Saturday, 11 July 2026

On This Day in Math - July 11

   


Ten decimal places of π are sufficient to give the circumference
of the earth to a fraction of an inch, 
and thirty decimal places would give the circumference of the visible universe
to a quantity imperceptible to the most powerful microscope.

~Simon Newcomb  


The 192nd day of the year; 192 is the smallest number that together with its double and triple contain every digit from 1-9 exactly once. There are three other values of n so that n, 2n, and 3n contain each non-zero digit exactly once. Can you find them?

192 is the sum of ten consecutive primes (5 + 7 + 11 + 13 + 17 + 19 + 23 + 29 + 31 + 37)

192 is the number of edges on a 6th dimension hypercube, it is the last day of the year which is the number of edges of a hypercube.

192 is a Happy number, summing the square of its digits and iterating leads to 1 in only three iterations. Its also a Hashard (Joy-giver) number, divisible by the sum of it's digits, 12.

Diophantus probably knew, and Lagrange proved, that every positive integer can be written as a sum of four perfect squares. Jacobi proved the stronger result that the number of ways in which a positive integer can be so written equals 8 times the sum of its divisors that are not multiples of 4. Use this theorem to prove that there are 192 ways to express 14 as a sum of four squares.




See More Math Facts for every year date here




EVENTS


1663 John Wallis, Savilian Professor of Geometry at Oxford, gave a specious proof of Euclid’s parallel postulate. See W. W. Rouse Ball, Mathematical Recreations and Essays, 6th edition, pp. 314– 315.*VFR


1686 Leibniz published his first paper on the integral calculus in Acta eruditorum.*VFR  This paper contains the first appearance in print of the elongated s integral notation used today. He had used the symbol earlier in a manuscript on Oct 29, 1675.

"Utile erit scribi 

\int pro omnia, ut \intl = omn. l, id est summa ipsorum l. [It will be useful to write \int for omn. so that \intl = omn. l, or the sum of all the l's.]  *SAU




1699 Halley's final log entry for his first voyage of discovery commanding the Paramore, “The Gunns and Gunners Stores were delivered to the Tower Officers and that Same Evening we moord our Shipp at Deptford” 

Halley was paid wages of £168 0s 0d, less deductions for the Royal Hospital for Seamen at Greenwich and for “bearing Supernumery’s”, leaving net pay of £140 2s 8d. Lieutenant Edward Harrison received £71 5s 2d (£71 0s 0d net), and the clerk Caleb Harmon was paid £15 19s 3d (£15 3s 1d net), which his father apparently collected.  Harrison was a ‘tarpaulin’, a man of sea-breeding, who rose to become a lieutenant in the Royal Navy. He is known to have been at sea by 1688, probably in the merchant service, and may have been ‘using the sea’ somewhat earlier.

He was first commissioned as a Royal Navy lieutenant on 16 February 1691

*halleyslog.wordpress.com




1700 Royal Prussian Academy of Sciences at Berlin founded. Leibniz was primarily responsible for the founding and directed it for sixteen years. [HM 2, p. 310; American Journal of Physics, 34(1966), p. 22]*VFR


1731 Alexis-Claude Clairaut elected to the French academy. He was only eighteen. *VFR


1738 Isaac Greenwood, the first Hollis Professor at Harvard, was “ejected” from his chair for drunk­enness. [I. B. Cohen, Some Early Tools of American Science, p. 36.]  *VFR

Greenwood travelled to London, where he lodged with John Theophilus Desaguliers and attended his lectures on Newtonian Experimental Philosophy. He later introduced the subject in the American Colonies and his book An Experimental Course of Mechanical Philosophy, published in Boston in 1726, owed much to Desaguliers. In London Greenwood met with Thomas Hollis, who wished to endow a chair at Harvard College for him. Hollis later fell out with Greenwood, over his financial imprudence. However, back in Boston, Greenwood was eventually appointed to the new Hollis Chair in 1727.

During his tenure, he wrote anonymously the first natively-published American book on mathematics – the Greenwood Book, published in 1729. This book made the first published statement of the short scale value for billion in the United States, which eventually became the value used in most English-speaking countries.

After he was removed from the chair for intemperance in 1737. Unable to support his family, he joined the Royal Navy as a chaplain aboard HMS Rose in 1742, transferring to HMS Aldborough in 1744. He was released from service in Charleston, South Carolina, on 22 May 1744 and died from the effects of alcohol on 22 October 1745. *Wik





1747 Benjamin Franklin writes to Peter Collinson, London Businessman and member of the Royal Society, to describe the, "wonderful effects of pointed bodies, both in drawing off and throwing off the electrical fire."* A history of physics in its elementary branches By Florian Cajori

Collinson showed Franklin’s letters to friends, read some of them to the Royal Society, and allowed copies to be made. He decided, late in 1750, to publish them, and they appeared in April 1751 with the title Experiments and Observations on Electricity, Made at Philadelphia in America, by Mr. Benjamin Franklin, and Communicated in several Letters to Mr. P. Collinson, of London, F.R.S., a thin pamphlet of 86 numbered pages, which included corrections and additions supplied by Franklin

The book outlines the existence of positive and negative charges, and the difference between insulators and conductors.  A list of electrical terms Franklin coined, *Fermat's Library


*Abe Books



 1801, French astronomer Jean-Louis Pons (24 Sep 1761 - 14 Oct 1831) discovers his first comet. In his lifetime he discovered or co-discovered up to 37 comets. Since 1789, when he got a post at the Observatory at Marseilles as concierge, Pons quickly learned how to make observations with the instruments. He had a remarkable ability to remember the star fields he observed and to recognize changes. He logged his first discovery of a comet on 11 July 1801, which he had to share with Messier who found it a day later. Interestingly, as Pons' made his first comet discovery, that comet was Messier's last. Almost once every year, thereafter until 1827 when his eyesight declined, Pons found a new comet. Jean-Louis Pons set the record for visual discoveries of comets by an individual. *TiS



1811 Italian scientist Amedeo Avogadro published his memoire about the molecular content of gases. *TIS

Avogadro wrote a memoria (concise note) in which he described the experimental gas law that now bears his name. He sent this memoria to De Lamétherie's Journal de Physique, de Chemie et d'Histoire naturelle, and it was published in the July 14, 1811 issue




1814 Amp`ere submitted a paper on general solutions of differential equations. It contains thought-provoking remarks and interesting examples which had to wait several decades for proper understanding and recognition. [Ivor Grattan-Guiness, Convolutions in French Mathematics, 1800– 1840, pp. 700ff, 1389]*VFR  

The SI unit of measurement of electric current, the ampere, is named after him. His name is also one of the 72 names inscribed on the Eiffel Tower. The term kinematic is the English version of his cinématique, which he constructed from the Greek κίνημα kinema ("movement, motion"), itself derived from κινεῖν kinein ("to move"). *Wik




1859 The Current Big Ben (the bell) is first heard ringing in the Westminster clock tower. Why Big Ben? After Benjamin Hall (1802-67). In Aug 1856 the bell, with Hall's name inscribed on it, was cast, but cracked after tests in October 1857. The substitute was also defective but worked sufficiently well to be hung in Oct 1858. Named Big Ben, it was first heard on 11 July 1859. Two months later it too cracked & fell silent for 4 years; it was repaired with help of Sir George Airy, astronomer royal, & rings to this day. *Oxford DNB@ODNB

Big Ben is the nickname for the Great Bell of the Great Clock of Westminster, at the north end of the Palace of Westminster in London, England, and the name is frequently extended to refer also to the clock and the clock tower. The official name of the tower in which Big Ben is located was originally the Clock Tower, but it was renamed Elizabeth Tower in 2012 to mark the Diamond Jubilee of Elizabeth II.*Wik

The second "Big Ben" (center) and the Quarter Bells from The Illustrated News of the World, 4 December 1858


1925  On July 11,1925, in a letter to Wolfgang Pauli, Werner Heisenberg revealed his new ideas, which were to revolutionise physics. The letter, preserved in the Wolfgang Pauli Archive at CERN, reveals Heisenberg’s efforts to liberate physics from the semi-classical picture of atoms as planetary systems, with electrons in orbit around the nucleus.

“All of my pitiful efforts are directed at completely killing off the concept of orbits – which, after all, cannot be observed—and replacing it with something more suitable,” he explains in his letter to Pauli.

In the picture, Wolfgang Pauli, Werner Heisenberg and Enrico Fermi (left to right) take a break by Lake Como during the 1927 International Congress of Physicists. *Cern



1962 Aerospace engineer John C. Houbolt, the leading proponent of the lunar orbit rendezvous (LOR) plan (chosen #OTD in 1962) which made possible John F. Kennedy's goal of sending astronauts to the Moon and bringing them back home safely before the end of the 1960 @NASA History



1976 K&E produced its last slide rule, which it presented to the Smithsonian Institution. A common method of performing mathematical calculations for many years, the slide rule became obsolete with the invention of the computer and its smaller, hand-held sibling, the calculator. (*This Day in History-Computer History Museum)

A 1930s high school class making electrical calculations on their slide rules. Note the demonstration-sized rule hanging on the blackboard. Keuffel & Esser Co., Drawing Instruments and Materials for High Schools, Preparatory Schools and Manual Training Schools (Hoboken, N.J., 1936), 62. NMAH Trade Literature Collection, Smithsonian Institution Libraries.  (My personal history research on slide rules suggests that few highschools used slide rules in HS math, but a few did use them as early as the twenties in science classes.



1979  U.S. space station, Skylab, re-entered the Earth's atmosphere. It disintegrated, spreading fragments across the southeastern Indian Ocean and over a sparsely populated section of western Australia, where a cow died after being struck by a piece of falling debris. *TIS (Proving the potential effectiveness of weapons in space?)

The do-it-yourself Skylab Protective Helmet promised users it would “do you absolutely no good at all!” JEFFREY HALL


A cattle rancher found this chunk of Skylab more than a decade after the space station reentered Earth’s atmosphere on 12 July 1979. PHOTO: RYAN HERNANDEZ; OBJECT: POWERHOUSE COLLECTION




In 1991, a solar eclipse cast a blanket of darkness stretching 9,000 miles from Hawaii to South America, lasting nearly seven minutes in some places. It was the so-called eclipse of the century. A total solar eclipse - the moon passing between the sun and the earth - is the moon casting its shadow on the earth's surface. Total eclipses occur almost once per year, but are often over an ocean or remote countries. The solar eclipse on July 11, 1991, was a thrill for scientists. It traveled over the several astronomical observatories on the top of Mauna Kea. Their 14,000 feet elevation was actually above the cloud level, which obstructed the view for those below. *TIS




2000 The da Vinci robot surgical system was the first to be approved by the U.S. Food and Drug Administration for use in gallbladder, gastroesophageal reflux, and gynecologic operations. The advanced medical device was an offshoot of robotic technology developed by the U.S. Dept of Defense for military applications. In the 1990s, Intuitive Surgical, Inc. and Computer Motion (which merged in 2000) developed robotic interfaces for use in human surgical applications. A three- or four-armed robot, manipulates instruments with precise wrist-like dexterity, remotely controlled by the surgeon from a computer console. Instruments and cameras are guided through quite small openings in the body, which is much less invasive than previous methods, enabling earlier release from hospital and more rapid healing. *TiS



2011 this day was about "one year" after, German astronomer Johanne Galle discovered Neptune ... One Neptunian year that is! *rmathematicus, Thony Christie;
On July 11, 2011, Neptune completed its first full barycentric orbit since its discovery on September 23, 1846, *Wik




BIRTHS


1732  Joseph Jérôme Le Français de Lalande, (11 July 1732 – 4 April 1807) was a an astronomer, born in Bourg-en-Bresse, France. He determined the Moon's parallax from Berlin for the French Academy (1751). He was appointed professor of Astronomy, Collège de France (1762), and subsequently, director of the Paris Observatory. He published his Traité d'astronomie in 1764 - tables of the planetary positions that were considered the best available for the rest of the century. In 1801 he also published a comprehensive star catalogue. He died in 1807, apparently of tuberculosis. *TIS
Thony Christie began an article about Lalande with this nice intro, "The cliché concept of a Frenchman is of the prime example of a chauvinist and the eighteenth century is not renowned as a period of equality for women, so it might come as somewhat of a surprise that an eighteenth century Frenchman very much championed the positive role of women in astronomy; that man was Joseph Jérôme Lefrançois de Lalande (1732–1807)." The remainder is equally informative and entertaining.




1811 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





1857 Sir Joseph Larmor (11 July 1857 Magheragall, County Antrim, Ireland – 19 May 1942 Holywood, County Down, Northern Ireland), Irish physicist, the first to calculate the rate at which energy is radiated by an accelerated electron, and the first to explain the splitting of spectrum lines by a magnetic field. His theories were based on the belief that matter consists entirely of electric particles moving in the ether. His elaborate mathematical electrical theory of the late 1890s included the "electron" as a rotational strain (a sort of twist) in the ether. But Larmor's theory did not describe the electron as a part of the atom. Many physicists envisioned both material particles and electromagnetic forces as structures and strains in that hypothetical fluid. *TIS




1857 Alfred Binet (July 11, 1857 – October 18, 1911) who introduced his famous IQ test in 1905. *VFR French experimental psychologist, the director of the psychological laboratory of the Sorbonne, Paris (1894). He made fundamental contributions to the measurement of intelligence.With Theodore Simon, Binet produced a series of graded tasks typical of the intellectual development of children of different ages (1905). This scale was extended (1908-11), and the tasks were assigned to the age level at which average children could manage them. Thus children could be scored for the level, or mental age, they reached. This test formed the basis for the Stanford-Binet Tests.*TIS (today in Science also gives Binet's birthdate on July 11th, with a different description:  French psychologist who was a pioneer in the field of intelligence testing of the normal mind. He took a different approach than most psychologists of his day: he was interested in the workings of the normal mind rather than the pathology of mental illness. He wanted to find a way to measure the ability to think and reason, apart from education in any particular field. In 1905 he developed a test in which he had children do tasks such as follow commands, copy patterns, name objects, and put things in order or arrange them properly. He gave the test to Paris schoolchildren and created a standard based on his data. From Binet's work, "IQ" (intelligence quotient), entered the vocabulary. The IQ is the ratio of "mental age" to chronological age, with 100 being average.)




1890 Giacomo Albanese (11 July 1890 – 8 June 1947) was an Italian mathematician known for his work in algebraic geometry. He took a permanent position in São Paulo, Brazil, in 1936. *Wik


1902 Samuel Abraham Goudsmit (The Hague, July 11, 1902 — Reno, December 4, 1978) Dutch-born U.S. physicist who, with George E. Uhlenbeck, a fellow graduate student at the University of Leiden, Neth., formulated (1925) the concept of electron spin. It led to recognition that spin was a property of protons, neutrons, and most elementary particles and to a fundamental change in the mathematical structure of quantum mechanics. Goudsmit also made the first measurement of nuclear spin and its Zeeman effect with Ernst Back (1926-27), developed a theory of hyperfine structure of spectral lines, made the first spectroscopic determination of nuclear magnetic moments (1931-33), contributed to the theory of complex atoms and the theory of multiple scattering of electrons, and invented the magnetic time-of-flight mass spectrometer (1948).*TIS




1907Helmut Grunsky (11 July 1904 – 5 June 1986) was a German mathematician who worked in complex analysis and geometric function theory. He introduced Grunsky's theorem and the Grunsky inequalities.

In 1936, he was appointed editor of Jahrbuch über die Fortschritte der Mathematik. In 1939 he was forced to leave this position after Ludwig Bieberbach accused him of employing Jewish referees in a notorious letter.[Bieberbach was enthusiastically involved in the efforts to dismiss his Jewish colleagues, including Edmund Landau and his former coauthor Issai Schur, from their posts. He also facilitated the Gestapo arrests of some close colleagues, such as Juliusz Schauder. ] 

Grunsky joined the Nazi Party on 1 April 1940, though he seems to have had little sympathy with its philosophy. He published in the journal Deutsche Mathematik. From 1949 he was Privatdozent at the University of Tübingen; later, he was professor at the University of Mainz and at the University of Würzburg  *Wik




1916 Alexander Mikhailovich Prokhorov (born Alexander Michael Prochoroff, Russian: Алекса́ндр Миха́йлович Про́хоров; 11 July 1916 – 8 January 2002) is the Soviet physicist who received, (with Nikolay G. Basov, USSR and Charles H. Townes, US), the Nobel Prize for Physics in 1964 "for fundamental work in the field of quantum electronics, which has led to the construction of oscillators and amplifiers based on the maser-laser principle." "Maser" stands for "microwave amplification by stimulated emission of radiation." An amplification can occur only if the stimulated emission is larger than the absorption, requiring that there should be more atoms in a high energy state than in a lower one. This state is called an inverted population. Prokhorov had researched the maser independently but simultaneously with the other prize recipients. *TiS




1922 John William Scott Cassels  (11 July 1922 – 27 July 2015)  initially worked on elliptic curves. After a period when he worked on geometry of numbers and diophantine approximation, he returned in the later 1950s to the arithmetic of elliptic curves, writing a series of papers connecting the Selmer group with Galois cohomology and laying some of the foundations of the modern theory of infinite descent. His best-known single result may be the proof that the Tate-Shafarevich group, if it is finite, must have order that is a square; the proof being by construction of an alternating form. Cassels has often studied individual Diophantine equations by algebraic number theory and p-adic methods. 
His publications include 200 papers. His advanced textbooks have influenced generations of mathematicians; some of Cassels's books have remained in print for decades. *Wik



1927 Theodore Harold Maiman (July 11, 1927 – May 5, 2007) Theodore Harold Maiman was an American physicist who built the first working laser. He began working with electronic devices in his teens, while earning college money by repairing electrical appliances and radios. In the 1960s, he developed, demonstrated, and patented a laser using a pink ruby medium. The laser is a device that produces monochromatic coherent light (light in which the rays are all of the same wavelength and phase). The laser has since been applied in a very wide range of uses, including eye surgery, dentistry, range-finding, manufacturing, even measuring the distance between the Earth and the Moon.*TiS

Maiman with his laser in July 1960.








 

DEATHS


1382 Nicole Oresme (c. 1320–5 – July 11, 1382), was a French mathematician who invented coordinate geometry long before Descartes. He was the first to use a fractional exponent and also worked on infinite series. *SAU
Oresme was Bishop of Liseux and died there, and was buried in the cathedral church there, says New World Encyclopedia.  I was recently (2011) at the Cathedral and cold find no mark of his life there.

"His most important contributions to mathematics are contained in "Tractatus de figuratione potentiarum et mensurarum difformitatum", still in manuscript. An abridgment of this work printed as "Tractatus de latitudinibus formarum" (1482, 1486, 1505, 1515), has heretofore been the only source for the study of his mathematical ideas. In a quality, or accidental form, such as heat, the Scholastics distinguished the intensio (the degree of heat at each point) and the extensio (e.g., the length of the heated rod): these two terms were often replaced by latitudo and longitudo, and from the time of St. Thomas until far on in the fourteenth century, there was lively debate on the latitudo formæ. For the sake of lucidity, Oresme conceived the idea of employing what we should now call rectangular co-ordinates: in modern terminology, a length proportionate to the longitudo was the abscissa at a given point, and a perpendicular at that point, proportional to the latitudo, was the ordinate. He shows that a geometrical property of such a figure could be regarded as corresponding to a property of the form itself only when this property remains constant while the units measuring the longitudo and latitudo vary. Hence he defines latitudo uniformis as that which is represented by a line parallel to the longitude, and any other latitudo is difformis; the latitudo uniformiter difformis is represented by a right line inclined to the axis of the longitude. He proves that this definition is equivalent to an algebraical relation in which the longitudes and latitudes of any three points would figure: i.e., he gives the equation of the right line, and thus forestalls Descartes in the invention of analytical geometry. This doctrine he extends to figures of three dimensions.
Besides the longitude and latitude of a form, he considers the mensura, or quantitas, of the form, proportional to the area of the figure representing it. He proves this theorem: A form uniformiter difformis has the same quantity as a form uniformis of the same longitude and having as latitude the mean between the two extreme limits of the first. He then shows that his method of figuring the latitude of forms is applicable to the movement of a point, on condition that the time is taken as longitude and the speed as latitude; quantity is, then, the space covered in a given time. In virtue of this transposition, the theorem of the latitude uniformiter difformis became the law of the space traversed in case of uniformly varied motion: Oresme's demonstration is exactly the same as that which Galileo was to render celebrated in the seventeenth century. Moreover, this law was never forgotten during the interval between Oresme and Galileo: it was taught at Oxford by William Heytesbury and his followers, then, at Paris and in Italy, by all the followers of this school. In the middle of the sixteenth century, long before Galileo, the Dominican Dominic Soto applied the law to the uniformly accelerated falling of heavy bodies and to the uniformly decreasing ascension of projectiles." 

*Catholic Encyclopedia online

Around 1377, Oresme wrote a treatise called Le livre du ciel et du monde (The Book of the Heavens and Earth), in which he discussed the matter of whether the earth might rotate on its axis. Oresme addressed all the old arguments against rotation, such as the claim that an arrow shot into the air on a rotating earth would land far to the west, by arguing that all motion is relative, and an arrow moving away from a stationary earth would act the same as one on a rotating earth. He pointed out how much simpler the cosmos would be if, instead of having every celestial object whirl around at incredible speeds every 24 hours, God simply rotated the earth at a much slower speed and achieved exactly the same effect. Oresme even maintained that those scriptural passages that suggest a stationary earth need not be read literally, since they were written for popular understanding.*Wik


A page from Oresme's Livre du ciel et du monde, 1377, showing the celestial spheres

*Wik






1733 Jakob Hermann (16 July 1678, Basel – 11 July 1733, Basel) was a Swiss mathematician who made contributions to dynamics.*SAU In 1729, he proclaimed that it was as easy to graph a locus on the polar coordinate system as it was to graph it on the Cartesian coordinate system. However, no one listened. He was a distant relative of Leonhard Euler. 

He appears to have been the first to show that the Laplace–Runge–Lenz vector is a constant of motion for particles acted upon by an inverse-square central force.*Wik

This work predated Pierre-Simon Laplace and Carl Runge by many decades, showing Hermann's pioneering role in mathematical physics. His discovery was particularly valuable for understanding the mechanics of elliptical orbits and provided a deeper mathematical framework for analyzing celestial motion beyond what Newton's laws alone could easily provide.





1807 George Atwood  (c. October 1745 – 11 July 1807) was an English mathematician best known for his invention of a low-friction pulley system.*SAU He is the author of Phoronomia, an early treatise on Mechanics. In 1729, he proclaimed that it was as easy to graph a locus on the polar coordinate system as it was to graph it on the Cartesian coordinate system. However, no one listened. He was a distant relative of Euler. *Wik

He is best known for the Atwood machine consists of two masses connected by a lightweight, inextensible string that passes over a pulley. When the masses are different, the system accelerates, with the heavier mass descending and the lighter one ascending.

The machine was revolutionary because it allowed for the precise study of uniformly accelerated motion. By carefully choosing the masses, experimenters could create very small accelerations that were much easier to measure accurately than free fall. This was crucial in the 18th and 19th centuries when timing instruments were far less precise than today.  Jakob Hermann had created a similar demonstration, years earlier.





1778 Joseph Stepling, (29 June 1716 in Regensburg; 11 July 1778 in Prague) His fields included astronomy, physics and mathematics. At the age of 17 he documented with great accuracy the 1733 lunar eclipse. Later Euler was among his long list of correspondents. He transposed Aristotelian logic into formulas, thus becoming an early precursor of modern logic. already adopted the atomistic conception of matter he radically refused to accept Aristotelian metaphysics and natural philosophy. In 1748, at the request of the Berlin Academy, he carried out an exact observation of a solar and lunar eclipse in order to determine the precise location of Prague. During Stepling's long tenure at Prague, he set up a laboratory for experimental physics and in 1751 built an observatory, the instruments and fittings of which he brought up to the latest scientific standard.
Even though he passed up a professorship in philosophy in favor of a chair in mathematics, Empress Maria Theresa appointed him director of the faculty of philosophy at Prague as part of the reform of higher education. He was very interested in cultivating the exact sciences and founded a society for the study of science modeled on the Royal Society of London. In their monthly sessions. over which he presided until his death, the group carried out research work and investigations in the field of pure mathematics and its appiication to physics and astronomy. A great number of treatises of this academy were published.
Stepling corresponded with the outstanding contemporary mathematicians and astronomers: Christian Wolf. Leonhard Euler. Christopher Maire, Nicolas-Louis de Lacaille, Maximilian Heli, Joseph Franz, Rudjer Boskovic, Heinrich Hiss, and others. Also, Stepling was particularly successful in educating many outstanding scientists, including Johann Wendlingen, Jakob Heinisch, Johannes von Herberstein, Kaspar Sagner, Stephan Schmidt, Johann Korber, and Joseph Bergmann. After his death, Maria Theresia ordered a monument erected in the library of the University of Prague *Joseph MacDonnell, Fairfield Univ web page




1745 George Atwood (Baptized October 15, 1745, Westminster,London – 11 July 1807, London) was an English mathematician who invented a machine for illustrating the effects of Newton's first law of motion. He was the first winner of the Smith's Prize in 1769. He was also a renowned chess player whose skill for recording many games of his own and of other players, including François-André Danican Philidor, the leading master of his time, left a valuable historical record for future generations.

He attended Westminster School and in 1765 was admitted to Trinity College, Cambridge. He graduated in 1769 with the rank of third wrangler and was awarded the inaugural first Smith's Prize. Subsequently he became a fellow and a tutor of the college and in 1776 was elected a fellow of the Royal Society of London.

In 1784 he left Cambridge and soon afterwards received from William Pitt the Younger the office of patent searcher of the customs, which required but little attendance, enabling him to devote a considerable portion of his time to mathematics and physics.

He died unmarried in Westminster at the age of 61, and was buried there at St. Margaret's Church. Over a century later, a lunar crater was renamed Atwood in his honour. *Wik




1871 Germain Sommeiller (February 15, 1815 - July 11, 1871) French-Italian engineer who built the Mount Cenis (Fréjus) Tunnel (1857-70) through the Alps, the world's first important mountain tunnel. The two track railway tunnel unites Italian Savoy (north of the mountains) through Switzerland with the rest of Italy to the south. At 8 miles long and it was more than double the length of any previous tunnel. In 1861, after three years of tedious hand-boring a mere eight inches a day into the rock face, Sommeiller introduced the first industrial-scale pneumatics for tunnel digging. He built a special reservoir, high above the tunnel entrance, to produce a head of water that compressed air (to 6 atm.) for pneumatic drills, able to dig up to 20 times faster. Authorised on 15 Aug 1857, the tunnel opened on 17 Sep 1871, as a major triumph of engineering.*TIS Note his death was only a few months before the opening of his great project.

Sommeiller's pneumatic rock-drilling machine




1909  Simon Newcomb (March 12, 1835 – July 11, 1909) died in Washington D.C. He was such a revered scientist that President Taft attended his funeral.*VFR  Canadian-American astronomer and and mathematician who prepared ephemerides (tables of computed places of celestial bodies over a period of time) and tables of astronomical constants. He was an astronomer (1861-77) before becoming Superintendent of the U.S. Nautical Almanac Office (1877-97). During this time he undertook numerous studies in celestial mechanics. His central goal was to place planetary and satellite motions on a completely uniform system, thereby raising solar system studies and the theory of gravitation to a new level. He largely accomplished this goal with the adoption of his new system of astronomical constants at the end of the century. *TIS

Newcomb is buried in Arlington National Cemetery 
Newcomb is often quoted as saying that heavier than air flight was impossible from a statement he made only two months before the Wright Brothers flight at Kitty Hawk, N.C.

"The mathematician of to-day admits that he can neither square the circle, duplicate the cube or trisect the angle. May not our mechanicians, in like manner, be ultimately forced to admit that aerial flight is one of that great class of problems with which men can never cope… I do not claim that this is a necessary conclusion from any past experience. But I do think that success must await progress of a different kind from that of invention."   He also is famously quoted for saying, "We are probably nearing the limit of all we can know about astronomy." 

1950 Arthur William Conway FRS PRIA (2 October 1875 – 11 July 1950) was a distinguished Irish mathematician and mathematical physicist who wrote one of the first books on relativity and co-edited two volumes of William Rowan Hamilton's collected works. He also served as President of University College Dublin between 1940 and 1947.

One of Conway's students was Éamon de Valera, whom he introduced to Hamilton's quaternions. De Valera warmed to the subject and engaged in research of this novelty of abstract algebra. Later, when de Valera became Taoiseach (he was also subsequently President of Ireland), he called upon Conway while forming the Dublin Institute for Advanced Studies.

He was an Invited Speaker of the ICM in Toronto in 1924, in 1932 in Zurich, and in 1936 in Oslo. He was elected President of the Royal Irish Academy from 1937 to 1940.

In October 1975, to mark the centenary of his birth, UCD hosted the AC Conway Memorial Mathematical Symposium. Speakers included Roger Penrose, Ian Sneddon, and William B. Bonnor.

In his obituary, E.T. Whittaker referred to Conway as the "most distinguished Irish Catholic man of science of his generation." *Wik

At the 1938 EMS colloquium in St Andrews




1995 Andrzej Alexiewicz (11 February 1917, Lwów, Poland – 11 July 1995) was a Polish mathematician, a disciple of the Lwow School of Mathematics. Alexiewicz was an expert at functional analysis and continued and edited the work of Stefan Banach. *Wik


2019 Werner Buchholz​  (24 October 1922 – 11 July 2019) He was a member of the teams that designed the IBM 701​ and Stretch models. Buchholz used term byte to describe eight bits—although in the 1950s, when the term first was used, equipment used six-bit chunks of information, and a byte equaled six bits. Buchholz described a byte as a group of bits to encode a character, or the numbers of bits transmitted in parallel to and from input-output. *CHM




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




Friday, 10 July 2026

The Rule(s) of Three and the Probability of Nothing

  


A Re-edit and Posting of a 2008 Blog


From 1827 Pike's Arithmetic



In my youth, back when dinosaurs roamed the earth, there was “the rule of three”… singular, one, and even then the name was often described as “archaic”. More modern books tended to develop “properties of proportions” or similar terms for the problems of proportionalities. Now there seem to be an abundance of them; including one for witches, and one about businesses. There is not space enough to talk about all of them so I will mention three, of course.
The first rule of three is as old as math, and shows up at least as early as the Hindu mathematician Brahmagupta, and in Fibonacci’s famous Liber Abaci(1202). It was once so common that it was introduced into common language. Abraham Lincoln is quoted in his biography as stating that he learned to "read, write, and cipher to the rule of 3."   So common that student's often wrote verse like the following, in their copy (practice) books.

Multiplication is vexation;
Division is as bad;
The Rule of Three doth puzzle me,
And Practice drives me mad

The most common and longest living form was the direct rule (although there was an inverse rule as well), in which case three numbers would be given and a fourth sought so that the ratio between the third and fourth would match the ratio between the first and second; a:b = c:d. Today students use the ideas in elementary school to complete fraction equivalences, “2/3 is the same as 10/?” Some of the ancient examples grew incredibly complicated.

I suppose the reason I chose to address three of the many “rules of three” is because of the rule of three from language and literature. Three just seems to be the right number for lots of things, there were Three Musketeers, Three Stooges, and Three Coins in the Fountain. It was Goldilocks and the Three Bears, and “bah bah black sheep” had “three bags full.” Comics in the newspaper usually have three panels and many jokes involve a three part ritual where the punch line is the third element, such as the t-shirt with “Great Cities of the World” on the top, and below, one after another, “Paris, Rome, Fargo”. The first two make the last funnier. In language the examples range from “Blood, sweat, and tears, to veni, vidi, vici. If you don’t think there really is a mental tendency to have three terms, consider that in Churchill’s speech, he actually used four; “I say to the House as I said to ministers who have joined this government, I have nothing to offer but blood, toil, tears, and sweat. “  But who cares what he said, you will hear the phrase almost always as "Blood, sweat, and tears, and it was common usage before and (however long they last) after the band.

The final rule of three I would mention is from statistics, and is of more recent origin. It is also, I think, a really clever solution to what is a really difficult problem. Suppose something never happens; how can you assign a probability to it? It is not that it might not happen some day, just not so far. It is just such a problem the statistical rule of there was created to handle. Suppose you stopped at the same gum ball machine every day, but unlike the normal gumball machine, this one did not have a glass you could see into the gumballs inside. You buy a gum ball every day and get red ones, and green ones, but never a blue one. After a while you begin to wonder if they even put a blue one in the machine. So one day, after 20 days of getting all the other colors, over lunch you ask your local statistician (doesn’t everyone have lunch with a statistician?) how to figure out if there really is a blue one in there. He pauses, fork poised in mid-air, and informs you that you can be 95% sure (a common statistical benchmark) that the proportion of blue gum balls is no greater than 14.3%. He had mentally taken three, and divided by one more than the number of failed efforts, to get 3/21 or 1/7 as the upper limit of the possible fraction.
The idea is base on a simple extension of the binomial probability. If you knew that P % of the gum balls were blue, then you could calculate the probability that None showed up in 20 days. The probability would be (1-p)20. Working back through this calculation many times you might notice that the number followed a pattern, a rule of thumb to calculate without tables and calculators, and that turns out to be 3/(n+1), the statistical rule of three, giving a probability for the Blue gum balls as 0< P < .143.  If you wanted greater certainty, you can use the rule of seven, which says that 7/(n+1) will give the 99% interval boundary. So in the case of your gumballs, you can be 99% sure the percentage of blue gumballs is less than 1/3. (Of course this problem assumes a population that constantly replaces the gum ball removed so that the probabilities remain constant.

But what if after a long string of failures, you have a success.  How does this change your confidence interval?   Thanks to a recent post from John D Cook I now can tell you that as well.  

So suppose you had worked your way as before with twenty failures to get the blue gumball, and then after the aforementioned lunch with a statistician,  you get a blue gumball on the 21st try.  Now what can you say about the expected percentage of blue gumballs.  

After the first success according to the Beta distribution would give a 95% confidence interval of appx. [.1/n, 4.7/n]  .  For our imagined 21 tries, this would be about [.0047, .224]  So our confidence interval has opened up considerably.  

It appears, if I understand correctly, that the blue gumball could have occurred anytime among the first 21 tries and thus would still be the CI.  So if we went another nine tries without success, we would adjust our CI to {.1/30, 4.7/30] ... [ .00333, .157], back much closer to our expectations before we ever had a success.

Comparing this interval to the binomial confidence interval you learned in high school math, p +/- 2 sqrt(p*(1-p)/n).  The customary warning on the normal expectation is beware of p being too high or too low.  Using one success in 30 tries we get a 95% CI of [-.03, .099]... perhaps the negative lower bound is a sign that we have strayed to close to zero with our p-hat.  A nice topic to spring on your AP stats teacher when you get to confidence intervals, but please be kind. 

 

On This Day in Math - July 10

   





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.

*Wik



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

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

*CHM



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."  

*SAU



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

*Wisconsin Life



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




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