One of the most baneful delusions by which the minds, not only of students, but even of many teachers of mathematics in our classical colleges, have been afflicted with is, that mathematics can be mastered by the favored few, but lies beyond the grasp and power of the ordinary mind.
~Florian Cajori, The Teaching and History of Mathematics in the United States
The 295th day of the year; 295 may be interesting only because it seems to be the least interesting day number of the year. (Willing to be contradicted, send your comments)
[Here are several of the best I received from David Brooks:
295 can be partitioned in 6486674127079088 ways.
295 is a 31-gonal number.]
And Derek Orr pointed out that "295 is the second proposed Lychrel number." A Lychrel number is a natural number that cannot form a palindrome through the iterative process of repeatedly reversing its digits and adding the resulting numbers. This process is sometimes called the 196-algorithm, after the most famous number associated with the process. In base ten, no Lychrel numbers have been yet proved to exist, but many, including 196, are suspected on heuristic and statistical grounds. The name "Lychrel" was coined by Wade Van Landingham as a rough anagram of Cheryl, his girlfriend's first name. (Who else thinks he probably mis-spelled her name and when she called him on it, he came up with the idea of a "rough anagram"? )
EVENTS1668 Leibniz writes to the German emperor to request permission to publish a "Nucleus Libareaus". This was the beginnings of the foundation of Acta Eruditorum, the first German scientific journal. Acta Eruditorum was founded in 1682 in Leipzig by Otto Mencke, with support from Gottfried Wilhelm Leibniz. Its purpose was to be a general learned journal: publishing reviews, excerpts, essays, notes, etc., largely in Latin. After Otto Mencke’s death in 1707, his son Johann Burckhardt Mencke took over. Later, in 1732, it changed its name to Nova Acta Eruditorum under subsequent editorship.
1685 Abraham De Moivre was a student of physics at the University, Collège d'Harcourt, in the 1680s. After the Revocation of the Edict of Nantes, (October 22, 1685 ) he went into seclusion in the priory of St. Martin (possibly that which became the Conservatoire National des Arts et Métiers ??) and then emigrated to England, having no contact with France until he was elected a Foreign Associate of the Academy of Sciences just before his death.*VFR known for de Moivre's formula, a formula that links complex numbers and trigonometry, and for his work on the normal distribution and probability theory.
He moved to England at a young age due to the religious persecution of Huguenots in France which reached a climax in 1685 with the Edict of Fontainebleau. He was a friend of Isaac Newton, Edmond Halley, and James Stirling. Among his fellow Huguenot exiles in England, he was a colleague of the editor and translator Pierre des Maizeaux.
De Moivre wrote a book on probability theory, The Doctrine of Chances, said to have been prized by gamblers. De Moivre first discovered Binet's formula, the closed-form expression for Fibonacci numbers linking the nth power of the golden ratio φ to the nth Fibonacci number. He also was the first to postulate the central limit theorem, a cornerstone of probability theory. *Wik
1746 Princeton chartered as the College of New Jersey -- the name by which it was known for 150 years -- Princeton University was British North America's fourth college. Located in Elizabeth for one year and then in Newark for nine, the College of New Jersey moved to Princeton in 1756. It was housed in Nassau Hall, which was newly built on land donated by Nathaniel FitzRandolph. Nassau Hall contained the entire College for nearly half a century. *Princeton Univ web page
In 1797, the first parachute jump was made by André-Jacques Garnerin, released from a balloon 2,230-ft above the Parc Monceau, Paris. He rode in a gondola fixed to the lines of a 23-ft diameter parachute, which was supported by a wooden pole and had its 32 white canvas gores folded like a closed umbrella. Lacking any vent in the top of the parachute, Garnerin descended with violent oscillations, and suffered the first case of airsickness. For his next jump, he added a hole in the top of the parachute. He made his fifth jump on 21 Sep 1802 over London, from a height of 3,000-ft. This was the first parachute descent made in England. He landed near St. Pancras Church. Having eliminated the center vent for this jump, he again suffered a fit of vomiting. *TIS See
1850 Fechner’s law introduced. [Springer’s 1985 Statistics Calendar] A pioneering though in many situations incorrect formulation of the relationship between the physical strength of a stimulus and its strength as perceived by humans, proposed by G. T. Fechner in 1860. Fechner postulated that sensation increases as the log of the stimulus. For example, by Fechner's law, if light A was twice as bright as light B (measured by an instrument), it would appear to the human eye to be log 2 (times a constant to allow for such factors as the units used) brighter than light B. Later experiments have shown conclusively that the Fechner's law doesn't generally apply. The Weber–Fechner laws are two related scientific laws in the field of psychophysics, known as Weber's law and Fechner's law. Both relate to human perception, more specifically the relation between the actual change in a physical stimulus and the perceived change. This includes stimuli to all senses: vision, hearing, taste, touch, and smell.
Ernst Heinrich Weber states that "the minimum increase of stimulus which will produce a perceptible increase of sensation is proportional to the pre-existent stimulus," while Gustav Fechner's law is an inference from Weber's law (with additional assumptions) which states that the intensity of our sensation increases as the logarithm of an increase in energy rather than as rapidly as the increase.
An illustration of the Weber–Fechner law. On each side, the lower square contains 10 more dots than the upper one. However the perception is different: On the left side, the difference between upper and lower square is clearly visible. On the right side, the two squares look almost the same.
The Weber–Fechner laws are two related scientific laws in the field of psychophysics, known as Weber's law and Fechner's law. Both relate to human perception, more specifically the relation between the actual change in a physical stimulus and the perceived change. This includes stimuli to all senses: vision, hearing, taste, touch, and smell.
Ernst Heinrich Weber states that "the minimum increase of stimulus which will produce a perceptible increase of sensation is proportional to the pre-existent stimulus," while Gustav Fechner's law is an inference from Weber's law (with additional assumptions) which states that the intensity of our sensation increases as the logarithm of an increase in energy rather than as rapidly as the increase.
An illustration of the Weber–Fechner law. On each side, the lower square contains 10 more dots than the upper one. However the perception is different: On the left side, the difference between upper and lower square is clearly visible. On the right side, the two squares look almost the same.
The Weber–Fechner laws are two related scientific laws in the field of psychophysics, known as Weber's law and Fechner's law. Both relate to human perception, more specifically the relation between the actual change in a physical stimulus and the perceived change. This includes stimuli to all senses: vision, hearing, taste, touch, and smell.
Ernst Heinrich Weber states that "the minimum increase of stimulus which will produce a perceptible increase of sensation is proportional to the pre-existent stimulus," while Gustav Fechner's law is an inference from Weber's law (with additional assumptions) which states that the intensity of our sensation increases as the logarithm of an increase in energy rather than as rapidly as the increase.
An illustration of the Weber–Fechner law. On each side, the lower square contains 10 more dots than the upper one. However the perception is different: On the left side, the difference between upper and lower square is clearly visible. On the right side, the two squares look almost the same.
1903 Simon Newcomb of Johns Hopkins decides to make it clear that aerial flight is impossible, less than two months before Kitty Hawk. "The Mathematicians of today admits that he can neither square the circle, or duplicate the cube, or trisect the angle. May not our mechanicians ... be ultimately forced to admit that aerial flight is one of the great class of problems with which man can never cope, and give up all attempts to grapple with it?""Imagine the proud possessor of the aeroplane darting through the air at a speed of several hundred feet per second! It is the speed alone that sustains him. How is he ever going to stop? Once he slackens his speed, down he begins to fall. He may, indeed, increase the inclination of his aeroplane. Then he increases the resistance necessary to move it. Once he stops he falls a dead mass. How shall he reach the ground without destroying his delicate machinery? I do not think the most imaginative inventor has yet even put upon paper a demonstrative, successful way of meeting this difficulty."
-- Simon Newcomb, "The Outlook for the Flying Machine," Independent, Oct. 22, 1903
1908 First meeting of the Spanish Association for the Advancement of Science was held October 22–29. Sixteen papers were read in the section of mathematics.*VFR
1922 M. C. ESCHER visited here(Alhambra) on 18 - 24 Oct 1922 and was impressed by the patterns, but he didn't really use them in his art until after his second visit on 22-26 May 1936 *VFR
1933 The Solvay Congress in Brussells opens on 22 October, 1933 which was attended by leading Nuclear physicists around the world. Attendees included two future key Manhattan Project scientists (Fermi and Lawrence), the future head of the Nazi atomic bomb program (Heisenberg), and numerous leading pre-war physicists. Among the group, three women seated in the front row, from left to right, Irene Joliet-Curie, Marie Curie, and Lise Meitner. The meeting would last through the 29th of the month.*PB
1938 In the back of a beauty shop in the Astoria section of Queens New York, Chester A. Carlson and his assistant Otto Kornei, conducted the first successful experiment in electrophotography. The message, “10.-22.-38 ASTORIA,” was even less inspiring than Alexander Graham Bell’s first phone conversation, but the effect was just as great. In 1949 Haloid Corporation marketed the Xerox Model A, a crude machine that required fourteen manual operations. Today five million copiers churn out 2,000 copies each year for every American citizen. *VFR
Carlson was an engineer who couldn't get a job in his field during the Great Depression, so he took work in the patent department of battery-manufacturer P.R. Mallory. A bottleneck in the work was making copies of patent documents: You had to copy them by hand (time and labor) or send them out to be photographed (time and expense).
Carlson set out to make a dry-copying process. He got his inspiration from the new field of photoconductivity: Light striking the surface of certain materials increases the flow of electrons. Carlson knew he could use the effect to make dry copies. Project an image of the original document onto a photoconductive surface, and current would flow only where light struck.
Four years of tinkering in his kitchen and in his mother-in-law's beauty salon in Astoria, Queens, in New York City finally produced results in October 1938. Carlson's research assistant, Otto Kornei, put a sulfur coating on a zinc plate, which was rubbed with a handkerchief to give it an electrostatic charge.
Evelyn (Boka) Van Orden Sent me a followup note, “On the 75th anniversary of Xerography — October 22, 2013 — I was privileged to attend an event titled "Chester Chester Chester" at Xerox PARC.”
George Shea first stumbled on Chester Carlson in 1981 when he came upon a passage about the little known inventor (even today, most Americans have never heard of Carlson) in an obscure book on the subject of "Copy Art."
George was fascinated by the tale of struggle, patience, late success, and spiritual enlightenment and began digging into Carlson's life. In 1988 he visited the former janitor's closet in Astoria in which Carlson made the world's first xerograhic copy on Oct. 22, 1938. The ceiling still displayed obvious sulfur stains from Chester’s and Otto Kornei’s experiments.
1975 the Soviet unmanned space mission Venera 9 lands on Venus. measurements taken included surface pressure of about 9,100 kilopascals (90 atm), temperature of 485 °C (905 °F), and surface light levels comparable to those at Earth mid-latitudes on a cloudy summer day. *the painter flynn
BIRTHS
1511 Erasmus Reinhold (October 22, 1511 – February 19, 1553) was a German astronomer and mathematician, considered to be the most influential astronomical pedagogue of his generation. He was born and died in Saalfeld, Saxony.
He was educated, under Jacob Milich, at the University of Wittenberg, where he was first elected dean and later became rector. In 1536 he was appointed professor of higher mathematics by Philipp Melanchthon. In contrast to the limited modern definition, "mathematics" at the time also included applied mathematics, especially astronomy. His colleague, Georg Joachim Rheticus, also studied at Wittenberg and was appointed professor of lower mathematics in 1536.
Reinhold catalogued a large number of stars. His publications on astronomy include a commentary (1542, 1553) on Georg Purbach's Theoricae novae planetarum. Reinhold knew about Copernicus and his heliocentric ideas prior to the publication of De revolutionibus and made a favorable reference to him in his commentary on Purbach. However, Reinhold (like other astronomers before Kepler and Galileo) translated Copernicus' mathematical methods back into a geocentric system, rejecting heliocentric cosmology on physical and theological grounds.
It was Reinhold's heavily annotated copy of De revolutionibus in the Royal Observatory, Edinburgh that started Owen Gingerich on his search for copies of the first and second editions which he describes in The Book Nobody Read. In Reinhold's unpublished commentary on De revolutionibus, he calculated the distance from the Earth to the sun. He "massaged" his calculation method in order to arrive at an answer close to that of Ptolemy.*Wik
1587 Joachim Jungius (22 Oct 1587 in Lübeck, Germany - 23 Sept 1657 in Hamburg) a German mathematician who was one of the first to use exponents to represent powers and who used mathematics as a model for the natural sciences. Jungius proved that the catenary is not a parabola (Galileo assumed it was). *SAU (I can not find the first use by Jungius anywhere, but Cajori gives Descartes 1637 use in Geometrie as the first example of the common form today. A year earlier, James Hume produced a copy of Viete's Algebra in which he used exponents as powers of numbers, but his exponents were Roman Numerals.)[Nicolas Chuquet (1445-1488) was the first to use numbers as exponents, and the first to use negative numbers as exponents, but didn't use raised -1 for inverse.]
1659 Georg Ernst Stahl (22 October 1659 – 24 May 1734) was a German chemist, physician and philosopher. He was a supporter of vitalism, and until the late 18th century his works on phlogiston were accepted as an explanation for chemical processesStahl used the works of Johann Joachim Becher to help him come up with explanations of chemical phenomena. The main theory that Stahl got from J. J. Becher was the theory of phlogiston. This theory did not have any experimental basis before Stahl. He was able to make the theory applicable to chemistry.Becher's theories attempted in explaining chemistry as comprehensively as seemingly possible through classifying different earths according to specific reactions. Terra pinguis was a substance that escaped during combustion reactions, according to Becher.[10] Stahl, influenced by Becher's work, developed his theory of phlogiston.People who dismiss Phlogiston theory as early ignorance should read The Renaissance Mathematicus blog, The Phlogiston Theory – Wonderfully wrong but fantastically fruitful.
1792 Guillaume-Joseph-Hyacinthe-Jean-Baptiste Le Gentil de la Galaziere (12 Sep 1725; 22 Oct 1792) was a French astronomer who attempted to observe the transit of Venus across the sun by travelling to India in 1761. He failed to arrive in time due to an outbreak of war. He stayed in India to see the next transit which came eight years later. This time, he was denied a view because of cloudy weather, and so returned to France. There, he found his heirs had assumed he was dead and taken his property.*TIS A more detailed blog about his life is at Renaissance Mathematicus
1843 John S Mackay graduated from St Andrews University and taught at Perth Academy and Edinburgh Academy. He was a founder member of the EMS and became the first President in 1883 and an honorary member in 1894. He published numerous papers on Geometry in the EMS Proceedings.*SAU
1881 Clinton Joseph Davisson (22 Oct 1881; 1 Feb 1958) American experimental physicist who shared the Nobel Prize for Physics in 1937 with George P. Thomson of England for discovering that electrons can be diffracted like light waves. Davisson studied the effect of electron bombardment on surfaces, and observed (1925) the angle of reflection could depend on crystal orientation. Following Louis de Broglie's theory of the wave nature of particles, he realized that his results could be due to diffraction of electrons by the pattern of atoms on the crystal surface. Davisson worked with Lester Germer in an experiment in which electrons bouncing off a nickel surface produced wave patterns similar to those formed by light reflected from a diffraction grating, and supporting de Broglie's electron wavelength = (h/p). *TIS
1895 Rolf Herman Nevanlinna ( 22 October 1895 – 28 May 1980) was a Finnish mathematician who made significant contributions to complex analysis.
When Nevanlinna earned his doctorate in 1919, there were no university posts available so he became a school teacher. His brother, Frithiof, had received his doctorate in 1918 but likewise was unable to take up a post at a university, and instead began working as a mathematician for an insurance company. Frithiof recruited Rolf to the company, and Nevanlinna worked for the company and as a school teacher until he was appointed a Docent of Mathematics at the University of Helsinki in 1922. During this time, he had been contacted by Edmund Landau and requested to move to Germany to work at the University of Göttingen, but did not accept.
After his appointment as Docent of Mathematics, he gave up his insurance job but did not resign his position as school teacher until he received a newly created full professorship at the university in 1926. Despite this heavy workload, it was between the years of 1922–25 that he developed what would become to be known as Nevanlinna theory.
From 1947 Nevanlinna had a chair in the University of Zurich, which he held on a half-time basis after receiving in 1948 a permanent position as one of the 12 salaried Academicians in the newly created Academy of Finland.
Rolf Nevanlinna's most important mathematical achievement is the value distribution theory of meromorphic functions. The roots of the theory go back to the result of Émile Picard in 1879, showing that a non-constant complex-valued function which is analytic in the entire complex plane assumes all complex values save at most one. In the early 1920s Rolf Nevanlinna, partly in collaboration with his brother Frithiof, extended the theory to cover meromorphic functions, i.e. functions analytic in the plane except for isolated points in which the Laurent series of the function has a finite number of terms with a negative power of the variable. Nevanlinna's value distribution theory or Nevanlinna theory is crystallised in its two Main Theorems. Qualitatively, the first one states that if a value is assumed less frequently than average, then the function comes close to that value more often than average. The Second Main Theorem, more difficult than the first one, states roughly that there are relatively few values which the function assumes less often than average.
A trivia footnote from Lee Guthrie: “One of his steerable antennas on display at Green Bank’s museum uses the differential axis out of a “T” model Ford.”
1907 Sarvadaman D. S. Chowla (22 October 1907, London–10 December 1995, Laramie, Wyoming) was a prominent Indian mathematician, specializing in number theory. Among his contributions are a number of results which bear his name. These include the Bruck–Chowla–Ryser theorem, the Ankeny–Artin–Chowla congruence, the Chowla–Mordell theorem, and the Chowla–Selberg formula, and the Mian–Chowla sequence.*Wik
1916 Nathan Jacob Fine (22 October 1916 in Philadelphia, USA - 18 Nov 1994 in Deerfield Beach, Florida, USA) He published on many different topics including number theory, logic, combinatorics, group theory, linear algebra, partitions and functional and classical analysis. He is perhaps best known for his book Basic hypergeometric series and applications published in the Mathematical Surveys and Monographs Series of the American Mathematical Society. The material which he presented in the Earle Raymond Hedrick Lectures twenty years earlier form the basis for the material in this text.*SAU
1927 Alexander Ivanovich Skopin (22 Oct 1927 in Leningrad (now St Petersburg), Russia - 15 Sept 2003 in St Petersburg, Russia) He was a Russian mathematician known for his contributions to abstract algebra. Skopin's student work was in abstract algebra, and concerned upper central series of groups and extensions of fields. In the 1970s, Skopin received a second doctorate concerning the application of computer algebra systems to group theory. From that point onward he used computational methods extensively in his research, which focused on lower central series of Burnside groups. He related this problem to problems in other areas of mathematics including linear algebra and topological sorting of graphs. *Wik
1941 Stanley Mazor was born in Chicago on October 22, 1941. He studied mathematics and programming at San Francisco State University. He joined Fairchild Semiconductor in 1964 as a programmer and then a computer designer in the Digital Research Department where he shares patents on the Symbol computer. In 1969, he joined Intel. In 1977, he began his teaching career in Intel's Technical Training group, and later taught classes at Stanford, University of Santa Clara, KTH in Stockholm and Stellenbosch, S.A. In 1984 he was at Silicon Compiler Systems. He co-authored a book on chip design language while at Synopsys 1988-1994. He was invited to present The History of the Microcomputer at the 1995 IEEE Proceedings. He is currently the Training Director at BEA Systems. *CHM.jpg)
1965 Henri Rene Darmon (born 22 October 1965) is a French-Canadian mathematician. He is a number theorist who works on Hilbert's 12th problem and its relation with the Birch–Swinnerton-Dyer conjecture. He is currently a professor of mathematics at McGill University.
Darmon received his BSc from McGill University in 1987 and his PhD from Harvard University in 1991 under supervision of Benedict Gross. From 1991 to 1996, he held positions in Princeton University. Since 1994, he has been a professor at McGill University.
Darmon was elected to the Royal Society of Canada in 2003. In 2008, he was awarded the Royal Society of Canada's John L. Synge Award.He received the 2017 AMS Cole Prize in Number Theory "for his contributions to the arithmetic of elliptic curves and modular forms", and the 2017 CRM-Fields-PIMS Prize, which is awarded in recognition of exceptional research achievement in the mathematical sciences. He was elected as a Fellow of the American Mathematical Society, in the 2025 class of fellows. He was awarded the 2026 Jeffery-Williams Prize, in recognition of his important and sustained contributions to number theory and arithmetic geometry.
Darmon is married to Galia Dafni, also a mathematician at Concordia University.*Wik
DEATHS
1950 Ada Isabel Maddison (13 April 1869 in Cumberland, England - 22 Oct 1950 in Martin's Dam, Wayne, Pennsylvania, USA) A British mathematician best known for her work on differential equations. Although Maddison passed an honors exam for the University of Cambridge, she was not given a degree there. Instead, she went to Bryn Mawr in Pennsylvania. In 1893, the University of London awarded her a bachelor's degree in mathematics with honors. After further study at the University of Göttingen where she worked under Felix Klein and David Hilbert — two of the most influential mathematicians of the period. Göttingen was at that time the world’s leading mathematical center, and Klein in particular encouraged women to pursue advanced studies there (even though women were not yet officially matriculated students),Maddison’s research at Göttingen focused on linear differential equations, specifically those with periodic coefficients. Her doctoral dissertation, completed later at Bryn Mawr College in 1896 under Charlotte Angas Scott, was titled:
“On Singular Solutions of Differential Equations of the First Order in Two Variables and the Geometrical Properties of Certain Invariants and Covariants of Their Complete Primitives.”
Maddison stayed Bryn Mawr, where she taught as well as doing time consuming administrative work. Her will endowed a pension fund for Bryn Mawr's administrative staff.*Wik
1977 Beniamino Segre (16 February 1903 – 22 October 1977) was an Italian mathematician who is remembered today as a major contributor to algebraic geometry and one of the founders of combinatorial geometry. Among his main contributions to algebraic geometry are studies of birational invariants of algebraic varieties, singularities and algebraic surfaces. His work was in the style of the old Italian School, although he also appreciated the greater rigor of modern algebraic geometry. Another contribution of his was the introduction of finite and non-continuous structures into geometry. In his best known paper he proved the following theorem: In a Desarguesian plane of odd order, the ovals are exactly the irreducible conics. Some critics felt that his work was no longer geometry, but today it is recognized as a separate sub-discipline: combinatorial geometry.
In 1938 he lost his professorship as a result of the anti-Jewish laws enacted under Benito Mussolini's government; he spent the next 8 years in Great Britain (mostly at the University of Manchester), then returned to Italy to resume his academic career *Wik
1979 Reinhold Baer (22 July 1902 in Berlin, Germany - 22 Oct 1979 in Zurich, Switzerland) Baer's mathematical work was wide ranging; topology, abelian groups and geometry. His most important work, however, was in group theory, on the extension problem for groups, finiteness conditions, soluble and nilpotent groups. *SAU
Credits :
*CHM=Computer History Museum
*FFF=Kane, Famous First Facts
*NSEC= NASA Solar Eclipse Calendar
*RMAT= The Renaissance Mathematicus, Thony Christie
*SAU=St Andrews Univ. Math History
*TIA = Today in Astronomy
*TIS= Today in Science History
*VFR = V Frederick Rickey, USMA
*Wik = Wikipedia
*WM = Women of Mathematics, Grinstein & Campbell
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