters and planetary nebulae. She compiled the catalogue Pismis of 24 open clusters and 2 globular clusters in the southern hemisphere.

In 1998, she published an autobiography entitled "Reminiscences in the Life of Paris Pişmiş: a Woman Astronomer". She died in 1999. According to her wish, she was cremated. Her daughter Elsa Recillas Pishmish, son-in-law Carlos Cruz-González, and grand-daughter Irene Cruz-González also became astronomers. *Wik




2004 Philip Hauge Abelson (April 27, 1913 – August 1, 2004) was an American physicist, scientific editor and science writer. He proposed the gas diffusion process for separating uranium-235 from uranium-238 which was essential to the development of the atomic bomb. In collaboration with the U.S. physicist Edwin M. McMillan, he discovered a new element, later named neptunium, produced by irradiating uranium with neutrons. At the end WW II, his report on the feasibility of building a nuclear-powered submarine gave birth to the U.S. program in that field. In 1946, Abelson returned to the Carnegie Institution and pioneered in utilizing radioactive isotopes. As director of the Geophysics Laboratory of the Carnegie Institution (1953-71), he found amino acids in fossils, and fatty acids in rocks more than 1,000,000,000 years old. *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

On This Day in Math - July 31

                                                     



I advise my students to listen carefully the moment
they decide to take no more mathematics courses.
They might be able to hear the sound of closing doors.

~Caballero, James

The 212th day of the year; Besides being the Fahrenheit boiling point of water at sea level, 212 produces a prime of the form k10+k9+...+k2+k+1, when k=212. Edward Shore@edward_shore sent me a note:" That number would be 184,251,916,841,751,188,170,917.")
(students might explore different values of k, and different maximum exponents to produce primes..ie when k is 2, then 26 +25+...+22+2+1 is prime

The smallest even three-digit integer, abc, such that (abc)/(a*b*c) is also prime. [ie 212/(2*1*2)= 53 ]*Prime Curios

212 is a palindrome whose square is also a palindrome, 2122= 44944. It is the last year date for which this is true. It is also a palindrome in base 3(21212) with a copy of it's base 10 representation.

And I just learned from @fermatslibrary that 212 is in a palindromic approximation for π

666/212 = 3.141509... good for four decimal places.  





EVENTS


1669 Lucasian professor Isaac Barrow sent John Collins a manuscript of Newton’s De analysi and thereby Newton’s anonymity began to dissolve. It was a summary of Newton’s work on the calculus and was written after Newton saw Nicholas Mercator’s Logarithmotechnia (1668).

\( ln(1+x) = x -\frac{x^2}{2} + \frac{x^3}{3} -\frac{x^4}{4}+\cdots \)

Newton wrote his paper in order that he would not lose credit for his work on infinite series. Collins immediately recognized Newton’s genius. Although not published until 1711, this paper led to Newton’s appointment as Lucasian professor on 29 October 1669.*VFR




1730 Goldbach proves that Fermat numbers are pairwise coprime. (Fermat had said that the he thought the numbers of the form \( 2^{2^n} +1 \) were all prime, although he could not prove it. The first five are (n=0...4) but Euler would prove the n=5 case was not prime by factoring it. No more primes have been found after n=4, but there is no proof there can not be more. I think this story, and Goldbach's discovery, make an interesting approach to proving the primes are infinite.) He claims that 1 is the only square among the Fermat numbers *Euler Goldbach Correspondence




1744   Euler to Goldbach , "All around here chess is played passionately." He then mentions a certain strong local player he had been taking lessons from, then adds, "I am winning most games with him."  Master of us all in more ways than I knew.  *S. Strogatz  

Shortlisted for the Royal Society Science Book Prize 2019 A magisterial history of calculus (and the people behind it) from one of the world's foremost mathematicians. This is the captivating story of mathematics' greatest ever idea: 





1790 The U.S. Patent Office issued its first patent to Samuel Hopkins of Vermont for his “process for making pot and pearl ashes,” whatever they are. Since George Washington and Thomas Jefferson signed Hopkins’ patent, more than 4 million have been issued. *VFR In 1790, the first U.S. patent was granted to Samuel Hopkins of Vermont for a process for making potash and pearl ashes. Potash was important as an ingredient in soap and fertilizer. The patent was granted for a term of 14 years and signed by President George Washington, who had the previous month signed the first U.S. patent statute into law on 10 April 1790. Hopkins did not get Patent with a serial No.1 as thousands of patents were issued before the Patent Office began to number them. Congress had passed the Patent Act on 10 Apr 1790. Two other patents were granted that year - one for a new candle-making process and the other the flour-milling machinery of Oliver Evans. The next year, 1791, Samuel Hopkins also was granted the first Canadian patent.*TIS
*C. Pickover


1802  Earliest date for a Iron Maiden torture device.  The iron maiden is a mythical torture device, (Not to be confused with a more modern heavy metal band which was torture for many older adults.) believed to have been first created in the 19th century. It consists of a solid iron cabinet with a hinged front and spike-covered interior, sufficiently tall to enclose a human being. While often popularly thought to have been used in the medieval period, there is no known mention of the iron maiden from before the 19th century. It has become a popular image in media involving the Middle Ages and torture chambers.
Wolfgang Schild, a professor of criminal law, criminal law history, and philosophy of law at the Bielefeld University, has argued that putative iron maidens were pieced together from artifacts found in museums to create spectacular objects intended for (commercial) exhibition. Several 19th-century iron maidens are on display in museums around the world, including the Museum of Us, the Meiji University Museum, and several torture museums in Europe.
The most famous iron maiden that popularized the design was that of Nuremberg, first displayed possibly as far back as 1802. The original was lost in the Allied bombing of Nuremberg in 1945. A copy "from the Royal Castle of Nuremberg", crafted for public display, was sold through J. Ichenhauser of London to the Earl of Shrewsbury in 1890 along with other torture devices, and, after being displayed at the World's Columbian Exposition, Chicago, Illinois, 1893, was taken on an American tour.[14] This copy was auctioned in the early 1960s and is now on display at the Medieval Crime Museum, Rothenburg ob der Tauber.*Wik 




1851 Gauss witnessed the opening ceremonies when the newly constructed railway from Cassel reached Gottingen. *VFR

1943 Ireland issued—as its first stamp with a mathematical theme—two stamps to celebrate the centenary of the discovery of Quaternions by Sir William Rowan Hamilton. [Scott #126-7]. *VFR



1990The U.S. government panel approved the use of gene therapy to treat human disease. Gene therapy uses DNA to treat disease, usually by replacing a faulty gene with a healthy copy. Recent clinical studies suggest this technique holds promise for the future treatment of Parkinson’s disease. *.rsc.org


In 2003, Felix Baumgartner became the first man to cross the English Channel by unpowered flight. He jumped from a plane about 9,800-m (30,000-ft) above Dover, England and glided 36-km (22-mi) across the Channel in a 10-min flight wearing a special suit with carbon-fibre wings across his back. In sub-zero air, the 34-yr-old Austrian's flight began at about 220 mph, slowing to around 135 mph by the time he landed by parachute at Cap Blanc-Nez, near Calais, in France. He was equipped with oxygen, cameras and hi-tech data monitors to enable his journey to be tracked. His wing span of 1.8-m was about 10-cm longer than another he used a few weeks earlier to win a race against an aeroplane in the U.S.*TiS
He is widely known for jumping to Earth from a helium balloon from the stratosphere on 14 October 2012 and landing in New Mexico, United States, as part of the Red Bull Stratos project. Doing so, he set world records for skydiving an estimated 39 km (24 mi), reaching an estimated top speed of 1,357.64 km/h (843.6 mph), or Mach 1.25. He became the first person to break the sound barrier relative to the surface without vehicular power on his descent *Wik




2015 The second full moon this month (the other was on the 2nd). This only happens “Once in a blue moon”—and this is the origin of the phrase. Consequently, there were be thirteen full moons this year.  The last "blue moon" was in 1985, and the next is predicted in 2018.
The next blue moon takes place on 31 August 2023. As this Moon is also a supermoon, it will be a Super Blue Moon.
Supermoon: A Full or New Moon that occurs when the center of the Moon is less than 360,000 kilometers (ca. 223,694 miles) from the center of Earth.

*Farmer's Almanac





BIRTHS

1704 Gabriel Cramer (31 July 1704 – 4 January 1752). He is best known for “Cramer’s Rule,” a method for solving systems of simultaneous linear equations using determinants. *VFR Gabriel Cramer (31 July 1704 – 4 January 1752) was a Swiss mathematician, born in Geneva. He showed promise in mathematics from an early age. At 18 he received his doctorate and at 20 he was co-chair of mathematics. In 1728 he proposed a solution to the St. Petersburg Paradox that came very close to the concept of expected utility theory given ten years later by Daniel Bernoulli. He published his best known work in his forties. This was his treatise on algebraic curves, "Introduction à l'analyse des lignes courbes algébriques", published in 1750. It contains the earliest demonstration that a curve of the n-th degree is determined by n(n + 3)/2 points on it, in general position. He edited the works of the two elder Bernoullis; and wrote on the physical cause of the spheroidal shape of the planets and the motion of their apsides (1730), and on Newton's treatment of cubic curves (1746). He was professor at Geneva, and died at Bagnols-sur-Cèze.*Wik

*Geeks For Geeks


1712 Samuel König (July 31, 1712, Büdingen – August 21, 1757, Zuilenstein near Amerongen) was a German mathematician who is best remembered for his part in a dispute with Maupertuis over the Principle of Least Action.*SAU

1718 John Canton (31 July 1718 – 22 March 1772) British physicist and teacher, born Stroud, Gloucestershire. He made a number of minor discoveries in physics and chemistry. As a result of preparing artificial magnets in 1749 he was elected to the Royal Society. In 1762, he demonstrated that water was slightly compressible. He invented a number of devices in connection with electricity. His notable work, between 1756 and 1759, was to record that on days when the aurora borealis was particularly bright, a compass needle behaved with more irregularity than usual. Thus he was the first to record this as an electromagnetic phenomenon for what is now known to be a magnetic storm.*TIS



1810 Oliver Byrne (31 July 1810 – 9 December 1880) was a civil engineer and prolific author of works on subjects including mathematics, geometry, and engineering. He is best known for his 'colored' book of Euclid's Elements. He was also a large contributor to Spon's Dictionary of Engineering.
His most innovative educational work was a version of the first six books of Euclid's Elements that used colored graphic explanations of each geometric principle. It was published by William Pickering in 1847.

The book has become the subject of renewed interest in recent years for its innovative graphic conception and its style which prefigures the modernist experiments of the Bauhaus and De Stijl movements. Information design writer Edward Tufte refers to the book in his work on graphic design and McLean in his Victorian book design of 1963. In 2010 Taschen republished the work in a facsimile edition and in 2017 a project was launched to extend the work to the remaining works of Euclid.

Byrne described himself as a mathematician, civil engineer, military engineer, and mechanical engineer and indicates on the title pages of one of his books that he was surveyor of Queen Victoria's settlement in the Falkland Islands. Evidence shows Byrne never traveled to the Falkland Islands.




1826 Daniel Friedrich Ernst Meisse (31 July 1826, 11 March 1895)  his mathematical work covers number theory, work on Möbius inversion and the theory of partitions as well as work on Bessel functions, asymptotic analysis, refraction of light and the three body problem. 
He worked on prime numbers and found, in the 1870s, a method for computing individual values of 
π(x), the counting function for the number of primes less than or equal to 𝑥.  His method was based on recurrences for partial sieving functions, and he used it to compute π(107), π(108), and π(109 ). He found that there are 664,599 primes less than π(107), there are 5,761,455 primes less than π(108)  and 50,847,478 primes less than π(109 ) . However Derrick Lehmer simplified and extended Meissel's method 70 years later, and showed Meissel's value of π(109) was too small by 56. *SAU



1835 George Albert Wentworth (July 31, 1835 – May 24, 1906) was an American teacher and author of textbooks on mathematics including algebra, geometry, and trigonometry.

Wentworth was born in 1835 in Wakefield, New Hampshire, the youngest of eight children. He enrolled at Phillips Exeter Academy (PEA) in Exeter, New Hampshire, in 1852 and went on to graduate from Harvard College in 1858. While an undergraduate at Harvard he began teaching at PEA, and was appointed professor of mathematics there on March 23, 1858. One of his early students was Robert Todd Lincoln, who enrolled at PEA in the fall of 1859, and was visited in Exeter by his father, Abraham Lincoln, the following spring. When the future president spoke in Exeter on March 3, 1860, Wentworth was toastmaster at the event.

Wentworth wrote a series of textbooks on mathematics, of which The Boston Globe noted in 1886, "his Complete Algebra and Elements of Geometry are used extensively by many of the more important schools in America, and doubtless will, with but very few changes, be employed as standard works for a half century to come."

Wentworth remained at PEA for over 30 years, including serving as interim principal in 1889. He resigned his position as a professor in 1892, after which he continued to write textbooks. He was named a PEA trustee in 1899. Wentworth was also involved in banking, serving as a director of the National Granite State Bank; later, he became president of the Exeter Banking Company upon its formation in 1894. In 1903, Wentworth and George S. Morison donated the funding for construction of a new dormitory at PEA, Hoyt Hall, named after a former mathematics instructor. Wentworth was considered "a leading citizen in many activities."

In 1900, while Wentworth was visiting New Orleans, The Times-Picayune wrote, "There are not many young people of this generation, who have reached the age of discretion, who have not seen a Wentworth's arithmetic, an algebra, geometry, trigonometry, or an analytical trigonometry." A 1904 update to his textbook Plane and Solid Geometry was lauded for its discussion of limits, "believed to be the best presentation of the subject in any elementary geometry."

Wentworth died in 1906 in Dover, New Hampshire. His wife, Emily née Hatch from Covington, Kentucky, had died in 1895. He was survived by two sons and a daughter. His estate was estimated to have a value over $1 million ($35.8 million in 2025). One of his sons continued to update the textbooks and issued new ones. In 1920, Wentworth's textbooks were still in active use and were considered "one of the notable successes of the textbook history."

In 1925, PEA named Wentworth Hall, one of three new dormitories, in his honor. The school maintains a "George Albert Wentworth Professor in Mathematics" position, which is held by Gwynneth Coogan as of January 2024. Since 1962, Wentworth has been honored on a New Hampshire historical marker in his hometown of Wakefield.*Wic  I have Wentworth's 1895 Geometry.





1843 Friedrich Robert Helmert (July 31, 1843 – June 15, 1917) German geodesist and an important writer on the theory of errors.
From 1887 Helmert was professor of advanced geodesy at the University of Berlin and director of the Geodetic Institute.
Helmert received many honours. He was president of the global geodetic association of "Internationale Erdmessung", member of the Prussian Academy of Sciences in Berlin, was elected a member of the Royal Swedish Academy of Sciences in 1905, and recipient of some 25 German and foreign decorations. *TIA



1858 Richard Dixon Oldham (31 July 1858 – 15 July 1936) Irish geologist and seismologist who discovered evidence for the existence of the Earth's liquid core (1906). In studying seismograms of great 1897 Indian Earthquake he identified P (primary) and S (secondary) waves. It is interesting that he did not get a clue to the presence of the core from the S waves, which are actually incapable of being transmitted through the liquid of the outer core. (The liquid core does not transmit the shear wave energy released during an earthquake.) Rather he noted the existence of a shadow zone in which P waves from an earthquake in the opposite hemisphere of the earth failed to appear*TIS



1863 George Abram Miller (31 July 1863 – 10 February 1951) was an early group theorist whose many papers and texts were considered important by his contemporaries, but are now mostly considered only of historical importance.
Miller helped in the enumeration of finite groups of degree 8, 9, and 10. Arthur Cayley had listed 198 groups of degree 8 in 1891, and Miller found two more making the total 200 in 1893. Camille Jordan had given a list for degree 9 in 1872, re-examined by Cole, and brought up to 258 groups by Miller. In 1894 Miller produced a list of 294 intransitive groups of degree 10. In consequence, the Academy of Science of Cracow awarded a prize and "Miller came to prominence in the mathematical world abruptly."

Miller was born in Lynnville, Lehigh County, Pennsylvania, and died in Urbana, Illinois.*Wik



1923 Joseph Bishop Keller (July 31, 1923 – September 7, 2016) is an American mathematician who specializes in applied mathematics. He is best known for his work on the "Geometrical Theory of Diffraction" (GTD).
He worked on the application of mathematics to problems in science and engineering, such as wave propagation. He contributed to the Einstein-Brillouin-Keller method for computing eigenvalues in quantum mechanical systems.
In 1988 he was awarded the U.S. National Medal of Science, and in 1997 he was awarded the Wolf Prize by the Israel-based Wolf Foundation. In 1996, he was awarded the Nemmers Prize in Mathematics.*Wik



1923 Beauregard Stubblefield (31 July 1923, Navasota, Texas, - 17 January 2013
Atlanta, Georgia,)  
Stubblefield was the son of the watchmaker Clayton S Stubblefield and his wife Josephine Odessa Taylor who was a teacher. He was the second of his parents four children, having an older brother Cedric, a younger sister Iris and a younger brother Elwyn. The family moved to Houston when he was a young child. He attended Burrus Elementary and Junior High School, moving to Booker T Washington High School, a school for African Americans in Dallas, Texas, graduating in 1940. He then entered Prairie View Agricultural and Mechanical College on 5 September 1940 where he was taught mathematics by Clarence Francis Stephens. His remarkable mathematical abilities were quickly seen by Stephens who gave him one-to-one tuition. Stubblefield had been taught watchmaking by his father and was able to earn enough money to support his education. He graduated with a Bachelor's Degree in 1943 and, continuing to study supported by a scholarship, he was awarded a Master's Degree in 1945. His Master of Science thesis, supervised by A W Randall, was Computation Of The Real And Complex Roots Of Algebraic And Transcendental Equations.

Despite his excellent record, he was turned down for graduate work at several universities. When he received no answer from the University of Michigan, he went there in person and, impressed by his determination, he was offered a place. When he was told that since he had funding from Texas, he would have to pay Michigan more, he left and worked for the Hollis Jewelery store as a watchmaker for several years earning money to continue his studies. Returning to the University of Michigan, he was awarded an M.S. in 1951. He was appointed Professor and Head of the Department of Mathematics at the University of Liberia at Monrovia from 1952-1956, then worked as a Research Mathematician at Detroit Arsenal 1957-59. During this time he was undertaking research for his Ph.D. He published results from his thesis in the paper Some imbedding and nonimbedding theorems for n-manifolds (1962).

He was an assistant Professor of Mathematics at Stevens Institute of Technology in Hoboken, New Jersey (1960-1961), then an associate Professor of Mathematics at Oakland University in Michigan (1961-1967). After a spell as a Visiting Professor and Visiting Scholar at Texas Southern University, he was appointed Director of Mathematics in the Thirteen College Curriculum Program in 1969. In the paper New Approaches to General Education Mathematics for Developing Colleges (1971) he explained about this Program:
The Thirteen College Curriculum Program is a consortium of developing colleges which aims to improve freshman instruction and curriculum materials. As a large and promising project it is supported by private and public funds. ... The Program was launched in the Summer of 1967 with a writing conference. The conferees devised a new freshman program which attempted to release students from intellectual ruts in formalism and boredom. The course was called "Quantitative and Analytical Thinking," and the materials and techniques were tested on the thirteen campuses the following academic year. (Participants worked in close liaison with curriculum experts of the Curriculum Resources Group of the Institute for Services to Education who provided much of the inspiration for the emergent Thirteen College philosophy and techniques.) This pattern was repeated in successive years.
He was Professor of Mathematics at Appalachian State University in Boone, North Carolina (1971-1976), and then at the U.S. Department of Commerce in Boulder, Colorado where he worked until he retired in 1992. He died on 17 January 2013 in Atlanta, Georgia. *SAU




1923 Stephanie Kwolek (31 Jul 1923; 18 Jun 2014 at age 90) American chemist and inventor of Kevlar. Shortly after graduating with a bachelor's degree in chemistry (1946), she began a career at DuPont's textile fibers department in Buffalo, New York. Kwolek was assigned to search for a new, high-performance fiber that would be acid- and base-resistant and stable at high temperatures, suitable to replace steel in radial tyres. After extensive experimentation, she created a polymer solution which, when spun into a fibre, was five times stronger than steel and had half the density of fiberglass. It was named Kevlar. Today, this fibre is used to make bullet-proof jackets military helmets, aircraft parts, inflatable boats, gloves, rope, and building materials. Kwolek never pursued a Ph.D. degree. She was the fourth woman inducted into the National Inventors Hall of Fame (1995).TiS




1927 Felix Earl Browder ( July 31, 1927 – December 10, 2016) was an American mathematician known for his work in nonlinear functional analysis. He received the National Medal of Science in 1999 and was President of the American Mathematical Society until 2000. His two younger brothers also became notable mathematicians, William Browder (an algebraic topologist) and Andrew Browder (a specialist in function algebras).
Felix Earl Browder was born in 1927 in Moscow, Russia, while his American father Earl Browder, born in Wichita, Kansas, was living and working there. He had gone to the Soviet Union in 1927. His mother was Raissa Berkmann, a Russian Jewish woman from St. Petersburg whom Browder met and married while living in the Soviet Union. As a child, Felix Browder moved with his family to the United States, where his father Earl Browder for a time was head of the American Communist Party and ran for US president in 1936 and 1940. A 1999 book by Alexander Vassiliev, published after the fall of the Soviet Union, said that Earl Browder was recruited in the 1940s as a spy for the Soviet Union.

Felix Browder was a child prodigy in mathematics; he entered MIT at age 16 in 1944 and graduated in 1946 with his first degree in mathematics. In 1946, at MIT he achieved the rank of a Putnam Fellow in the William Lowell Putnam Mathematical Competition. In 1948 (at age 20), he received his doctorate from Princeton University.





1932 Elliott Hershel Lieb (July 31, 1932,  ) is an American mathematical physicist. He is a professor of mathematics and physics at Princeton University. Lieb's works pertain to the quantum and classical many-body problems, atomic structure, the stability of matter, functional inequalities, the theory of magnetism, and the Hubbard model.

Lieb was born in Boston in 1932. His family moved to New York when he was five. His father, from Lithuania, was an accountant, while his mother, from Bessarabia, worked as a secretary. 

Lieb received his B.S. in physics from the Massachusetts Institute of Technology in 1953 and his PhD in mathematical physics from the University of Birmingham in England in 1956. Lieb was a Fulbright Fellow at Kyoto University, Japan (1956–1957), and worked as the Staff Theoretical Physicist for IBM from 1960 to 1963. In 1961–1962, Lieb was on leave as professor of applied mathematics at Fourah Bay College, the University of Sierra Leone. In 1963, he joined the Yeshiva University as an associate professor. He has been a professor at Princeton since 1975, following a leave from his professorship at MIT.

Lieb is married to fellow Princeton professor Christiane Fellbaum.

For years, Lieb has rejected the standard practice of transferring copyright of his research articles to academic publishers. Instead, he would only give publishers his consent to publish.

Awards
Lieb has been awarded several prizes in mathematics and physics, including the Heineman Prize for Mathematical Physics of the American Physical Society and the American Institute of Physics (1978), the Max Planck Medal of the German Physical Society (1992), the Boltzmann medal of the International Union of Pure and Applied Physics (1998), the Schock Prize (2001), the Henri Poincaré Prize of the International Association of Mathematical Physics (2003), and the Medal of the Erwin Schrödinger Institute for Mathematics and Physics (2021).

In 2022 Lieb was awarded the Medal for Exceptional Achievement in Research from the American Physical Society for ″major contributions to theoretical physics through obtaining exact solutions to important physical problems, which have impacted condensed matter physics, quantum information, statistical mechanics, and atomic physics″ and the Carl Friedrich Gauss Prize at the International Congress of Mathematicians ″for deep mathematical contributions of exceptional breadth which have shaped the fields of quantum mechanics, statistical mechanics, computational chemistry, and quantum information theory.″ Also in 2022 he received the Dirac Medal of the ICTP jointly with Joel Lebowitz and David Ruelle.

Lieb is a member of the U.S. National Academy of Sciences and has twice served (1982–1984 and 1997–1999) as the president of the International Association of Mathematical Physics. Lieb was awarded the Austrian Decoration for Science and Art in 2002. In 2012 he became a fellow of the American Mathematical Society and in 2013 a Foreign Member of the Royal Society.

In 2023 Lieb received Kyoto Prize in Basic Sciences for his achievements in many-body physics. *Wik





1943 Ireland issued—as its first stamp with a mathematical theme—two stamps to celebrate the centenary of the discovery of Quaternions by Sir William Rowan Hamilton. [Scott #126-7].*VFR



1945 John O'Connor (31st July 1945 in Luton, Bedfordshire, England.- )
Lists his Research interests A lapsed topologist, I am interested in Computational Algebra.
I am interested in the History of Mathematics and at present am supervising two research students in this area. * His Personal web page
He is best known as one of the creators of the MacTutor History of Mathematics archive. *SAU





Yu Deng (: Dèng Yù, born June 1989) is a Chinese mathematician and a professor of mathematics at the University of Chicago. He is known for his contributions to partial differential equations, fluid dynamics, and probabilistic analysis. He was awarded the Fields Medal in 2026.

Early life and education
Deng was born in June 1989 in China. His father was a software engineer and his mother was a gastroenterologist. He was raised in Shenzhen, Guangdong, and began participating in mathematics competitions in primary school.

As a child, Deng excelled in tournaments of the Chinese strategy board game Go. In 2001, while in middle school, he competed professionally but failed to qualify for the national Go tournament in China. He later recalled, "Either Go or math. Since I lost, I decided to move my focus to math." As a first-year student at Shenzhen Senior High School, he won first prize at the Chinese Mathematical Olympiad. He then represented China in the 2006 International Mathematical Olympiad, where he won a gold medal at age 16.

Granted exemption from the Gaokao, Deng was admitted to Peking University in 2007, alongside Hong Wang. He was an undergraduate there until June 2009, transferring to the Massachusetts Institute of Technology (MIT), where he graduated with a Bachelor of Science in mathematics in 2011. He then received a Ph.D. in mathematics from Princeton University in 2015. As a doctoral student at Princeton, Deng won a Jacobus Fellowship, the university's highest honor for graduate students. His doctoral dissertation, completed under Alexandru D. Ionescu, was titled, "Long time behavior of some nonlinear dispersive equations". Ionescu described Deng in 2015 as "a brilliant student".

After receiving his doctorate, Deng was an instructor at the Courant Institute of Mathematical Sciences at New York University from 2015 to 2018. He became an assistant professor of mathematics at the University of Southern California in Los Angeles in 2018 and a full professor there in April 2024.

In September 2024, Deng joined the faculty of the University of Chicago as an associate professor of mathematics and was promoted to a full professorship in June 2025.

Deng works in partial differential equations and mathematical physics, particularly on probabilistic and combinatorial methods for nonlinear wave and particle systems. With Andrea Nahmod and Haitian Yue, he developed tools known as random tensors to study rough random initial data for the two-dimensional nonlinear Schrödinger equation, proving invariance of the associated Gibbs measure. With Zaher Hani at the University of Michigan, he subsequently used combinatorial expansions of interacting waves to rigorously derive the wave kinetic equation from the Schrödinger equation over the time scales predicted by physics.

Deng and his collaborators adapted these methods to systems of hard spheres. They derived the Boltzmann equation from Newtonian particle dynamics over long time scales, overcoming the repeated-collision problem that had restricted earlier results to very short times. For a periodic-box model, their work combined with earlier Boltzmann-to-Navier–Stokes limits to establish a rigorous passage from microscopic particle motion to macroscopic fluid behaviour in a major case of Hilbert's sixth problem.

In 2021, Yu received a Sloan Research Fellowship in recognition of outstanding early-career research. In 2025, he was awarded the Oberwolfach Prize for "his outstanding achievements in analysis and applied mathematics". In 2026, he was awarded the Clay Research Award for "remarkable derivation of the Boltzmann equation for long times, starting from a system of hard spheres".

On 23 July 2026, Yu was awarded the Fields Medal alongside Hong Wang, John Pardon, and Jacob Tsimerman at the International Congress of Mathematicians in Philadelphia, Pennsylvania. He and Hong Wang are the first Chinese citizens to be awarded the Fields Medal.*Wik








DEATHS


1726 Nikolaus II Bernoulli died (February 6, 1695, Basel, Switzerland – July 31, 1726, St. Petersburg, Russia). *VFR Nicolaus(II) Bernoulli was the favourite of three sons of Johann Bernoulli. He made important mathematical contributions to the problem of trajectories while working on the mathematical arguments behind the dispute between Newton and Leibniz.*SAU



1784 Denis Diderot died. (October 5, 1713 – July 31, 1784) was a French philosopher, art critic, and writer. He was a prominent persona during the Enlightenment and is best-known for serving as co-founder and chief editor of and contributor to the Encyclopédie. *Wik





1896 Ludwig Christian Wiener (7 December 1826 Darmstadt – 31 July 1896 Karlsruhe) was a German mathematician, physicist and philosopher, known for his explanation of Brownian motion , which identified him as a skillful experimenter. He mainly dealt with geometry.*Wik




1913 John Milne (30 December 1850 – 31 July 1913) English seismologist who invented the horizontal pendulum seismograph (1894) and was one of the European scientists that helped organize the seismic survey of Japan in the last half of the 1800's. Milne conducted experiments on the propagation of elastic waves from artificial sources, and building construction. He spent 20 years in Japan, until 1895, when a fire destroyed his property, and he returned home to the Isle of Wight. He set up a new laboratory and persuaded the Royal Society to fund initially 20 earthquake observatories around the world, equipped with his seismographs. By 1900, Milne seismographs were established on all of the inhabited continents and he was recognized as the world's leading seismologist. He died of Bright's disease*TIS


Milne died of Bright's disease on 31 July 1913 and, after a service in St. Paul's Church, Newport, was buried in the civic cemetery to the north of the church. His Japanese wife Tone returned to Japan in 1919 and died in 1926.*Wik





1980 Ernst Pascual Jordan ( 18 October 1902 – 31 July 1980) was a German theoretical and mathematical physicist who made significant contributions to quantum mechanics and quantum field theory. He contributed much to the mathematical form of matrix mechanics, and developed canonical anticommutation relations for fermions. He introduced Jordan algebras in an effort to formalize quantum field theory; the algebras have since found numerous applications within mathematics.

Jordan joined the Nazi Party in 1933, but did not follow the Deutsche Physik movement, which at the time rejected quantum physics developed by Albert Einstein and other Jewish physicists. After the Second World War, he entered politics for the conservative party CDU and served as a member of parliament from 1957 to 1961.




2016   Seymour Papert ( 1 Mar 1928, 31 Jul 2016) American computer scientist who invented the Logo computer programming language, an educational computer programming language for children. He studied under Piaget, absorbing his educational theories. He has studied ways to use mathematics to understand better how children learn and think, and about the ways in which computers can aid in a child's learning. With Marvin Minsky, he co-founded the Artificial Intelligence Lab at MIT. In the mid-80s he worked in Costa Rica to develop a nationwide program of intensive computer use throughout the public education system. Costa Rica, which now has the highest literacy rate in the A mericas, continues to serve as a model for large-scale deployment of computer technology in education. *TiS
Papert with a Turtle robot




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