If you are afraid of something, measure it, and you will realize it is a mere trifle.
~Renato CaccioppoliThe 20th day of the year; 20 is the smallest number that cannot be either prefixed or followed by one digit to form a prime. (What is next smallest?)
The 20th palindromic prime (929) has a digit sum of 20. *jim wilder @wilderlab ... There is no larger nth prime palindrome for which digit sum = n less than \(10^7\) *Derek Orr & *David @InfinitelyManic
\(e^{\pi}-\pi\) = 20, well, almost, It's about19.99909997..... (e^pi is often called Gelford's number after Aleksandr Gelford, who proved it was transcendental.) John H Conway noticed this approximation in 1988.
20 is involved in a challenge by Fermat in 1647 to "find a cube, that when increased by the sum of its aliquot parts, is a square, "
And in Paul Halcke observed that 20 was one of three (all rather modestly sized) numbers for which the product of their aliquot divisors equaled their square. Can you find others?
And in Paul Halcke observed that 20 was one of three (all rather modestly sized) numbers for which the product of their aliquot divisors equaled their square. Can you find others?
In 1633, Galileo, at age 68, left his home in Florence, Italy, to face the Inquisition in Rome. By 22 Jun 1633, he buckled under the threats and interrogation by the Inquisition, and renounced his belief that the Earth revolved around the Sun. *TIS According to the legend, after recanting he whispered under his breath, "But still, it moves."
1748 In a surprising letter of January 20, 1748, D'Alembert wrote to Euler [Euler 1980] to suggest a new theory: perhaps the moon (or at least its distribution of mass) was not spherical. If, after all, we only see one side from the Earth, we can't know how far back it truly extends. And perhaps if it extends far enough back, the apsidal motion would indeed be 3 degrees, as observed. In an even more surprising response written less than four weeks later [Euler 1980], Euler says that he too had considered this idea, and had worked out the details! He found that moon would have to extend back about 2 1/2 Earth diameters in the direction away from us, which seemed untenable. *VFR
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1758 Marie-Anne Pierrette Paulze Lavoisier, later Countess of Rumford, (20 January 1758 – 10 February 1836) was a French chemist and noblewoman. Madame Lavoisier's first husband was the chemist and nobleman Antoine Lavoisier. She acted as his laboratory companion, using her linguistic skills to write up his work and bring it to an international audience. She also played a pivotal role in the translation of several scientific works, and was instrumental to the standardization of the scientific method.
Her father, Jacques Paulze, worked primarily as a parliamentary lawyer and financier. Most of his income came from running the Ferme Générale (the General Farm) which was a private consortium of financiers who paid the French monarchy for the privilege of collecting certain taxes. Her mother, Claudine Thoynet Paulze, died in 1761, leaving behind Marie-Anne, then aged 3, and two sons. After her mother's death Paulze was placed in a convent where she received her formal education. She was for a time a pupil of the artist, Jacques-Louis David, who painted the Portrait of Antoine and Marie-Anne Lavoisier seen here
At the age of thirteen, Paulze received a marriage proposal from the 50-year-old Count d'Amerval. Jacques Paulze tried to object to the union, but received threats about losing his job with the Ferme Générale. To indirectly thwart the marriage, Jacques Paulze made an offer to one of his colleagues to ask for his daughter's hand instead. This colleague was Antoine Lavoisier, a French nobleman and scientist. Lavoisier accepted the proposition, and he and Marie-Anne were married on 16 December 1771. Lavoisier was about 28, while Marie-Anne was about 13.
Portrait of M. and Mme Lavoisier by Jacques-Louis David, 1788 (Metropolitan Museum of Art, Manhattan, New York City)
Lavoisier continued to work for the Ferme-Générale but in 1775 was appointed gunpowder administrator, leading the couple to settle down at the Arsenal in Paris. Here, Lavoisier's interest in chemistry blossomed after having previously trained at the chemical laboratory of Guillaume François Rouelle, and, with the financial security provided by both his and Paulze's family, as well as his various titles and other business ventures, he was able to construct a state-of-the-art chemistry laboratory. Paulze soon became interested in his scientific research and began to participate in her husband's laboratory work actively.
As her interest developed, she received formal training in the field from Jean Baptiste Michel Bucquet and Philippe Gingembre, both of whom were Lavoisier's colleagues at the time. The Lavoisiers spent most of their time together in the laboratory, working as a team conducting research on many fronts. She also assisted him by translating documents about chemistry from English to French. In fact, the majority of the research effort put forth in the laboratory was actually a joint effort between Paulze and her husband, with Paulze mainly playing the role of laboratory assistant.
In 1793 Lavoisier, due to his prominent position in the Ferme-Générale, was branded a traitor during the Reign of Terror by French revolutionaries. Lavoisier was tried, convicted of treason, and executed on 8 May 1794 in Paris, at the age of 50. Jacques Paulze was also executed on the same day.[
Ten years after Lavoisier's executation, Paulze remarried Benjamin Thompson in 1804, following a four-year courtship and engagement; she was his second wife. In 1785, he travelled to Bavaria to become aide-de-camp to the Prince-elector, Charles Theodore. In 1791 he was elevated to Count of the Holy Roman Empire, taking the title of Reichsgraf von Rumford, after the town of Rumford in New Hampshire, where he was first married. By the time he had met the widowed Anne-Marie Lavoisier, he had become one of the most well-known physicists at the time. However, the marriage between the two was difficult and short-lived; they separated after three years. Paulze insisted throughout her life that she retain her first husband's last name, demonstrating her undying devotion to him. Rumford had moved to Paris where he continued his work until his death in 1814. He was buried at Auteuil, Paris.
Marie died very suddenly in her home in Paris on 10 February 1836, at the age of 78. She is buried in the cemetery of Pere-Lachaise in Paris.
1896, X-rays were reported by Henri Poincaré reading a letter from Wilhelm Roentgen to the weekly meeting of the Academie des Sciences in Paris, and members viewed some of his X-ray photographs. Henri Becquerel was present, and took note that X-rays seemed to come from the phosphorescent patch on the glass tube where the cathode rays struck it. This inspired him to study if the phosphorescence of minerals was related to X-rays. (Instead, a few weeks later, he discovered the radioactivity of a uranium mineral.) *TIS
Image of Becquerel's photographic plate which has been fogged by exposure to radiation from a uranium salt. The shadow of a metal Maltese Cross placed between the plate and the uranium salt is clearly visible. *Wik
1969, the New York Times made public the news of the discovery a few days earlier of the first optical pulsar by astronomers at the University of Arizona on 16 Jan 1969. It was the result of a year's search using a stroboscopic technique. Flashes of light in the optical range were found coming from the same location in the Crab Nebula as a previously known pulsar emitting radio bursts. The rate of pulsation of the two signals was found to be the same, and thus presumed to be from a single star. Other observatories were immediately notified and the flashing was confirmed by the McDonald Observatory and by the powerful 84-inch reflector telescope at the Kitt Peak National Observatory in Arizona. The star was flashing at a rate of about 30 times per second, with intermediate flashes of lesser intensity. *TIS
This image is of the Crab Nebula in visible light photographed by the Hale Observatory optical telescope in 1959. The faint object at the centre had been identified as a pulsar and is thought to be the remains of the original star. It has been observed as a pulsar in visible light, radio wave, x-rays, and gamma-rays.*The Hindu Digital
1983 The Department of Commerce officially withdrew the commercial standard for the sizing of women's apparel on January 20, 1983. In the mid-1940's, the Mail-Order Association of America, a trade group representing catalog businesses such as Sears Roebuck and Spiegel, asked the Commodity Standards Division of the National Bureau of Standards (NBS, now NIST )to conduct research to provide a reliable basis for industry sizing standards for women's clothing. Men's clothing had become somewhat standardized as early as the American Civil War due to demands for quick manufacture of uniforms. The resulting commercial standard was distributed by NBS to the industry for comment in 1953, formally accepted by the industry in 1957, and published as Commercial Standard (CS)215-58 in 1958.
However, with the passage of time, the standard became outdated. Both American men and women were becoming heavier. Whereas the average woman's figure once came a little closer to approaching the hourglass shape of the fashion magazines, she was now becoming more pear-shaped, with a thicker waist and fuller hips. At the same time that the average woman's body was changing shape, manufacturers discovered the advantage of appealing to women's vanity. They began selling bigger clothes labeled with smaller size numbers. Today only pattern makers consistently use the old commercial standard.*NIST
1988 IBM's PS/2 Technology to be Cloned
A group of small computer companies announces that they have succeeded in making microprocessors and software that would eventually allow clones of IBM's PS/2 line of personal computers, which had recently been released. In response, IBM threatened legal action to protect its technology. *CHM
1989 Statistician and political scientist Edward R Tufte sent a letter to the New York Times with a copy of his book on statistical graphics. On a visit later to New York, the Times called it as "founding document of New York Times Graphics" *
Edward Tufte@EdwardTufte
1573 Simon Marius (20 Jan 1573, 26 Dec 1624) (Also known as Simon Mayr) German astronomer, pupil of Tycho Brahe, one of the earliest users of the telescope and the first in print to make mention the Andromeda nebula (1612). He studied and named the four largest moons of Jupiter as then known: Io, Europa, Ganymede and Callisto (1609) after mythological figures closely involved in love with Jupiter. Although he may have made his discovery independently of Galileo, when Marius claimed to have discovered these satellites of Jupiter (1609), in a dispute over priority, it was Galileo who was credited by other astronomers. However, Marius was the first to prepare tables of the mean periodic motions of these moons. He also observed sunspots in 1611 *TIS Galileo initially named his discovery the Cosmica Sidera ("Cosimo's stars"), but names that eventually prevailed were chosen by Simon Marius and were suggested by Johannes Kepler, in his Mundus Jovialis, published in 1614. *Wik You can find a nice blog about the conflict with Galileo by the Renaissance Mathematicus.
1775 André-Marie Ampère (20 January 1775 – 10 June 1836) was a French physicist and mathematician who is generally regarded as one of the main discoverers of electromagnetism. The SI unit of measurement of electric current, the ampere, is named after him.*Wik
In September 1820, Ampère's friend and eventual eulogist François Arago showed the members of the French Academy of Sciences the surprising discovery by Danish physicist Hans Christian Ørsted that a magnetic needle is deflected by an adjacent electric current. Ampère began developing a mathematical and physical theory to understand the relationship between electricity and magnetism.
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1907 Edward John Routh FRS (20 January 1831–7 June 1907), was an English mathematician, noted as the outstanding coach of students preparing for the Mathematical Tripos examination of the University of Cambridge in its heyday in the middle of the nineteenth century. He also did much to systematize the mathematical theory of mechanics and created several ideas critical to the development of modern control systems theory.*Wik
Routh's theorem, is first given by him in his Treatise on Analytical Statics with Numerous Examples, 1891. Routh's theorem determines the ratio of areas between a given triangle and a triangle formed by the pairwise intersections of three cevians. The problem and solution had appeared with a proof in Solutions of the Cambridge Senate-house Problems and Riders for the Year 1878, i.e., the mathematical tripos of that year,
1834 William Watson born in Nantucket, MA. In 1862 he earned his Ph.D. at the University of Jena, being the first American to receive a Ph.D. in mathematics at a foreign university. Later he taught at Harvard and MIT. In the same year Yale was the first American school to grant a Ph.D. in mathematics (to J. H. Worall).*VFR
1895 Gabor Szego, Professor Emeritus at Stanford. He co-authored with George (originally Gy¨orogy) P´olya the renown book Problems and Theorems in Analysis. *VFR worked in the area of extremal problems and Toeplitz matrices.*SAU
1904 Renato Caccioppoli ( 20 January 1904 – 8 May 1959) was an Italian mathematician. His most important works, out of a total of around eighty publications, relate to functional analysis and the calculus of variations. Beginning in 1930 he dedicated himself to the study of differential equations, the first to use a topological-functional approach. Proceeding in this way, in 1931 he extended the Brouwer fixed point theorem, applying the results obtained both from ordinary differential equations and partial differential equations. *Wik
1920 Edwin Hewitt (January 20, 1920, Everett, Washington – June 21, 1999) was an American mathematician known for his work in abstract harmonic analysis and for his discovery, in collaboration with Leonard Jimmie Savage, of the Hewitt–Savage zero–one law. [The Hewitt–Savage zero–one law is a theorem in probability theory, similar to Kolmogorov's zero–one law and the Borel–Cantelli lemma, that specifies that a certain type of event will either almost surely happen or almost surely not happen.]
He received his Ph.D. in 1942 from Harvard University, and served on the faculty of mathematics at the University of Washington from 1954.
Hewitt pioneered the construction of the hyperreals by means of an ultrapower construction (Hewitt, 1948).
Hewitt wrote the 1975 English translation of A. A. Kirillov's 1972 Russian monograph Elements of the Theory of Representations (Элементы Теории Представлений), and co-authored Abstract Harmonic Analysis with Kenneth A. Ross (1st edn., 1st vol. in 1963; 1st edn., 2nd vol. in 1970), an extensive work in two volumes. *Wik
1931 David M. Lee (20 Jan 1931, ) American physicist who, with Robert C. Richardson and Douglas D. Osheroff, was awarded the Nobel Prize for Physics in 1996 for their joint discovery of superfluidity in the isotope helium-3.*TIS
The work that led to Lee's Nobel Prize was performed in the early 1970s. Lee, together with Robert C. Richardson and graduate student, Doug Osheroff used a Pomeranchuk cell to investigate the behaviour of 3He at temperatures within a few thousandths of a degree of absolute zero. They discovered unexpected effects in their measurements, which they eventually explained as phase transitions to a superfluid phase of 3He.*Wik
1590 Giovanni Battista Benedetti died. In one of his books he forecast his death for 1592. Hence, on his deathbed, he recomputed his horoscope and declared that an error of four minutes must have been made in the original data, thus evincing his lifelong faith in the doctrines of judicial astrology.*VFR "The essence of Galileo’s laws of fall can be found in the work of Giambattista Bendetti: *RMAT
In his works Resolutio omnium Euclidis problematum (1553)[2] and Demonstratio proportionum motuum localium (1554), Benedetti proposed a new doctrine of the speed of bodies in free fall. The accepted Aristotelian doctrine at that time was that the speed of a freely falling body is directly proportional to the total weight of the body and inversely proportional to the density of the medium. Benedetti's view was that the speed depends on just the difference between the specific gravity of the body and that of the medium. As opposed to the Aristotelian theory, his theory predicts that two objects of the same material but of different weights would fall at the same speed, and also that objects of different materials in a vacuum would fall at different though finite speeds.
1760 John Colson (1680–20 January, 1760) was an English clergyman and mathematician, Lucasian Professor of Mathematics at Cambridge University.
Colson was educated at Lichfield School before becoming an undergraduate at Christ Church, Oxford, though he did not take a degree there. He became a schoolmaster at Sir Joseph Williamson's Mathematical School in Rochester, and was elected Fellow of the Royal Society in 1713. He was Vicar of Chalk, Kent from 1724 to 1740. He relocated to Cambridge and lectured at Sidney Sussex College, Cambridge. From 1739 to 1760 he was Lucasian Professor of Mathematics. He was also Rector of Lockington, Yorkshire.
In 1726 he published his Negativo-Affirmativo Arithmetik advocating a modified decimal system of numeration. It involved "reduction [to] small figures" by "throwing all the large figures 9, 8, 7, 6 out of a given number, and introducing in their room the equivalent small figures respectively".
He translated several of Isaac Newton's works into English, including De Methodis Serierum et Fluxionum in 1736. It was Colsen who mistranslated the name of the curve that Maria Gaetana Agnesi called 'versiera' to become the Witch of Agnesi.*Wik
1864 Giovanni Antonio Amedeo Plana (6 November 1781 – 20 January 1864) was an Italian astronomer and mathematician.
His contributions included work on the motions of the Moon, as well as integrals, elliptic functions, heat, electrostatics, and geodesy. In 1820 he was one of the winners of a prize awarded by the Académie des Sciences in Paris based on the construction of lunar tables using the law of gravity. In 1832 he published the Théorie du mouvement de la lune. In 1834 he was awarded with the Copley Medal by the Royal Society for his studies on lunar motion. He became astronomer royal, and then in 1844 a Baron. At the age of 80 he was granted membership in the prestigious Académie des Sciences. He died in Turin. He is considered one of the premiere Italian scientists of his age.
The crater Plana on the Moon is named in his honor.*Wik
1907 Agnes Mary Clerke (10 Feb 1842, 20 Jan 1907) Irish astronomical writer who was a diligent compiler of facts rather than a practicing scientist. Nevertheless, by 1885, her exhaustive treatise, A Popular History of Astronomy in the Nineteenth Century gained international recognition as an authoritative work. In 1903, with Lady Huggins, she was elected an honorary member of the Royal Astronomical Society, a rank previously held only by two other women, Caroline Herschel and Mary Somerville. Her publications included several books and 55 pieces in the Edinburgh Review. She contributed some astronomer biographies to the Dictionary of National Biography and some astronomical entries in the Encyclopaedia Britannica. *TIS
1921 Mary Watson Whitney (11 Sep 1847, 20 Jan 1921) American astronomer who trained with Maria Mitchell and succeeded her as professor and director of the Vassar College Observatory. As Mitchell had before her, Whitney championed science education the advancement of professional opportunities for women. She developed the astronomy department. Four years before her 1910 retirement, there were 160 students and eight different astronomy courses, including some of the first courses anywhere on astrophysics and on variable stars. During her tenure as director, the Observatory staff published 102 papers in major astronomical journals reporting their work on comets, asteroids, and variable stars. From 1896, photographic plates were used to study and measure star clusters.*TIS
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1922 Camille Jordan (5 Jan 1838, 20 Jan 1922) French mathematician and engineer who prepared a foundation for group theory and built on the prior work of Évariste Galois. As a mathematician, Jordan's interests were diverse, covering topics throughout the aspects of mathematics being studied in his era. The topics in his published works include finite groups, linear and multilinear algebra, the theory of numbers, topology of polyhedra, differential equations, and mechanics.*TIS (His date of death is listed as 22 Jan by *SAU & *Wik)
1944 James McKeen Cattell (25 May 1860, 20 Jan 1944) American psychologist who had a talent in mathematics from a young age, and accordingly applied objective, quantitative methods with his career in experimental psychology. As a university professor, he was the first in America to teach a course in statistical analysis. From 1890, he termed his investigations “mental testing,” with such goals as measuring the amount of pressure required to produce pain, or reaction time to sounds. He developed the order of merit ranking method. Fields in which he applied psychology were broad, including education, business, industry, and advertising. The ideas in Galton's eugenics theory also interested him, and he did support such concepts as sterilization of persons of lower intelligence. He originated professional directories, published scientific periodicals and founded the Science Press (1923) *TIS
1971 Jan Arnoldus Schouten (28 Aug 1883 in Nieuwer Amstel (now part of Amsterdam), Netherlands - 20 Jan 1971 in Epe, The Netherlands) worked on tensor analysis and its applications. He produced 180 papers and 6 books on tensor analysis, applying tensor analysis to Lie groups, general relativity, unified field theory, and differential equations. Influenced by Weyl and Eddington, Schouten investigated affine, projective and conformal mappings. Klein's Erlanger Programm of 1872 looked at geometry as properties invariant under the action of a group. This approach had a large influence on Schouten's approach to his topic. *SAU
2001 Crispin St. John Alvah Nash-Williams (December 19, 1932 – January 20, 2001) was a British and Canadian mathematician. His research interest was in the field of discrete mathematics, especially graph theory.
He is known for the Nash-Williams theorem.
Hilton writes that "Themes running through his papers are Hamiltonian cycles, Eulerian graphs, spanning trees, the marriage problem, detachments, reconstruction, and infinite graphs." In his first papers Nash-Williams considered the knight's tour and random walk problems on infinite graphs; the latter paper included an important recurrence criterion for general Markov chains, and was also the first to apply electrical network techniques of Rayleigh to random walks. His dissertation, which he finished in 1958, concerned generalizations of Euler tours to infinite graphs. *Wik
Credits :
*CHM=Computer History Museum
*FFF=Kane, Famous First Facts
*NSEC= NASA Solar Eclipse Calendar
*RMAT= The Renaissance Mathematicus, Thony Christie
*SAU=St Andrews Univ. Math History
*TIA = Today in Astronomy
*TIS= Today in Science History
*VFR = V Frederick Rickey, USMA
*Wik = Wikipedia
*WM = Women of Mathematics, Grinstein & Campbell
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