That which is not good for the bee-hive cannot be good for the bees. ~ Marcus Aurelius
The 191st day of the year; 191 is a palindromic prime and when it is doubled and one is added to this result, the resulting number is yet another palindromic prime. (Students might consider why 11 is the only palindromic prime with an even number of digits.)
By adding up the values of the common US coins, one obtains 191 ¢ (silver dollar + half dollar + quarter + dime + nickel + penny) *From Number Gossip (This ignores the once minted 5 mil, or half-cent coin and the briefly lived 2 cent coins) Canadians would have a larger sum of coins since Canada has had a $1 coin (The Loonie) since 1987 and a $2 coin (The Toonie) for about 10 years. I think the Canadian total would be 341 (no half dollar) so maybe we can squeeze them in by the end of the year.
191 is the smallest palindromic prime p such that neither 6p - 1 nor 6p + 1 is prime. Also, The smallest multidigit palindromic prime that yields a palindrome when multiplied by the next prime: 191 * 193 = 36863. *Prime Curios
191 is the first prime in a prime quadruplet, 191, 193, 197, 199. The sum of their digits are also prime 11, 13, 17, and 19. This is the last prime quadruplet that are year days.
The prime quadruplet {11, 13, 17, 19} is alleged to appear on the Ishango bone although this is disputed.
Around 1960 an ancient mathematical record on bone was uncovered in the African area of Ishango, near Lake Edward. While it was at first considered an ancient (9000 BC) tally stick, many now think it represents the oldest table of prime numbers.
See More Math Facts for every year date here
EVENTS
1600 Kepler’s interest in optics arose as a direct result of his observations of the partial solar eclipse of 10 July 1600. Following instructions from Tycho Brahe, he constructed a pinhole camera; his measurements, made in the Graz marketplace, closely duplicated Brahe’ and seemed to show that the moon’s apparent diameter was considerably less than the sun’s. Kepler soon realized that the phenomenon resulted from the finite aperture of the instrument; his analysis, assisted by actual threads, led to a clearly defined concept of the light ray, the foundation of modern geometrical optics.
Kepler’s subsequent work applied the idea of the light ray to the optics of the eye, showing for the first time that the image is formed on the retina. He introduced the expression “pencil of light,” with the connotation that the light rays draw the image upon the retina; he was unperturbed by the fact that the image is upside down. *Encyclopedia.com
The "pinhole camera" mentioned above was more likely a darkened room with a pinhole aperture, called a camera obscura, a term that many assert was coined by Kepler himself.
1610 Galileo receives a letter from Cosimo II agreeing to his salary requests, and confirming him as "First Mathematician of our Stadium in Pisa" but with no requirements that he live or lecture in Pisa, "except when it may please you as an honor." *The Copernican Question: Prognostication, Skepticism, and Celestial Order By Robert S. Westman
1637 First meeting of the Acad´emie Fran¸caise. *VFR
1676 Flamsteed began living at the Observatory with his two servants. On 19 July, his long series of Greenwich observations began? *Rebekah Higgitt, Teleskopos
1794 Star in a crescent moon? Astronomer Royal Investigates. The results are read to the Royal Society..."An Account of an Appearance of Light, like a Star, Seen Lately in the Dark Part of the Moon, by Thomas Stretton, in St. John's Square, Clerkenwell, London; with Remarks upon This Observation, and Mr. Wilkins's. Drawn up, and Communicated by the Rev. Nevil Maskelyne, D. D. F. R. S. and Astronomer Royal" *Phil. Trans. R. Soc. Lond. January 1, 1794 84:435-440;
In the "Philosophical Transactions" for 1794 it is stated:--Three persons in Norwich, and one in London, saw a star on the evening of March 7th, 1794, in the dark part of the moon, which had not then attained the first quadrature; and from the representations which are given the star must have appeared very far advanced upon the disc. On the same evening there was an occultation of Aldebaran, which Dr. Maskelyne thought a singular coincidence, but which would now be acknowledged as the cause of the phenomenon."
Some suspect a bright crescent moon appears larger and stars near the periphery might look inside the crescent.
1796 Date of the entry EγPHKA! num=Δ+Δ+Δ in Gauss’s scientific diary, recording his discovery that every positive integer is the sum of three triangular numbers. [Thanks to Howard Eves]
Gauss was 19 at this time, and would go on to study sums of other figurate numbers. This particular result is connected to what would later become part of Waring's problem and the study of quadratic forms.
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1826 Cauchy presented a proof to the Acad´emie dealing with existence theorems for first-order differential equations. [Ivor Grattan-Guiness, Convolutions in French Mathematics, 1800–1840, pp. 758 and 1401] *VFR
1843 Jacques Philippe Marie Binet, age 57, elected to the Acad´emie des Sciences to succeed Lacroix. He is an example of a mathematician who published much late in life. He worked in mechanics, elasticity, perturbation theory, determinants, and the calculus. [Ivor Grattan-Guiness, Convo¬lutions in French Mathematics, 1800–1840, pp. 191 and 1410] *VFR
Binet's formula for the Fibonacci numbers using the "Golden Mean".
1908 at 5:45 in the morning, Kammerlingh Onnes, of Leiden, wins the race to produce liquified helium. 75 liters of liquid air is used to condense 20 liters of liquid oxygen, from which 20 milli-liters of liquid helium under reduced pressure. *Quantum Generations: A History of Physics in the Twentieth Century By Helge Kragh
1925 The “Monkey Trial” of John T. Scopes began in Dayton, Tennessee. Clarence Darrow defended him. The prosecution, conducted by William Jennings Bryan, presented a strong case, and he was convicted of violating a state law prohibiting the teaching of evolution. Although the law was later overturned, this case provided a strong blow to science education. Scopes was not a biologist and never taught evolution. Rather he was a mathematics and physics teacher who volunteered to stand trial to furnish a test case. *VFR
The trial ran for 12 days. A local school teacher, John Scopes, was prosecuted under the state's Butler Act, but was supported by the American Civil Liberties Union. This law, passed a few months earlier (21 Mar 1925) prohibited the teaching of evolution in public schools. The trial was a platform to challenge the legality of the statute. Local town leaders,(wishing for the town to benefit from the publicity of the trial) had recruited Scope to stand trial. He was convicted (25 Jul) and fined $100. On appeal, the state supreme court upheld the constitutionality of the law but acquitted Scopes on the technicality that he had been fined excessively. The law was repealed on 17 May 1967. *TIS
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| Scopes Marker Paducah Ky |
1950 France honors Lazar Carnot (1753–1823) with a postage stamp. [Scott #B251]. *VFR
1950 The German Democratic Republic, to celebrate the 250th anniversary of the founding of the Academy of Sciences, Berlin, issued postage stamps picturing Leonhard Euler and Gottfried von Leibniz. [Scott #58, 66]. *VFR And others," leonhard euler, alexander freiherr von humboldt, theodor mommsen, wilhelm freiherr von humboldt, hermann von helmholtz, max planck, jacob grimm, walther nernst, gottfried wilhelm leibniz, adolf harnack"
Leibniz was also honored with stamp issues in 1980 and 1996 it seems.
1962 Trans-Atlantic television and other communications became a reality as the Telstar communications satellite was launched. A product of AT&T Bell Laboratories, the satellite was the first orbiting international communications satellite that sent information to tracking stations on both sides of the Atlantic Ocean. Initial enthusiasm for making phone calls via the satellite waned after users realized there was a half-second delay as a result of the 25,000-mile transmission path.*CHM
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1993 MASH fans will remember that there was always a sign telling how many miles to Toledo and frequently they talked of the hotdogs at Tony Pacos (they are good). On this date the Cake Walk and Jazz Band (I believe the band is called "The Cakewalken Jass Band") celebrated their twenty-fifth anniversary with a live broadcast at Tony Pacos that was broadcast on public radio in Toledo. So what does this have to do with mathematics? Well, Ray Heitger, their clarinetist, leader, and one of the founding members happens to be a math teacher. If you can’t get to Toledo to hear them play, perhaps you can find one of their six LPs.*VFR
Tony Packo's Cafe is restaurant that started in the Hungarian neighborhood of Birmingham, on the east side of Toledo, Ohio at 1902 Front Street. The restaurant gained notoriety by its mention in several M*A*S*H episodes and is famous for its signature sandwich and large collection of hot dog buns signed by celebrities. In 2024 it is still there. *Wik
2026 The Association for Women in Mathematics (AWM) and the Society for Industrial and Applied Mathematics (SIAM) announce that Fioralba Cakoni has been selected as the 2026 Sonia Kovalevsky Lecturer.
Fioralba Cakoni is a Distinguished Professor of Mathematics at Rutgers University, New Brunswick, where she has been since 2015. Prior to joining Rutgers, she was a postdoctoral Alexander von Humboldt Research Fellow at the University of Stuttgart, Germany, and later a faculty member in the Department of Mathematical Sciences at the University of Delaware. She has also held visiting research positions at École Polytechnique and École Nationale Supérieure de Technique Avanceés (ENSTA) in Paris. Professor Cakoni was named a Simons Fellow in Mathematics in 2016, elected a Fellow of the American Mathematical Society in 2019, and a Fellow of the Society for Industrial and Applied Mathematics in 2023.
Professor Cakoni works in inverse scattering for inhomogeneous media, noniterative reconstruction methods, spectral methods in inverse scattering, and inverse problems for partial differential equations. She is one of the founders and leading proponents of the qualitative approach to inverse scattering theory, a development that has been described as a paradigm shift in the field of inverse problems. Her influential research in this area has shaped the design of new methods in nondestructive testing and wave-based imaging.
Please join AWM in congratulating Professor Cakoni! Her lecture will be delivered at the2026 SIAM Annual Meeting taking place in Cleveland, Ohio, July 6 –10, 2026. *AWM
#onthisdayinmath
BIRTHS
1682 Roger Cotes born (10 July 1682 — 5 June 1716). In January 1706 he was named the first Plumian professor of astronomy and natural philosophy at Cambridge. It was Cotes who first showed that e was the natural base to choose for the logarithm. *VFR He did not realize his full potential because he died at age 33, leaving an unfinished series of imposing researches on optics and a large number of other unpublished manuscripts. Newton, who seldom spoke well of anyone else, said of Cotes, "If Cotes had lived, we might have known something."
Thony Christie at the Renaissance Mathematicus has a nice post about Cotes.
"Those who assume hypotheses as first principles of their speculations ... may indeed form an ingenious romance, but a romance it will still be."
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1832 Alvan Graham Clark (July 10, 1832 – June 9, 1897) U.S. astronomer, one of an American family of telescope makers and astronomers who supplied unexcelled lenses to many observatories in the U.S. and Europe during the heyday of the refracting telescope. He began a deep interest in astronomy while still at school, then joined the family firm of Alvan Clark & Sons, makers of astronomical lenses. In 1861, testing a new lens, he looked through it at Sirius and observed faintly beside it, Sirius B, the twin star predicted by Friedrich Bessel in 1844. Carrying on the family business, after the deaths of his father and brother, Clark made the 40" lenses of the Yerkes telescope (still the largest refractor in the world). Their safe delivery was a source of anxiety. He died shortly after their first use. *TIS
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1856 Nikola Tesla (10 July 1856 – 7 January 1943)Serbian-American inventor and researcher who designed and built the first alternating current induction motor in 1883. [This statement seems to be in error,according to Wikipedia which states," In 1824, the French physicist François Arago formulated the existence of rotating magnetic fields, termed Arago's rotations, which, by manually turning switches on and off, Walter Baily demonstrated in 1879 as in effect the first primitive induction motor. Practical alternating current induction motors seem to have been independently invented by Galileo Ferraris(1885) and then Tesla (1887).]He emigrated to the United States in 1884. Having discovered the benefits of a rotating magnetic field, the basis of most alternating-current machinery, he expanded its use in dynamos, transformers, and motors. Because alternating current could be transmitted over much greater distances than direct current, George Westinghouse bought patents from Tesla the system when he built the power station at Niagara Falls to provide electricity power the city of Buffalo, NY. [Born in Croatia of Serbian parents. Some sources give birthdate as 9 Jul; he is said to have been born on the stroke of midnight.]
1878 Oliver Dimon Kellogg (10 July 1878 in Linwood, Pennsylvania, USA - 26 July 1932 in Greenville, Maine, USA) was appointed to the University of Missouri in 1905 where, despite a heavy teaching and administrative load he was able to publish impressive papers on potential theory. In 1908 he published three papers, namely Potential functions on the boundary of their regions of definition and Double distributions and the Dirichlet problem, both in the Transactions of the American Mathematical Society, and A necessary condition that all the roots of an algebraic equation be real in the Annals of Mathematics. In 1912 he published the important work Harmonic functions and Green's integral in the Transactions of the American Mathematical Society. This paper includes what today is called 'Kellogg's theorem' on harmonic and Green's functions. *SAU
1883 Frank Albert Benford, Jr., ((see note below about date of birth)1883 Johnstown, Pennsylvania – December 4, 1948) was an American electrical engineer and physicist best known for rediscovering and generalizing Benford's Law, a statistical statement about the occurrence of digits in lists of data.
Benford is also known for having devised, in 1937, an instrument for measuring the refractive index of glass. An expert in optical measurements, he published 109 papers in the fields of optics and mathematics and was granted 20 patents on optical devices.
His date of birth is given variously as May 29 or July 10, 1883. After graduating from the University of Michigan in 1910, Benford worked for General Electric, first in the Illuminating Engineering Laboratory for 18 years, then the Research Laboratory for 20 years until retiring in July 1948. He died suddenly at his home on December 4, 1948. *Wik
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1917 Donald Jeffry Herbert (July 10, 1917 – June 12, 2007), better known as Mr. Wizard, was the creator and host of Watch Mr. Wizard (1951–65, 1971–72) and Mr. Wizard's World (1983–90), which were educational television programs for children devoted to science and technology. He also produced many short video programs about science and authored several popular books about science for children. It was said that no fictional hero was able to rival the popularity and longevity of "the friendly, neighborly scientist". In Herbert's obituary, Bill Nye wrote, "Herbert's techniques and performances helped create the United States' first generation of homegrown rocket scientists just in time to respond to Sputnik. He sent us to the moon. He changed the world." Herbert is credited with turning "a generation of youth" in the 1950s and early 1960s on to "the promise and perils of science".
1920 Owen Chamberlain (July 10, 1920 – February 28, 2006) was an American physicist who shared with Emilio Segrè the Nobel Prize in Physics for the discovery of the antiproton, a sub-atomic antiparticle.
In 1948, having completed his experimental work, Chamberlain returned to Berkeley as a member of its faculty. There he, Segrè, and other physicists investigated proton-proton scattering. In 1955, a series of proton scattering experiments at Berkeley's Bevatron led to the discovery of the anti-proton, a particle like a proton but negatively charged. Chamberlain's later research work included the time projection chamber (TPC), and work at the Stanford Linear Accelerator Center (SLAC).
Chamberlain was politically active on issues of peace and social justice, and outspoken against the Vietnam War. He was a member of Scientists for Sakharov, Orlov, and Shcharansky, three physicists of the former Soviet Union imprisoned for their political beliefs. In the 1980s, he helped found the nuclear freeze movement. In 2003 he was one of 22 Nobel Laureates who signed the Humanist Manifesto.
Chamberlain was diagnosed with Parkinson's disease in 1985, and retired from teaching in 1989. He died of complications from the disease on February 28, 2006, in Berkeley at the age of 85. *Wik
1928 Errett Albert Bishop (July 10, 1928 – April 14, 1983) (His) work is so wide ranging that it is difficult to give an overview in a biography such as this. Let us look at the book Selected papers which was published in 1986 and reprints some of Bishop's most significant contributions. The book divided Bishop's papers into five categories:
(1) Polynomial and rational approximation. Examples are extensions of Mergelyan's approximation theorem and the theorem of Frigyes Riesz and Marcel Riesz concerning measures on the unit circle orthogonal to polynomials. Bishop found new methods in dealing with these problems;
(2) The general theory of function algebras. Here Bishop worked on uniform algebras (commutative Banach algebras with unit whose norms are the spectral norms) proving results such as antisymmetric decomposition of a uniform algebra, the Bishop-DeLeeuw theorem, and the proof of existence of Jensen measures. In 1965 Bishop wrote an excellent survey Uniform algebras examining the interaction between the theory of uniform algebras and that of several complex variables.
(3) Banach spaces and operator theory. An examples of a paper by Bishop on this topic is Spectral theory for operators on a Banach space (1957). He introduced the condition now called the Bishop condition which turned out to be very useful in the theory of decomposable operators.
(4) Several complex variables. Examples of Bishop's papers in this area are Analyticity in certain Banach spaces (1962). He proved important results in this area such as the biholomorphic embedding theorem for a Stein manifold as a closed submanifold in Cn, and a new proof of Remmert's proper mapping theorem.
(5) Constructive mathematics. Bishop become interested in foundational issues around 1964, about the time he was at the Miller Institute. He wrote a famous text Foundations of constructive analysis (1967) which aimed to show that a constructive treatment of analysis is feasible.*SAU
DEATHS
1851 Louis-Jacques-Mandé Daguerre (18 November 1787 – 10 July 1851) French painter and physicist who invented the daguerreotype, the first practical process of photography. Though the first permanent photograph from nature was made in 1826/27 by Joseph-Nicéphore Niepce of France, it was of poor quality and required about eight hours' exposure time. The process that Daguerre developed required only 20 to 30 minutes. The two became partners in the development of Niepce's heliographic process from 1829 until the death of Niepce in 1833. Daguerre continued his experiments, and he discovered that exposing an iodized silver plate in a camera would result in a lasting image after a chemical fixing process.*TIS
Daguerre around 1840
1910 Johann Gottfried Galle (9 June 1812 – 10 July 1910) German astronomer who on 23 Sep 1846, was the first to observe the planet Neptune, whose existence had been predicted in the calculations of Leverrier. Leverrier had written to Galle asking him to search for the new planet at a predicted location. Galle was then a member of the staff of the Berlin Observatory and had discovered three comets. In 1838, while assistant to Johann Franz Encke, Galle discovered the dark, inner C ring of Saturn at the time of the maxium ring opening. In 1851, he became professor of astronomy at Breslau and director of the observatory there. In 1872, he proposed the use of asteroids rather than regular planets for determinations of the solar parallax, a suggestion which was successful in an international campaign (1888-89). *TIS
1916 John Emory McClintock (19 Sept 1840 in Carlisle, Pennsylvania , USA - 10 July 1916 in Bay Head, New Jersey, USA) was for many years the leading actuary in America. He published 30 papers between 1868 and 1877 on actuarial questions. His publications were not confined to questions relating tolife insurance policies however. He published about 22 papers on mathematical topics. One paper treats difference equations as differential equations of infinite order and others look at quintic equations which are soluble algebraically. He published A simplified solution of the cubic in 1900 in the Annals of Mathematics. Another work, On the nature and use of the functions employed in the recognition of quadratic residues (1902), published in the Transactions of the American Mathematical Society, is on quadratic residues.*SAU
1933 Harold DeForest Arnold (September 3, 1883 – July 10, 1933) was an electronics engineer and pioneer of radio communication and telephony. He served as the first director of research at Bell Telephone Laboratories from 1925 to his death.
He initially studied under Albert A. Michelson but when he confided to Robert Andrews Millikan that he would probably have to commit suicide as he could not meet Michelson's requirement, Millikan took Arnold over as his own student. When Frank B. Jewett was looking for someone to work on repeaters for transcontinental telephony, Arnold was suggested by Millikan. Arnold worked at the University of Chicago from 1907 to 1909 and served as a professor at Mount Allison University, from 1909 to 1910 and then at University of Chicago (1910). In 1911 he joined the Western Electric Company under Edwin H. Colpitts. His earliest work was in the development of a vacuum-tube based amplifiers beginning with improvements to Lee De Forest's triode “audion”. He worked on innovations that made it possible to demonstrate the first radio transmission between Arlington, Virginia, and Paris, France, in October 1915. During World War I he served as a captain in the signal corps. He developed and refined manufacturing techniques for vacuum tubes, oxide coatings for filaments, and other innovations for reliability and ease of replacement. Permalloy and Perminvar were developed by his team and this helped improve signal quality in undersea cables. Arnold received the John Scott Medal in 1928 *Wik
1936 Salvatore Pincherle (March 11, 1853 — July 10, 1936) worked on functional equations and functional analysis. Together with Volterra, he can claim to be one of the founders of functional analysis.*SAU
2007 Paulette Libermann (14 November 1919 – 10 July 2007) was a French mathematician, specializing in differential geometry.
After attending the Lycée Lamartine, she began her university studies in 1938 at the École normale supérieure de jeunes filles, a college in Sèvres for training women to become school teachers. Due to the reforms of the new director Eugénie Cotton, who wanted her school to be at the same level of École Normale Supérieure, Libermann benefited from being taught by leading mathematicians as Élie Cartan, Jacqueline Ferrand and André Lichnerowicz.
Two years later, upon completion of her studies, she was prevented from taking the agrégation and becoming a teacher because of the anti-Jewish laws instituted by the German occupation. However, thanks to a scholarship provided by Cotton, she began doing research under Cartan's supervision.
In 1942, she and her family escaped Paris for Lyon, where they hid from the persecutions by Klaus Barbie for two years. After the liberation of Paris in 1944, she returned to Sèvres and completed her studies, obtaining the agrégation.
Libermann's research involved many different aspects of differential geometry and global analysis. In particular, she worked on G-structures and Cartan's equivalence method, Lie groupoids and Lie pseudogroups, higher-order connections, and contact geometry.
In 1987 she wrote together with Charles-Michel Marle one of the first textbooks on symplectic geometry and analytical mechanics.
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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