Logarithm is the combination of two Greek roots, logos, reason or ratio, and arithmus, number. The ratio refers to the original method of constructing logarithms by geometric sequences. The name, and the original method were created by John Napier, although Joost Burgi had discovered logarithms at about the same time. Napier first used the term in the Latin form, then subsequently into English in Correspondence with Henry Briggs, who would add a table of logarithms in base ten, with log(1)=0 and log(10) = 1.
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The mathematical (and other) thoughts of a (now retired) math teacher,
Friday, 21 March 2025
Logarithms, from Math Terms Notes, Etymology and History
On This Day in Math - March 21
Fourier Series approximation of a square wave, *Mathworld |
True greatness is when your name is like ampere, watt, and fourier—when it's spelled with a lower case letter.
~Richard Hamming (creator of the hamming code, with a lower case h)
The 80th day of the year; There are 80 four-digit primes which are concatenations of two-digit primes. (3137 is one example, can you find the rest?) *Prime Curios! ***
1522 Copernicus read the German version of his treatise, Modus cudendi monetam (The Way to Strike Coin), before the Royal Prussian Assembly attended by King Sigismund Is envoys at Grudziądz (Graudenz). Copernicus discusses general issues related to the theory of money and formulates inter alia a law of bad money driving out good. In the second he focused on the current monetary situation in Royal Prussia and in particular on the decline in the value of Prussian coinage, and concluded his presentation with a proposal to mint three Prussian szelągi as an equivalent of one Polish grosz (groshen) and thus to equalize the value of the new Prussian coinage with that issued by the Crown. *Leszek Zygner
Nicolaus Copernicus University (Students may not know that, in addition to being a respected astronomer, Copernicus was a respected economist.)
1543 Copernicus’ De Revolutionibus published, {{{This date seems incorrect, Thony Christie sent me a note that, "in his An Annotated Census of Copernicus' De Revolutionibus Owen Gingerich writes, 'The printing was finished on 20 April 1543 when Rheticus autographed a presentation copy of the completed work. (Copernicus himself did not receive the final pages until a month later, the day on which he died.)' However I have a note from a post by Teresa Borawska of Nicolaus Copernicus University that says, "There is no information whether a copy of the book printed shortly before 21 March 1543 ever reached Warmia before the astronomers death." and gives no other publication date.}}} The book was so technically complex that only true astronomers could read through it so the 400 copies didn't even sale out. In addition Osiander had written a disclaimer (without, it seems, the dying Copernicus' permission) that readers should view it as a useful mathematical fiction with no physical reality, thereby somewhat shielding it from accusations of blasphemy. But eventually it was banned. It was placed on the Index of Forbidden Books by a decree of the Sacred Congregation of March 5, 1616 as part of the Galileo "incident". [while I was researching this note I came across a nice bit of information that I am not sure where else I could use. De revolutionibus was printed in Hans Petreiuss printing shop in Nuremberg. The building of Petreiuss former printing shop at 9, Öberg Street, (located near Albrecht Durers birthplace) luckily survived the ravages of WWII. You can see in the banner an image of the shop at The Renaissance Mathematicus blog.]
1599 Tycho sends a letter to Longomontanus, in which he reports his revised theory on the movement of the moon. On January 31, During an observation of the lunar eclipse, he had discovered that his predictive theory about the movement of the Moon was wrong since the eclipse started 24 minutes before his calculations predicted.*Wik
1665-6 Hooke writes to C. Huygens to send him a paper on Gravity he has written and presented to the Royal Society.
1684 Giovanni Domenico Cassini discovered two moons of Saturn: Tethys and Dione, using a refractor telescope with an aperture of 108mm. He had previously discovered two other satellites of Saturn: Iapetus (Sep 1671) and Rhea (1672). Christiaan Huygens was the first to discover a moon of Saturn, when he viewed Titan (the largest and easiest to see) on 25 Mar 1655.*TIS
1797 Gauss makes an entry in his diary that the perimeter of the lemniscate can be divided into five equal parts by ruler and compass. Abel would show in 1827 that the division of the lemniscate with classical tools is possible for the same numbers n as the circle. This is an important theorem in elliptic functions. *John Stillwell, Mathematics and Its History
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Lemniscate of Bernoulli *Wik |
1801 Thomas Jefferson to Joseph Priestly:
DEAR SIR,*The Letters of Thomas Jefferson, http://www.let.rug.nl/
-- I learnt some time ago that you were in Philadelphia, but that it was only for a fortnight; supposed you were gone. It was not till yesterday I received information that you were still there, had been very ill, but were on the recovery. I sincerely rejoice that you are so. Yours is one of the few lives precious to mankind, for the continuance of which every thinking man is solicitous.
1816 John Dalton makes the first entry in the second volume of his meteorological notebook. Dalton came to his views on atomism through his interest in meteorology. The volumes contain daily meteorological observations, vol. 1 covering from 1 Apr 1803 to 20 Mar 1816. Volume II would continue until 31 Aug, 1827
In 1925, Wolfgang Pauli published his “exclusion principle.” At the young age of 24, in an article in Zeitschrift für Physik, Pauli introduced the idea that two nearby electrons cannot be in exactly the same state at the same time. For this, now fundamental, contribution to quantum mechanics, he was awarded a Nobel Prize in 1945. *TIS
1925 The Butler Act is signed into law. A law in Tennessee prohibiting the teaching of Darwin’s theory of evolution passed the state senate on March 13, and was signed into law by Governor Austin Peay (for whom the university in Clarksville, Tennessee is named) on March 21. The Butler Act was a Tennessee law:
That it shall be unlawful for any teacher in any of the Universities, Normals and all other public schools of the State which are supported in whole or in part by the public school funds of the State, to teach any theory that denies the Story of the Divine Creation of man as taught in the Bible, and to teach instead that man has descended from a lower order of animals.It would remain the law in Tennessee until repealed on September 1, 1967. *Wik Within a few months, John Scopes became a willing defendant in the “Scopes Monkey Trial,” which began 10 Jul 1925, and received world attention as the statute was tested. He was convicted and fined $100, which was overturned on appeal. *TIS
1943 Joseph Needham, 43, known at that point as a brilliant biologist, arrives in China for the first time. By the time he left, he would be well on his way to being the foremost student of China in the Western World. His "Science and Civilization in China", would alter the basis and direction of math/science history. *Simon Winchester, The Man Who Loved China
1963 When this date is written in the form 3/21/63, the product of the first two numbers is the third. This happens 212 times each century. *VFR (you have 211 left to find)
1989 NCTM released its Curriculum and Evaluation Standards for School Mathematics, a document intended to change fundamentally the way mathematics is taught. *VFR It may have planned to be a fundamental change in how math was taught, ane it may have actually been such a change, but whether that change was for the good or bad is still an open question.
2016 France issues stamp honoring Sophie Germain.
2016 Sphere packing for 24 dimensions is solved by Maryna Viazovska. In 1611, Kepler conjectured that there was no way to pack spheres more densely than the way we would normally stack oranges or cannonballs, with every triangle of three supporting another nestled above (and below) tangent to all of the first three. By 1831 Gauss had managed to prove the conjecture for 3d. In her paper on May 14th Viazovska proved no packing of unit balls in Euclidean space R8 has density greater than that of the E8-lattice packing. One week later, (March 21) building on her work, with collaboration of four others, they were able to prove that the Leech lattice is the densest packing of congruent spheres in twenty-four dimensions, and that it is the unique optimal periodic packing. *arxiv.
1768 Baron Jean-Baptiste-Joseph Fourier (21 Mar 1768; 16 May 1830 at age 62) French mathematician, Egyptologist and administrator who exerted strong influence on mathematical physics through his Théorie analytique de la chaleur (1822; The Analytical Theory of Heat). He introduced an infinite mathematical series to aid in solving conduction equations. This analysis technique allows the function of any variable to be expanded into a series of sines of multiples of the variable, which is now known as the Fourier series. His equations spawned many new areas of study in mathematics and physics, including the branch of optics named for him, have subsequently been applied other natural phenomena such as tides, weather and sunspots.*TIS His work on heat was termed by Maxwell, “a great mathematical poem.” He traveled to Egypt with Napoleon and became convinced that desert heat was ideal for good health. Consequently, he wore many layers of garments and lived in rooms of unbearably high heat. This hastened his death, by heart disease, so that he died, thoroughly cooked. [Eves, History of Mathematics, 362] *VFR
1831 Dorothea Beale LL.D. (21 March 1831 – 9 November 1906) Dorothea studied at Queen's College, London where she became the first female mathematics tutor.
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Beta Aurigae |
1884 George David Birkhoff (21 Mar 1884, 12 Nov 1944) American mathematician, foremost of the early 20th century, who formulated the ergodic theorem. As the first American dynamicist, Birkhoff picked up where Poincaré left off, gaining distinction in 1913 with his proof of Poincaré's Last Geometric Theorem, a special case of the 3-body problem. Although primarily a geometer, he discovered new symbolic methods. He saw beyond the theory of oscillations, created a rigorous theory of ergodic behavior, and foresaw dynamical models for chaos. His ergodic theorem transformed the Maxwell- Boltzmann ergodic hypothesis of the kinetic theory of gases (to which exceptions are known) into a rigorous principle through use of the Lebesgue measure theory. He also produced a mathematical model of gravity. *TIS
1909 Founder of ACM Edmund Berkeley Is Born:
Edmund Berkeley, founder of the Association of Computing Machinery, is born. A graduate of Harvard University, Berkeley participated in the development of Harvard's Mark II while enlisted in the Navy during World War II. In addition to co-founding the ACM in 1947, he wrote one of the first books on computers intended for a general audience, "Giant Brains, or Machines that Think." *CHM
1913 Guillermo Haro Barraza ( 21 March 1913 – 26 April 1988) was a Mexican astronomer who was working as a newspaper reporter, when he interviewed (1937) Luis Erro of Tonantzintla Observatory. By 1943, Haro’s increasing interest in astronomy was rewarded with a staff position there, despite no formal training. His name remains associated with Herbig-Haro objects, that he and George Herbig discovered independently. These seemed to be stars much younger than the rest of the stars in the sky, and had distinquishing anomalies in their spectra which remained unexplained for many years. Haro’s career of contributions marked the emergence of serious astronomy in Mexico, recognized when he was elected (1959) as the first foreign associate of the Royal Astronomical Society from a developing country. *TIS
1920 John Michael Hammersley (21 March 1920 in Helensburgh, Dunbartonshire, Scotland - 2 May 2004 in Oxford, England) British mathematician best-known for his foundational work in the theory of self-avoiding walks and percolation theory. (Wikipedia) when introduced to guests at Trinity College, Oxford, he would say he did difficult sums". He believed passionately in the importance of mathematics with strong links to real-life situations, and in a system of mathematical education in which the solution of problems takes precedence over the generation of theory. He will be remembered for his work on percolation theory, subadditive stochastic processes, self-avoiding walks, and Monte Carlo methods, and, by those who knew him, for his intellectual integrity and his ability to inspire and to challenge. Quite apart from his extensive research achievements, for which he earned a reputation as an outstanding problem-solver, he was a leader in the movement of the 1950s and 1960s to re-think the content of school mathematics syllabuses. (Center for Mathematical Sciences, Cambridge)
During his lifetime, great changes were made in the teaching of mathematics at schools, a matter on which he held strong and opposed, but by no means reactionary, views. He published widely and gave many lectures critical of soft theory at the expense of problem-solving and beauty in mathematics. His best known work, `On the enfeeblement of mathematical skills by `Modern Mathematics' and by similar soft intellectual trash in schools and universities' (published in the Bulletin of the Institute of Mathematics and its Applications, 1968), is now regarded as a force for good at a crossroads of mathematics education. *from his Independent obituary
1927 Halton Christian "Chip" Arp (March 21, 1927 – December 28, 2013) was an American astronomer. He was known for his 1966 book Atlas of Peculiar Galaxies, which documented peculiarities among galaxies. Also noted for challenging the theory that red shifts of quasars indicate their great distance. Arp is one of the key actors in the contemporary debate on the origin and evolution of galaxies in the universe. His landmark compilation of peculiar galaxies led him to challenge the fundamental assumption of modern cosmology, that redshift is a uniform indicator of distance. Astronomers have debated Arp's assertion that quasars are related to peculiar galaxies since the late 1960's. Most astronomers believe that quasars are unrelated to the peculiar galaxies. Yet, no one has been able to explain why the quasars seem to be more numerous around the peculiar galaxies. *TIS
1951 David Nualart (21 March 1951 - ) is a Spanish mathematician working in the field of probability theory, in particular on aspects of stochastic processes and stochastic analysis.
He obtained his PhD titled "Contribución al estudio de la integral estocástica" in 1975 at the University of Barcelona under the supervision of Francesc d'Assís Sales Vallès. After positions at the University of Barcelona and the Polytechnique University of Barcelona he took up a professorship at Kansas University and is currently the Black-Babcock Distinguished Professor in its Mathematics Department.
He published hundreds of scientific articles in his field, served on several scientific committees, has been an associate editor of many journals and from 2006 to 2008 was the Chief Editor of Electronic Communications in Probability.
He has been elected a Fellow of the Institute of Mathematical Statistics in 1997. He received a Doctor Honoris Causa by the University Blaise Pascal of Clermond-Ferrand in 1998. He received the Prize IBERDROLA de Ciencia y Tecnologia in 1999. He has been a Corresponding Member of the Real Academia de Ciencias Exactas Fisicas y Naturales of Madrid since 2003. He has been a member of the Reial Academia de Ciencies i Arts of Barcelona since 2003. He received the Research Prize of the Real Academia de Ciencias de Madrid in 1991.
In March 2011 the International Conference on Malliavin Calculus and Stochastic Analysis in honor of David Nualart took place at University of Kansas. *Wik
A post at the Renaissance Mathematicus about Weigel and some of his lesser known students (most student's would be "lesser known" compared to Leibniz) also pointed out that "Another Weigel innovation in celestial cartography was his eclipse map from 1654. An eclipse map is a map that shows the path on the surface of the earth from which a solar eclipse will be visible. Weigel’s was the first such printed map ever produced. This honor is usually falsely accredited to Edmund Halley for his 1715 eclipse map."
For religious reasons, he wanted to rename all the constellations, and made several globes of the sky with his renamed constellations.
1762 Abbé Nicolas Louis de Lacaille (15 Mar 1713; 21 Mar 1762 at age 48) was a French astronomer who named 15 of the 88 constellations in the sky. He spent 1750-1754 mapping the constellations visible from the Southern Hemisphere, as observed from the Cape of Good Hope, the southernmost part of Africa. In his years there, he was said to have observed over 10,000 stars using just his 1/2-inch refractor. He established the first southern star catalogue containing 9776 stars (Caelum Australe Stelliferum, published partly in 1763 and completely in 1847), and a catalogue of 42 nebulae in 1755 containing 33 true deep sky objects (26 his own discoveries).*TIS
1822 D'Amondans Charles de Tinseau (19 April 1748 in Besançon, France - 21 March 1822 in Montpellier, France) wrote on the theory of surfaces, working out the equation of a tangent plane at a point on a surface, and he generalised Pythagoras's theorem proving that the square of a plane area is equal to the sum of the squares of the projections of the area onto mutually perpendicular planes. He continued Monge's study of curves of double curvature and ruled surfaces, being in a sense Monge's first follower. Taton writes that Tinseau's works, "... deal with topics in the theory of surfaces and curves of double curvature: planes tangent to a surface, contact curves of circumscribed cones or cylinders, various surfaces attached to a space curve, the determination of the osculatory plane at a point of a space curve, problems of quadrature and cubature involving ruler surfaces, the study of properties of certain special ruled surfaces (particularly conoids), and various results in the analytic geometry of space."
Two papers were published in 1772 on infinitesimal geometry Solution de quelques problèmes relatifs à la théorie des surfaces courbes et des lignes à double courbure and Sur quelques proptiétés des solides renfermés par des surfaces composées des lignes droites. He also wrote Solution de quelques questions d'astronomie on astronomy but it was never published. He did publish further political writings, as we mentioned above, but other than continuing to correspond with Monge on mathematical topics, he took no further part in mathematics. *SAU
1864 Luke Howard, FRS (28 November 1772 – 21 March 1864) was a British manufacturing chemist and an amateur meteorologist with broad interests in science. His lasting contribution to science is a nomenclature system for clouds, which he proposed in an 1802 presentation to the Askesian Society.
He has been called "the father of meteorology" because of his comprehensive recordings of weather in the London area from 1801 to 1841 and his writings, which transformed the science of meteorology. *Wik
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*LH |
1928 Edward Walter Maunder (12 Apr 1851, 21 Mar 1928 at age 76) English astronomer who was the first to take the British Civil Service Commission examination for the post of photographic and spectroscopic assistant at the Royal Observatory, Greenwich. For the next forty years that he worked there, he made extensive measurements of sunspots. Checking historical records, he found a period from 1645 to 1715 that had a remarkable lack of reports on sunspots. Although he might have questioned the accuracy of the reporting, he instead attributed the shortage of report to an actual dearth of sunspots during that period. Although his suggestion was not generally accepted at first, accumulating research has since indicated there are indeed decades-long times when the sun has notably few sunspots. These periods are now known as Maunder minima.*TIS
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*Wik |
1933 Enrico D'Ovidio (11 Aug 1842 in Campobasso, Italy - 21 March 1933 in Turin, Italy) D'Ovidio was to work for 46 years in the University of Turin. He was chairman of the Faculty of Science in 1879-80 and rector of the University between 1880 and 1885. Another spell as chairman of the Faculty of Science between 1893 and 1907 ended when he was appointed Commissioner of the Polytechnic of Turin.
Euclidean and noneuclidean geometry were the areas of special interest to D'Ovidio. He built on the geometric ideas which had been introduced by Lobachevsky, Bolyai, Riemann and Cayley. D'Ovidio's most important work is probably his paper of 1877 The fundamental metric functions in spaces of arbitrarily many dimensions with constant curvature.
D'Ovidio also worked on binary forms, conics and quadrics. He had two famous assistants, Peano (1880-83) and Corrado Segre (1883-84). D'Ovidio and Corrado Segre built an important school of geometry at Turin. *SAU
1934 Thomas Muir (25 Aug 1844 in Stonebyres, Falls of Clyde, Lanarkshire, Scotland
- 21 March 1934 in Rondebosch, South Africa) He is noted for a four volume work on the history of determinants. *VFR He also proved an important lemma about determinants of skew symmetric matrices
1960 Sheila Scott Macintyre (née Sheila Scott, April 23, 1910 - March 21, 1960) was a Scottish mathematician well known for her work on the Whittaker constant. Macintyre is also well known for creating a multilingual scientific dictionary: written in English, German, and Russian; at the time of her death, she was working on Japanese.
2020 Walter Volodymyr Petryshyn (Vladimir Petryshin) (22 January 1929, Liashky Murovani, Lviv - 21 March 2020) is a famous Ukrainian mathematician. He had commenced his studies in Lviv during World War II, but he became a displaced person at the end of the war and continued his schooling in Germany. In 1950 he emigrated from Germany to the United States and completed his education there, living in Paterson, New Jersey. He studied at Columbia University and was awarded a B.A. in 1953, an M.S. in 1954, and a Ph.D. in 1961. Petryshyn's main achievements are in functional analysis. His major results include the development of the theory of iterative and projective methods for the constructive solution of linear and nonlinear abstract and differential equations.*Wik
***For those who care, the 80 primes made by the concatenation of primes with two digits are:
1117, 1123, 1129, 1153, 1171, 1319, 1361, 1367, 1373, 1723, 1741, 1747, 1753, 1759, 1783, 1789, 1913, 1931, 1973, 1979, 1997, 2311, 2341, 2347, 2371, 2383, 2389, 2917, 2953, 2971, 3119, 3137, 3167, 3719, 3761, 3767, 3779, 3797, 4111, 4129, 4153, 4159, 4337, 4373, 4397, 4723, 4729, 4759, 4783, 4789, 5323, 5347, 5923, 5953, 6113, 6131, 6143, 6173, 6197, 6719, 6737, 6761, 6779, 7129, 7159, 7331, 7919, 7937, 8311, 8317, 8329, 8353, 8389, 8923, 8929, 8941, 8971, 9719, 9743 and 9767
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
Thursday, 20 March 2025
On This Day in Math - March 20
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Newton Statue in Trinity Chapel, Cambridge UK *R.B. |
The mathematical education of the young physicist [Albert Einstein] was not very solid, which I am in a good position to evaluate since he obtained it from me in Zurich some time ago.
~Hermann Minkowski
The 79th day of the year, 78*79 = 6162 (note that the product of consecutive numbers produces a number that is the concatenation of two successive numbers 61 and 62 in ascending order (and 61 is prime). (Can you find another number, not necessarily prime, so that n(n-1)= a concatenation of consecutive numbers?)
79 = 27 - 72
79 is the smallest number that can not be represented with less than 19 fourth-powers. (Before you read blithely on, there are three more year days that also require the sum of 19 fourth-powers... find one.) It's also the smallest prime whose digit sum is a fourth power, the second smallest is its reversal, 97
79 = 11 + 31 + 37. Curiously, the sum holds for the reversals: 97 = 11 + 13 + 73, and all are primes.
279 is the smallest power of 2 which is greater than Avogadro's number
1079 has been called the "Universe number" because it is considered a reasonable lower limit estimate for the number of atoms in the observable universe. *Prime Curios
EVENTS
71 A.D.: A hybrid solar eclipse is noted by the scholar Plutarch from Greece where it was total. *David Dickinson @Astroguyz
1664 (1665 NS) Robert Hooke becomes the Gresham Professor of Mathematics. The failure of many of the professors to give their lectures had caused the College to go into decline. Hooke wrote in his diary that he frequently gave no lecture as “no one attended”. The College is generally in decline for the next 100-200 years. Hooke held the position until his death in 1703.
1732 Laura Maria Caterina Bassi first (The next was Émilie du Châtelet in 1746.) woman elected to Bologna Academy of Science:
The University of Bologna is the oldest university in Europe and at the beginning of the eighteenth century students were still examined by public disputation, i.e. the candidate was expected to orally defend a series of academic theses. At the beginning of 1732 Bassi took part in a private disputation in her home with members of the university faculty in the presence of many leading members of Bolognese intellectual society. As a result of her performance during this disputation she was elected a member of the prestigious Bologna Academy of Science on 20th March. Rumours of this extraordinary young lady quickly spread and on 17th April she defended forty-nine theses in a highly spectacular public disputation. On 12th May following a public outcry she was awarded a doctorate from the university in a grand ceremony in the city hall of Bologna. Following a further public disputation the City Senate appointed her professor of philosophy at the university, making her the first ever female professor at a European university.
See more at *Thony Christie, The Renaissance Mathematicus
1774 Ben Franklin to Condorcet on capacity of African American Slaves
*Science and the Founding Fathers, I. Bernard Cohen
1749 Euler provides what he believes is the outline of a proof for the hypothesis that every prime number of the form 4n+1 is a sum of two squares. *VFR
In 1800, Alessandro Volta dated a letter announcing his invention of the voltaic pile to Sir Joseph Banks, president of the Royal Society, London. “On the electricity excited by the mere contact of conducting substances of different kinds"” described his results of stacking sandwiches of copper and zinc metal discs between pads of moist material. The letter had to pass from Italy, through France, which was then at war with Britain, so Volta sent the message in two parts. When the first pages arrived, Banks showed them to Anthony Carlisle, a London surgeon, who with William Nicholson immediately began trying to repeat Volta's experiments. By 2 May 1800, they stumbled upon electrolysis of water.*TIS
It was an article by Nicholson about the way the Torpedo fish produced it's electric shock that had inspired Volta's latest experiments. He had been sparring with Galvani about the possibility of mechanical energy for years. In the same letter mentioned above, he credits Nicholson, "The hypothesis of this learned and laborious philosopher …. is indeed very ingenious."
His image, and of the battery named for him, appear on the 10,000 Lira note before Italy converted to the Euro.

1816 John Dalton makes the last entry in his first meteorological notebook. Dalton came to his views on atomism through his interest in meteorology. The volumes contain daily meteorological observations, vol. 1 covering from 1 Apr 1803 to 20 Mar 1816. He would begin a second volume the next day.
1897 Baseball's pitching machine, or at that time, the "pitching gun" was invented by Charles H. Hinton at Purdue. On March 20, the invention, a gunpowder operating baseball gun, was featured in Harper's Magazine. The machine had adjustable speeds and could throw curve balls by the use of two rubber coated "fingers" at the end of the muzzle. Hinton was also a early writer in the fourth dimension, and coined the term tesseract. More about Hinton at my "Baseball and the Fourth Dimension"
Einstein's Theory of General Relativity was titled “Die Grundlagen der allgemeinen Relativitästheorie.” This theory accounted for the slow rotation of the elliptical path of the planet Mercury, which Newtonian gravitational theory failed to do. Fame and recognition came suddenly in 1919, when the Royal Society of London photographed the solar eclipse and publicly verified Einstein's general theory of relativity. In 1921 he was awarded the Nobel Prize for Physics for his photoelectric law and work in the field of theoretical physics, but such was the controversy still aroused by this theories on relativity that these were not specified in the text of the award. *TIS
1997 Cellular Phone Encryption Is "Cracked," Highlighting Privacy Concerns:
Computer security experts announce that they have cracked the code designed to protect the privacy of calls made with digital cellular phones. The breakthrough showed that cellular phone transmissions remained insecure despite recent developments. The National Security Agency, however, cautioned against more advanced encryption that might allow terrorists to conspire by telephone.*chm
2016 Spring officially comes to Possum Trot, Ky. The equinox passed last night in the dark, daffodils are blooming and dogwoods are budding nicely. The word equinox is derived from the Latin words meaning “equal night.” The spring and fall equinoxes are the only dates with equal daylight and dark as the Sun crosses the celestial equator. At the equinoxes, the tilt of Earth relative to the Sun is zero, which means that Earth’s axis neither points toward nor away from the Sun. *Farmer's Almanac
2017 On this day the public schools of the city of Boston, Mass briefly put spherical and projective geometry in the news. On that date the schools began converting their classroom maps from the common Mercator Projection, to the little known Gall-Peters Projection. The Mercator projection makes some areas, Greenland and Alaska, for example, look much larger than other similar sized areas by comparison. The Gall–Peters projection maps all areas such that they have the correct sizes relative to each other. Like any equal-area projection, it achieves this goal by distorting most shapes.
BIRTHS
1546 Baha ad-din Muhammad ibn Husayn al-Amili (20 Mar 1546; 20 Aug 1622 at age 76)
Syrian-Iranian theologian, mathematician and astronomer, a.k.a. Shaykh Baha'i). He became a very learned Muslim whose genius touched every field of knowledge from mathematics and philosophy to architecture and landscape design. He revived the study of mathematics in Iran. His treatise on the subject, Khulasat al-hisab (“The Essentials of Arithmetic”), and translations from the original Arabic was in use as a textbook until the end of the 19th century. His treatise in astronomy, Tashrihu'l-aflak ("Anatomy of the Heavens") summarised the works of earlier masters. He was born within a year of William Gilbert in England and Tycho Brahe in Denmark, and was still a child when his family left Syria to escape religious persecution.*TIS
1664 Johann Baptist Homann (20 March 1664 – 1 July 1724) was a German geographer and cartographer, who made maps of the Americas.
Homann was born in Oberkammlach near Kammlach in the Electorate of Bavaria.
Homann acquired renown as a leading German cartographer, and in 1715 was appointed Imperial Geographer by Emperor Charles VI. Giving such privileges to individuals was an added right that the Holy Roman Emperor enjoyed. In the same year he was also named a member of the Prussian Academy of Sciences in Berlin. Of particular significance to cartography were the imperial printing privileges (Latin: privilegia impressoria). These protected for a time the authors in all scientific fields such as printers, copper engravers, map makers and publishers. They were also very important as recommendation for potential customers.
In 1716 Homann published his masterpiece Grosser Atlas ueber die ganze Welt (Grand Atlas of all the World). Numerous maps were drawn up in cooperation with the engraver Christoph Weigel the Elder, who also published Siebmachers Wappenbuch.
Homann died in Nuremberg. He was succeeded by the Homann heirs company, in business until 1848. *Wik A beautiful pocket globe he created can be seen at the Vault, Slate's History blog.
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*Wik |
1750 Martin(us) van Marum (20 March 1750, Delft – 26 December 1837, Haarlem) was a Dutch physician, inventor, scientist and teacher, who studied medicine and philosophy in Groningen. Van Marum introduced modern chemistry in the Netherlands after the theories of Lavoisier, and several scientific applications for general use. He became famous for his demonstrations with instruments, most notable the Large electricity machine, to show statical electricity and chemical experiments while curator for the Teylers Museum.
Many people are aware of Mertens contributions since his elementary proof of the Dirichlet theorem appears in most modern textbooks. However he made many deep contributions including Mertens' theorems, three results in number theory related to the density of the primes. He proved these results using Chebyshev's theorem, a weak version of the prime number theorem. *SAU
In his youth, Mertens moved to Berlin where he became a student at Berlin
University, and where he studied under Kronecker and Kummer. Mertens first worked in Krakow, and then moved to Austria. Ernst Fischer and Schrodinger, for instance, were students of Mertens at the University of Vienna. *Julio Gonzalez Cabillon, Historia Matematica Discussions
1856 Frederick Winslow Taylor (20 Mar 1856, 21 Mar 1915 at age 58) was an American engineer and inventor who is known as the father of scientific management. His system of industrial management has influenced the development of virtually every country enjoying the benefits of modern industry. He introduced a scientific approach (1881) to “time and motion study” while chief engineer at Midvale Steel Company, Philadelphia, Pa. Taylor and his associates used stop-watches to time the laborers as they performed various tasks, counted the number of shovel-loads they each moved, and the load per shovel. Thus he was able to determine an optimum shovel size and length. Such careful observations, aimed at recognizing wasted effort and minimizing time used, increased the efficiency of actions of factory workers.*TIS
The term "scientific management" was coined by US Supreme Court justice Louis Brandeis to describe Taylor's principles, and in 1911, Taylor published his life's work in the book The Principles of Scientific Management. Taylor was an accomplished tennis and golf player. He and Clarence Clark won the inaugural United States National tennis doubles championship at Newport Casino in 1881 Taylor was a lifelong member of the Philadelphia Country Club, and finished fourth in the 1900 Olympic individual golf event. *Wik *Sports Reference
1884 Philipp Frank (20 Mar 1884; 22 Jul 1966 at age 82) Austrian-American physicist and mathematician whose theoretical work covered a broad range of mathematics, including variational calculus, Hamiltonian geometrical optics, Schrödinger wave mechanics, and relativity. Frank had a deep and lasting interest in the philosophy of science. In a number of writings, he strove to reconcile science and philosophy and “bring about the closest rapprochement between” them. The 1907 paper he wrote analyzing the law of causality caught Einstein's attention, who in 1912 recommended Frank as his successor as professor of theoretical physics at the German University of Prague. He held that position until 1938, when he moved to Harvard University in the U.S., first as visiting lecturer, but remaining there until retirement in 1954. He wrote on misinterpretations of the Theory of Relativity.*TIS
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1920 Douglas George Chapman (20 Mar 1920; 9 Jul 1996 at age 76) was a Canadian-born U.S. mathematical statistician and an expert on wildlife statistics. He was one of the scientific advisors to the International Whaling Commission that warned in the 1960s that the number of whales being taken by the whaling industry was far in excess of what the population could stand, and proposed annual fin whale catch quotas that would permit the depleted populations of this species to recover. His later research on fish farming expanded to include mollusk aquaculture and he directed a program to develop quantitative methods to aid in the management of fisheries resources.*TIS
1921 Alfréd Rényi (20 March 1921 – 1 February 1970) was a Hungarian mathematician who made contributions in combinatorics, graph theory, number theory but mostly in probability theory. He proved, using the large sieve, that there is a number K such that every even number is the sum of a prime number and a number that can be written as the product of at most K primes. See also Goldbach conjecture.
In information theory, he introduced the spectrum of Rényi entropies of order α, giving an important generalisation of the Shannon entropy and the Kullback-Leibler divergence. The Rényi entropies give a spectrum of useful diversity indices, and lead to a spectrum of fractal dimensions. The Rényi–Ulam game is a guessing game where some of the answers may be wrong.
He wrote 32 joint papers with Paul Erdős, the most well-known of which are his papers introducing the Erdős–Rényi model of random graphs. Rényi, who was addicted to coffee, invented the quote: "A mathematician is a device for turning coffee into theorems.", which is generally ascribed to Erdős. The sentence was originally in German, being a wordplay on the double meaning of the word Satz (theorem or residue of coffee). *Wik
Renyi's wife Catherine (she went by Kato') was also a mathematician and co-authored at least one paper with him on counting K trees. She died during the completion of this work which carried this footnote.
1938 Sergi Petrovich Novikov (20 Mar 1938, ) Russian mathematician who was awarded the Fields Medal in 1970 for his work in algebraic topology. His parents were both mathematicians, and Novikov showed his own talent while a youth. In 1960, the year he obtained his first degree, he published a paper on some problems in the topology of manifolds connected with the theory of Thom spaces. In 1965, he proved his famous theorem on the invariance of Pontryagin classes. He was unable receive the Fields Medal in person because Soviet authorities would not permit his travel. Thereafter he pursued an interest in mathematical physics, including the theory of solitons, quantum field theory and string theory. *TIS
DEATHS
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D'Aguilon was born in Brussels. He became a Jesuit in 1586. In 1611, he started a special school of mathematics, in Antwerp, which was intended to perpetuate mathematical research and study in among the Jesuits. This school produced geometers like André Tacquet and Jean Charles della Faille.
His book, Opticorum Libri Sex philosophis juxta ac mathematicis utiles (Six Books of Optics, useful for philosophers and mathematicians alike), published in Antwerp in 1613, was illustrated by famous painter Peter Paul Rubens. It was notable for containing the principles of the stereographic and the orthographic projections, and it inspired the works of Desargues and Christiaan Huygens. *Wik
1726/7 Isaac Newton (25 December 1642 – 20 March 1726 [NS: 4 January 1643 – 31 March 1727) English physicist and mathematician, who made seminal discoveries in several areas of science, and was the leading scientist of his era. His study of optics included using a prism to show white light could be split into a spectrum of colors. The statement of his three laws of motion are fundamental in the study of mechanics. He was the first to describe the moon as falling (in a circle around the earth) under the same influence of gravity as a falling apple, embodied in his law of universal gravitation. As a mathematician, he devised infinitesimal calculus to make the calculations needed in his studies, which he published in Philosophiae Naturalis Principia Mathematica (Mathematical Principles of Natural Philosophy, 1687)*TIS
Newton died intestate. Immediately his relatives began to quarrel over the division of his estate, which amounted to a considerable fortune. Thomas Pellet examined Newton’s manuscript holdings in hopes of turning a quick profit. His “thick clumsy annotations ‘Not fit to be printed,’ now seem at once pitiful and ludicrous.” See Whiteside, Newton Works, I, xvii ff for details. *VFR
1878 (Julius) Robert Mayer (25 Nov 1814; 20 Mar 1878) a German physicist. While a ship's doctor sailing to Java, he considered the physics of animal heat. In 1842, he measured the mechanical equivalent of heat. His experiment compared the work done by a horse powering a mechanism which stirred paper pulp in a caldron with the temperature rise in the pulp. He held that solar energy was the ultimate source of all energy on earth, both living and nonliving. Mayer had the idea of the conservation of energy before either Joule or Helmholtz. The prominence of these two scientists, however, diminished credit for Mayer's earlier insights. James Joule presented his own value for the mechanical equivalent of heat. Helmholtz more systematically presented the law of conservation of energy. *TIS
1895 Ludwig Schläfli (15 Jan 1814 in Grasswil, Bern, Switzerland - 20 March 1895 in Berne, Switzerland) Schläfli is best known for the so-called Schläfli symbols which are used to classify polyhedra. In this work, Theorie der vielfachen Kontinuität (Theory of continuous manifolds), Schläfli introduced polytopes (although he uses the word polyschemes) which he defines to be higher dimensional analogues of polygons and polyhedra. Schläfli introduced what is today aclled the Schläfli symbol. It is defined inductively. {n} is a regular n-gon, so {4} is a square. There {4, 3} is the cube, since it is a regular polyhedron with 3 squares {4} meeting at each vertex. Then the 4 dimensional hypercube is denoted as {4, 3, 3}, having three cubes {4, 3} meeting at each vertex. Euclid, in the Elements, proves that there are exactly five regular solids in three dimensions. Schläfli proves that there are exactly six regular solids in four dimensions {3, 3, 3}, {4, 3, 3}, {3, 3, 4}, {3, 4, 3}, {5, 3, 3}, and {3, 3, 5}, but only three in dimension n where n ≥ 5, namely {3, 3, ..., 3}, {4, 3, 3, ....,3}, and {3, 3, ...,3, 4}.
Most of Schläfli's work was in geometry, arithmetic and function theory. He gave the integral representation of the Bessel function and of the gamma function. His eight papers on Bessel functions played an important role in the preparation of G N Watson's major text Treatise on the theory of Bessel functions (1944). *SAU
1962 Andrew Ellicott Douglass (5 Jul 1867, 20 Mar 1962 at age 94) American astronomer and archaeologist who coined the name dendrochronology for tree-ring dating, a field he originated while working at the Lowell Observatory, Flagstaff, Ariz. (1894-1901). He showed how tree rings could be used to date and interpret past events. Douglass also sought a connection between sunspot activity and the terrestrial climate and vegetation. The width of tree rings is a record of the rainfall, with implications on the local food supply in dry years. Archaeologist Clark Wissler collaborated in this work by furnishing sections of wooden beams from Aztec Ruin and Pueblo Bonito so Douglass could cross-date the famous sites. Thus the study of tree rings enables archaeologists to date prehistoric remains. *TIS
1983 Ivan Matveyevich Vinogradov (2 Sep 1891, 20 Mar 1983 at age 91) Soviet mathematician known for his contributions to the analytical theory of numbers, including a partial solution of the Goldbach conjecture proving that every sufficiently large odd integer can be expressed as the sum of three odd primes. He described his methods in his most celebrated piece of work Some Theorems Concerning the Theory of Prime Numbers (1937).*TIS
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1993 Polykarp Kusch (26 Jan 1911; 20 Mar 1993) German-American physicist who shared the Nobel Prize for Physics in 1955 for his accurate determination that the magnetic moment of the electron is greater than its theoretical value. This he deduced from researching the hyperfine structure of the energy levels in certain elements, and in 1947 found a discrepancy of about 0.1% between the observed value and that predicted by theory. Although minute, this anomaly was of great significance and led to revised theories about the interactions of electrons with electromagnetic radiation, now known as quantum electrodynamics. (He shared the prize with Willis E. Lamb, Jr. who performed independent but related experiments at Columbia University on the hyperfine structure of the hydrogen atom.)*TIS
2007 Albert Vinicio Báez ( 15 Nov, 1912 – 20 March, 2007) was a Mexican-American physicist, and the father of singers Joan Baez and Mimi Fariña. He was born in Puebla, Mexico; his family moved to the United States when he was two years old because his father was a Methodist minister, having left Catholicism when his son was two. The son grew up in Brooklyn, and considered becoming a minister, before turning to mathematics and physics. He made important contributions to the early development of X-ray microscopes and later X-ray telescopes. He also influenced John Baez's, his nephew, interest in science. *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