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Friday, 21 March 2025

Logarithms, from Math Terms Notes, Etymology and History

 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.

The name was introduced by John Napier (1550-1617), the inventor of logarithms, in his 1614 work on logarithms, Mirifici logarithmorum canonis descriptio, [Description of the wonderful canon of logarithms .... but it is usually called "The Descripto"]. It was originally written in Latin and subsequently translated into English. Here is a site where you can find a digital copy of the English text.

It seems that Pietro Mengoli (1625-1686) was the first to use the term "natural logarithm". Boyer writes, "Mercator took over from Mengoli the name 'natural logarithm' for values that are derived by means of this series." The term Mengoli and Mercator actually used was "logarithmus naturalis". In a discussion group, Jeff Miller suggested that it might be this use of noun before adjective that prompted the use of the symbol "ln" for natural log rather than "nl". According to Cajori, the symbol "ln" was first used for the natural logarithm (log base e) in 1893 by Irving Stringham (1847-1909). Stringham introduces the notation without comment in a list of symbols following the table of contents, then uses it for the first time on page 41, shown below.
Thanks to Dave Renfro for help in getting this digital pic.
I also recently heard in a correspondence from George Zeliger that when he was a student in Russia (around 1989) it was common to use "lg" for the common logarithm (log base ten).

When Napier constructed his tables he used a base that was slightly smaller than one (1-10^(-7)) and so as the number, n, got bigger, the logarithm, l, got smaller. It was common at the time in trigonometry tables to divide the radius of a circle into 10,000,000 parts. Because the main intention of his creation was focused on addressing the difficulty in performing trigonometric computations, Napier also divided his basic unit into 107 parts. Then to avoid having to use fractions, he multiplied each value by 107. In notation of today's mathematics, the form of Napier's logs would look like :
107 (1-10^(-7)) L=N. Then L is the Naperian logarithm of N.

According to e: The Story of a Number by Eli Maor,

In the second edition of Edward Wright's translation of Napier's Descripto (London, 1618), in an appendix probably written by William Oughtred, there appears the equivalent of the statement that loge10 = 2.302585.
Since the actual tables contains no decimals it was probably given as 2302585 without the decimal point.
In a famous meeting between Napier and Henry Briggs, Briggs suggested the use of a base of 10 instead of 1- 10^(-7) and to have the logarithm of one equal to zero. This Napier agreed to but the task of constructing tables of "common" logarithms fell to Briggs, and they were often called Brigg's Logarithms in his honor.


Robin Wilson, in his Gresham College lecture on the number e, that "Early ideas of logarithms are given in works of Chuquet and Stifel around the year 1500. They listed the first few powers of 2 and noticed that to multiply any two of them it is enough to add their exponents." Maor notes that Joost Burgi of Switzerland probably created a table of logarithms before Napier by several years, but did not publish until later, and he is almost forgotten today. Burgi may also have independently discovered the method of Prosthaphaeresis and gave it to Tycho Brahe. Burgi is also remembered as the person who taught Kepler Algebra.

Joost Burgi




[[[Prosthaphaeresis (from the Greek προσθαφαίρεσις) was an algorithm used in the late 16th century and early 17th century for approximate multiplication and division using formulas from trigonometry. For the 25 years preceding the invention of the logarithm in 1614, it was the only known generally applicable way of approximating products quickly. Its name comes from the Greek prosthen (πρόσθεν) meaning before and aphaeresis (ἀφαίρεσις), meaning taking away or subtraction.]]]

The impact of logarithms on the working scientist of the period is hard to appreciate, but one may get an idea from this quote by Pierre Laplace, "Logarithms, by shortening the labors, doubled the life of the astronomer." While it is Napier's work on logarthms that he is remembered for today, in his own time he was famous for the calculating method called Napier's rods and a method of calculating spherical right triangle trigonometry. He thought his most important work had been published 21 years earlier in 1593. In that year he published a mathematical analysis of the book of Revelations in the Bible, A Plaine Discovery of the Whole Revelation of Saint John. In the book he revealed that the Pope was the antichrist, and that the world would end in the year 1786. Fortunately for us, he was wrong on at least that one point. To his credit, he more accurately predicted the development of the machine gun, the submarine, and the tank.

Gordon Fisher recently posted a time line of the development of the use of the abbreviation "log" for lograrithms. Here is his post with a few notes thrown in
Log. (with a period, capital "L") was used by Johannes Kepler (1571-1630) in 1624 in Chilias logarithmorum (Cajori vol. 2, page 105)
log. (with a period, lower case "l") was used by Bonaventura Cavalieri (1598-1647) in Directorium generale Vranometricum in 1632 (Cajori vol. 2, page 106).
log (without a period, lower case "l") appears in the 1647 edition of Clavis mathematicae by William Oughtred (1574-1660) (Cajori vol. 1, page 193).
Kline (page 378) says Leibniz introduced the notation log x (showing no period), but he does not give a source.
loga was introduced by Edmund Gunter (1581-1626) according to an Internet source. [I do not see a reference for this in Cajori.]
Many students (and teachers) have heard colorful legends about the reasoning behind the use of "ln" for the natural logarithm (from the French for something, or something about the name Napier). Most of them seem to me to be more myth than fact. The facts, as best I know them, is that the first use of the terms "natural" and "logarithm" together was by Nicholas Mercator (not the cartographer) in 1668 in his logarithmo technica in which he used the Latinized "log naturalis". [[[In early 2005 a post from Jeff Miller pointed out that, according to Carl Boyer, Pietro Mengoli used the term before Mercator. Both were working with values derived from a series, Mercator with the expansion of log(1+x)]]] The first use of "ln" as a symbol was, as Gordon points out(below), by Stringham (I have not seen this book and do not know if he gives an explanation). As to the correct pronunciation of "ln(x)", whatever your teacher says is correct, but high school students should be aware that many college mathematicians find the symbol disturbing. In his 1984 biography, Paul Halmos described the symbol as "childish". It is, however, very commonly used in computer science.
ln (for natural logarithm) was used in 1893 by Irving Stringham (1847-1909) in Uniplanar Algebra (Cajori vol. 2, page 107).
The same note from Jeff Miller mentioned above pointed out that Anton Steinhauser used the abbreviation "log.nat." in 1875
William Oughtred (1574-1660) used a minus sign over the characteristic of a logarithm in the Clavis Mathematicae (Key to Mathematics), "except in the 1631 edition which does not consider logarithms" (Cajori vol. 2, page 110). The Clavis Mathematicae was composed around 1628 and published in 1631 (Smith 1958, page 393). Cajori shows a use from the 1652 edition.
I also recently saw a post that suggested that in computer classes it is sometimes common to use "lg" for the base two log.

In 1647 the French mathematician Saint-Vincent showed that the area under the hyperbola y = 1/x were like the logarithm function, that is, the area from 1 to 2 plus the area from 1 to 3 was equal to the area from 1 to 6, 2x3.  

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! ***


 80 in Roman Numerals is not suitable for minors, LXXX, 

 The Pareto principle (sometimes called the 80-20 rule)says that, for many events, roughly 80% of the effects come from 20% of the causes, ie, ≈80% of the accidents are caused by 20% of the drivers. 

 n2n1  gives the number of edges (segments) in a n-dimensional cube, and in the 5th dimension, (went there once in a dream) there are 80 edges, 524 (It also has 80 two-dimensional square faces.) 

 And 80 is the smallest number diminished by taking its sum of letters (writing out its English name and adding the letters using a=1, b=2, c=3, ...) *Tanya Khovanova 

 In 1719 Paul Halcke showed that the product of the aliquot divisors of 80 equals the fourth power of 80. The only year numbers for which this is true is 48 and 80.

EVENTS

---Commonly considered the first day of spring, a tradition dating from the Council of Nicaea in A.D. 325. The most recent year in which this was in fact true in the U.S. was 1979, when the vernal equinox occurred at 12:22 a.m. EST. The next time the vernal equinox will be on March 21 is in 2103 when it will occur at 1:09:04 a.m. EST. This computation uses a tropical year of 365 days, 5 hours, 48 minutes, and 46 seconds. [Mathematics Magazine, 55(1982), 46–47] *VFR

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.]
Original 1543 Nuremberg edition





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


Lemniscate of Bernoulli *Wik




1801 Thomas Jefferson to Joseph Priestly:
DEAR SIR,

-- 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.
*The Letters of Thomas Jefferson, http://www.let.rug.nl/



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  
Scopes is buried in Paducah, Ky  




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.




2006 The origins of Twitter came out of a brainstorming session at the podcasting company Odeo. The initial concept was to share short messages via SMS text messaging with a small group. Jack Dorsey was the primary designer of what was then code-named “twttr” and sent the first message at 9:50am on March 21st, 2006 - "just setting up my twttr." Twitter would be released to the public that July and found its first major success at the South by Southwest Interactive conference in 2007, shortly after it had been spun-off as its own company, Twitter, Inc.
Dorsey came up with the idea that eventually became Twitter while studying at New York University. While working on dispatching as a programmer Dorsey moved to California.  In 2000 Dorsey started his company in Oakland to dispatch couriers, taxis, and emergency services from the Web. His other projects and ideas at this time included networks of medical devices and a "frictionless service market". Inspired in part by LiveJournal and by AOL Instant Messenger, he had the idea for a Web-based realtime status/short message communication service




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.





BIRTHS 

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. 
From age thirteen to sixteen Beale educated herself at home. Although Beale's father considered arithmetic to be a waste of time, Beale's parents did not actively prevent her from learning mathematics. So, during her three years of self-education, Beale taught herself arithmetic with Bishop Colenso's Arithmetic Exercises with Answers (1843). She was fortunate in that she had access to two large libraries, the London Institution and Crosby Hall, and she spent much of her time working alone there, making some progress with algebra, and even calculating the distance to the moon. She commented 
I borrowed a Euclid, and without any help read the first six books, carefully working through the whole of the fifth, as I did not know what was usually done. It did not occur to ask my father for lessons in such subjects.
Beale also attended the lectures by the Gresham Professor of Astronomy, Joseph Pullen, at Crosby Hall. These lectures had a substantial impact on her, inspiring a passionate desire to know more about mathematics and the processes described in the lectures.

Beale's younger brothers attended Merchant Taylor's School, where the education was no better or worse than the other public schools of the time. However the boys 
... suffered much from the unintelligent teaching prevalent in the boys' school of that day, and received help in their Latin and Mathematics from their clever elder sister.
Under Beale's leadership Cheltenham Ladies' College flourished. There were only 69 pupils at the school when she took over but a rapid increase in pupil numbers saw the College move into new building in 1873. Three years later the buildings were extended since by this time the number of pupils had risen to over 300. Expansion in numbers continued with 500 pupils by 1880. Continual additions to the buildings were necessary to accommodate these numbers. By the time of Beale's death in 1906 there were nearly 1000 pupils at the school.

In 1864 the Schools' Inquiry Commission was set up to inquire into the condition of post-elementary education in the country and Beale was summoned to give evidence before the Commission on 19 April 1866. For details of her evidence see THIS LINK.

Cheltenham Ladies' College was one of the first colleges to establish courses to train secondary teachers and in 1885 Beale opened St Hilda's College, Cheltenham. Beale was convinced of the need for proper training of teachers of all levels, therefore the Training Department offered three courses. There was a one year course for the training of secondary school mistresses, a three year course for the training of elementary school mistresses ,and a course extending over two years and a term for the training of Kindergarten and Junior Mistresses. The secondary course was shorter as it focused on one subject and pedagogy whereas the other two courses involved the study of many subjects including Geography, English and Music. The training was offered in partnership with four practising schools, Cheltenham Ladies' College, the Ladies' College School, St Stephen's Primary School and Kindergarten, and a public Elementary School. The trainee teachers had the opportunity to observe and learn from accomplished teachers.



1866 Antonia Coetana de Paiva Pereira Maury (21 Mar 1866; 8 Jan 1952 at age 85) was an American astronomer and ornithologist whose painstaking classifications of stars by their spectra included elaborate work on 681 bright stars of the northern skies published in Annals of Harvard College Observatory (1896), a significant early catalog. Yet she was unappreciated by her observatory director, Edward C. Pickering. Her work was important in Ejnar Hertzsprung's verification of the distinction between dwarf stars and giant stars, as now seen in the Hertzsprung-Russell diagram. After Pickering discovered the first spectroscopic binary star, Mizar, she was first to measure its period, 104 days(and the first to detect and calculate the orbit of any spectroscopic binary)
In 1889, she identified the second such star, Beta Aurigae, with a period of about 4 days. Antonia was the niece of astronomer Henry Draper, and the granddaughter of John William Draper who pioneered in the use of photography in astronomy.*TIS  (After his untimely early death from double pleurisy, his widow Mary Anna Draper funded the Henry Draper Medal for outstanding contributions to astrophysics and a telescope, which was used to prepare the Henry Draper Catalog of stellar spectra. Mostly funded at the Harvard observatory. )
In 1897, having examined 4,800 photographs, she published her findings on 681 bright northern stars in the Annals of the Harvard College Observatory. It was the first Harvard observatory publication credited to a woman, which she had insisted on, writing to Pickering, “I worked out the theory at the cost of much thought and elaborate comparison and I think that I should have full credit for my theory of the relations of the star spectra.” *Time
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





DEATHS

1699 Erhard Weigel (December 16, 1625 – March 21, 1699) was a German mathematician, astronomer and philosopher. He earned his Ph.D. from the University of Leipzig. From 1653 until his death he was professor of mathematics at Jena University. He was the teacher of Leibniz in 1663, and other notable students. He also worked to make science more widely accessible to the public, and what would today be considered a populariser of science. Through Leibniz, Weigel is the intellectual forefather of a long tradition of mathematicians that connects a great number of professionals to this day. The Mathematics Genealogy Project lists more than 50,000 "descendants" of Weigel's, including Lagrange, Euler, Poisson and several Fields Medalists. *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
A depiction of a cumulostratus cloud, included in Howard's 'On the modification of clouds'





1910 Gaspard-Félix Tournachon (5 April 1820 – 20 March 1910[1]), known by the pseudonym Nadar, was a French photographer, caricaturist, journalist, novelist, balloonist, and proponent of heavier-than-air flight. In 1858, he became the first person to take aerial photographs.
 Nadar specialized in portraits and photographed many notable French men and women during his career.  But we are more interested here in his second avocation as a balloonist.  Nadar first took a camera up into a hot-air balloon in 1858, thereby becoming the first aerial photographer we know about.  He was then seized by a desire to build his own balloon, and he wanted it to be the largest ever constructed and flown.  By 1863, Le Géant was ready to ascend.  Almost 200 feet tall, it was stitched together from 22,000 yards of silk.  The usual open basket was replaced with a wicker apartment, with parlors, a darkroom, and a full balcony on top .  The ballooning world had seen nothing like it.
Le Géant made its first ascent on Oct. 4, 1863, carrying 12 passengers.  Half-a million people watched it take off from the Champs de Mars in Paris.  This first flight was short, as the balloon descended after only 15 minutes.  A second ascent was readied for Oct. 18 (fourth image, below).  This time the balloon stayed aloft, drifted up toward Belgium, and then east overnight into German airspace, where the passengers watched a glorious sunrise.  But then came disaster. Nadar, worried about the heat of the rising sun and its effect on the gas bag, had the balloon descend to a lower altitude.  They encountered a windstorm near the ground and, unable to rise again, the gondola was dragged across the ground at high speeds, narrowly missing a train, and spilling all the occupants out across the countryside like tipped cows, before the balloon burst and the gondola careened to a halt.
The second flight of the Le Géant became as famous as the first flights of the Montgolfier brothers back in 1783, and the Le Géant and its bouncing finale were widely reported and imaged in the press.  Louis Figuier, only a few years later, published his 4-volume Les merveilles de la science (1867), and he included in his second volume an account of the 1863 ascents, including a wood-engraving of the balloon ascending, and another of the gondola being dragged across the ground .  Le Géant was repaired and made three more flights before being retired, and Nadar kept his interest in ballooning, but soon, more and more of his time was taken up with his successful photographic business. *LH
Nadar's balloon on display at Chrystal Palace, 1863
and Poster in my guest room from Lithograph by Honoré Daumier from Los Angeles County Museum of Art, 1979 *PB, 
*LH





1915 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




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
 A modern version of the Mauder's sunspot "butterfly diagram". (This version from the solar group at NASA Marshall Space Flight Center.)
*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.
Between 1926 and 1928 she attended Edinburgh Ladies' College (now The Mary Erskine School) where she graduated as Dux (in Scottish schools, the top pupil in a class or school)
 in Mathematics and joint Dux of the College. She studied at the University of Edinburgh, graduating in 1932 with an MA in mathematics and natural philosophy. Afterwards, she continued her studies at Girton College, Cambridge, taking the Mathematical Tripos.[2] In her final year at the University she worked on a research project under the supervision of Mary Cartwright. This resulted in her first published work On the Asymptotic Periods of Integral Functions
Between 1947 and 1958 she published another 10 papers during a period where the couple had three children. Of her research during this time, Wright wrote "... good as her research was there would have been more of it had she not had a family to look after." In 1956 she and Edith Witte published the book German-English Mathematical Vocabulary.

*Wik




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

  

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   

"How can you decide if a number is the sum of two squares?  Euler begins with the dumbest possible algorithm you can think of:  take the number, subtract a square, and check if the remainder is a square.  If not, repeat, repeat, repeat. But Euler, being Euler, finds a way of converting all those subtractions into additions. Then he does several things to speed up the computation even more.  He applies this to 1,000,009, and - in less than a page- finds that there are two ways to express this as a sum of two squares, hence, by Euler's work in E228, it is not a prime.  Amusingly, when he later described how to prepare a table of primes(E 467) he includes this number as a prime. So then he feels obligated to write another paper, E699, use another refinement of his method, to show that 1,000,009 is not prime."  *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.
In addition to transforming our understanding of chemistry and colour blindness, Dalton was also a fervent weather watcher, becoming an important figure in the field of meteorology. He kept a daily weather diary, producing a detailed record of local weather conditions over 57 years—over 200,000 entries in total. Even in poor health, he continued to journal about the weather, and made his final entry mere hours before his death on 27 July 1844.
Dalton was interested in the composition of the atmosphere and, by extension, in how components mix together to form gases. He formulated the Law of Partial Pressures in 1801, according to which the pressure of a mixed gas is the sum of the pressures that each of its components would exert if occupying the same space. He also developed the law of the thermal expansion of gases. 






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" 


1916 Albert Einstein submitted his general theory of relativity to Annalen der Physik. *A. Hellemans and B. Bunch, The Timetables of Science
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
Here’s another equinox phenomenon. You might hear that the sun rises due east and sets due west at the equinox. Is that true? Yes it is. In fact, it’s the case no matter where you live on Earth, with the exception of the North and South Poles. At the equinoxes, the sun appears overhead at noon as seen from Earth’s equator, as the illustration below shows. This illustration shows the sun’s location on the celestial equator, every hour, on the day of the equinox. *EarthSky

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.

2023  The latest batch of IAU (International Astronomical Union) minor planet namings was released on 20 March 2023. The list includes two English female amateur astronomers, Alice Grace Cook (1877-1958) and Mary Adela Blagg (1858-1944). Cook lived in Stowmarket, Suffolk while Blagg lived in Cheadle, Staffordshire. Both of these astronomers can be viewed as pioneers of female emancipation. They were among the very first lady fellows elected to the RAS (Royal Astronomical Society) in January 1916. Miss Cook’s planet was previously known as 2000 EY156, or 50739 and is now known as Gracecook.(In September 2021 it was announced that a new school in her home town, Stowmarket, was to be named after Grace Cook.)
The citation reads “After joining the British Astronomical Association, she observed the 1914 Mercury
transit from her own observatory, and was elected a Fellow of the Royal Astronomical Society in 1916.
Known for meteor and auroral observations, she received the E.C.Pickering Fellowship in 1920.”
Miss Blagg’s planet was previously known as 2000 EO177, or 50753 and is now known as Maryblagg.(She also has a crater on the moon named Blagg, after her.)
The citation reads “After joining the British Astronomical Association, she helped develop a uniform
system of lunar nomenclature and was later elected as a Fellow of the Royal Astronomical Society. She
joined the Lunar Commission of the IAU in 1920, standardizing lunar nomenclature in Named Lunar
Formations.”
Both planets are Solar System objects orbiting the Sun within the main asteroid belt, Gracecook has a
semi-major axis of 2.56AU and is 4.75km (2.95 miles) in diameter (Astronomical Units, 1AU is the Sun-Earth distance, or approximately 93 million miles). Whereas Maryblagg orbits a little further out at 2.7AU, and is slightly smaller at 3.49km (2.2 miles) in diameter. Both orbits are inclined to the ecliptic in excess of 10°. *Society for the History of Astronomy







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
18th century copy of a miniature depicting Shaykh Baha'i, falsely attributed to Sadiqi Beg. This drawing is presumably a copy of a lost original by Sadiqi Beg



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.

*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.

He researched on the validity of Boyle's law on gases other than air. He found that ammonium gas deviated from Boyle's law with increasing pressure, and it liquified at 7 atm. With this, he was the first to liquify ammonium. *Wik 
In the early 1780s, Van Marum constructed the largest electrostatic machine in the world; it stood over ten feet tall, with spinning disks fully six feet across, and it could produce extremely long sparks. Van Marum was also the founder of Teylers Museum in Haarlem, which is one of the finest small science museums in the world, and where his electrical machine is still on display. It used to be prominently featured in the famous "Oval Room" of the museum, as we see in a painting of around 1800.*LH

*LH



1840 Franz Carl Joseph Mertens (20 March 1840 in Schroda, Posen, Prussia (now Środa Wielkopolska, Poland) - 5 March 1927 in Vienna, Austria) Mertens worked on a number of different topics including potential theory, geometrical applications to determinants, algebra and analytic number theory, publishing 126 papers. Bruce C Berndt writes, "Mertens is perhaps best known for his determination of the sign of Gauss sums, his work on the irreducibility of the cyclotomic equation, and the hypothesis which bears his name. "
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

*SAU



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


Rubens illustration of projection
1617 François d'Aguilon (also d'Aguillon or in Latin Franciscus Aguilonius) (4 January 1567 – 20 March 1617) was a Belgian Jesuit mathematician, physicist and architect.
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
Statue of Julius Robert von Mayer, town hall square, Heilbronn, Baden-Württemberg, Germany (Wikimedia commons)






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
*Wik



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