Tuesday, 15 September 2026

Narcissisitic Numbers .... The History and Etymology of Math Terms

   Narcissisitic Numbers  The term seems to come from the pen of Joseph S. Madachy in his Mathematics on Vacation, 1966.  His definition is broader than the current use (at least as I know them.) "A Narcissistic number is one which can be represented as some function of its digits ." He includes examples like 145 = 1! + 4! + 5!. It also would include things like n=(sum of digits of n)^(number of digits in n).  

Today the term(s) is used for numbers n (in a particular base) in which the digits are each raised to the power of the number of digits n has and then summed and found to be equal to n.  An early example is 153 = 1^3 + 5^3 + 3^3.  It has been proven that there are only 89 numbers in base ten that have this quality.   


G H Hardy's A Mathematician's Apology mentions the four three-digit solutions, 153, 370, 371, 407, (without using any particular name for them) but dismisses them with, "There is nothing in these odd facts which appeals to the mathematician." 

Another related problem is is there a number A in n digits where the sum of the digits of A raised to the power n = some Other number B and so that the same function of B, gives A again. Are there any that form three-cycles A-> B -> C ->A etc. (Pssst, the answer is yes)

Other names that have been used for these numbers are Armstrong Numbers and PluPerfect digital invariants, which is usually abbreviated PPDI, and is from the Latin past tense for "more than perfect".  
Armstrong numbers is from the name of  Michael F. Armstrong, a computer science teacher who died in 2020.  It seems to have been created shortly after the Narcissistic name, and grew in popularity as one finding these numbers became a popular task for programming classes.  

There is actually a little more to the story of 153.   
Pick any old number you want, and multiply by three (or just pick a number that is a multiple of three).
Now take all the digits and cube them and add the cubes together.
For example, if you picked 231, you would add 2^3 + 3^3 + 1^3 to get 36. 
Yeah, So what you're probably thinking... but take that new number and do the same thing... cube the digits and add them up... Nothing?  Keep going... eventually you get to 153, and then when you  do it again, you get 153 forever.
In slightly more formal language, it seems that 153 is the fixed point attractor of any multiple of three under the process of summing the cubes of the digits.  And if you are wondering what happens if you use a number that is NOT divisible by three, you can find my exploration of them here, The Cubic Attractiveness of 153,  some fun.



(Find more at OEIS   or in Shyam Sunder Gupta, Digital Invariants and Narcissistic Numbers, Exploring the Beauty of Fascinating Numbers, Springer The link takes you to the book on Amazon.






Monday, 14 September 2026

On This Day in Math - September 15

   




Once a sage asked why scholars always flock to the doors of the rich, whilst the rich are not inclined to call at the doors of scholars. "The scholars" he answered , "are well aware of the use of money, but the rich are ignorant of the nobility of science".
~Al-Biruni


The 258th day of the year; 258 is a sphenic (wedge) number (the product of three distinct prime factors..258 = 2·3·43) it is also the sum of four consecutive primes 258 = 59 + 61 + 67 + 71

(Jim Wilder@Wilderlab pointed out that 2,5,&8 are the numbers in the center column of a phone or calculator.)  Jim's comment reminded me of a math type phone joke I saw at  Wolfram Mathworld:
 "I'm sorry, the number you have dialed is an imaginary number. Please rotate by 90o and try again."

Prime Curios also states that if you take all six permutations of 258, put them in order, and make the 18 digit concatenation of them, it is the composite number between a prime pair. Can you find others like this?  (Sort of an easy way to learn two eight digit primes that happen to be a prime pair.

And 258 is the sum of four consecutive Prime numbers, 59 + 81 + 67 +71 and also the sum of two consecutive primes 127 + 131.

258 = 6^3 + 6^2 + 6, or 1110 in base six. Tomorrow that will be 1111.

The Number Zoo gives a Magic square using 16 consecutive primes, with a constant of 258

see More Math Facts for every Year Day here



EVENTS

1668  Robert Hooke delivered some of his most perceptive and far sighted views of the geology of what he called this "terraqueous globe"  in lectures beginning on May 28,1664 and ending on 15 September 1668, and published posthumously.  In these lectures he shared ideas novel to his contemporaries, including "the organic origin, and significance of fossils; cyclicity of the processes of sedimentation,  erosion, consolidation, uplift, and denudation; various processes of petrification; subterraneous eruptions  and earthquakes; biologic evolution; the oblate spheroid shape of the Earth; Polar wandering, and universal gravitation. "  *Ellen Tan Drake; Hooke's Ideas of the Terraqueous  Globe and a Theory of Evolution




1739 Euler, in a letter to Johann Bernoulli, begins the general treatment of the homogeneous linear differential equation with constant coefficients. *VFR  Within a year Euler had completed this treatment by successfully dealing with repeated quadratic factors and turned his attention to the non-homogeneous linear equation. *John E. Sasser, HISTORY OF ORDINARY DIFFERENTIAL EQUATIONS -THE FIRST HUNDRED YEARS



1749  Euler's interest in lotteries began at the latest in 1749 when he was commissioned by Frederick the Great to render an opinion on a proposed lottery that would be similar to the Lottery in Genoa. The first of two letters began 15 September 1749. A second series began on 17 August 1763. E812. Read before the Academy of Berlin 10 March 1763 but only published posthumously in 1862. "Reflexions sur une espese singulier de loterie nommée loterie genoise." Opera postuma I, 1862, p. 319–335. The paper determined the probability that a particular number be drawn. *Euler’s Correspondence Translated by Richard J. Pulskamp, Department of Mathematics & Computer Science, Xavier University,
Cincinnati, OH


1782 Lagrange, in a letter to Laplace, told of finishing his M´ecanique analytique. Legendre undertook the editing of the work for the press. *VFR


1784 Balloon Corner in London earns its name. 'Vincent' Lunardi, "The Daredevil Aeronaut", demonstrated a hydrogen balloon flight at the Artillery Ground of the Honourable Artillery Company in London before over a reported crowd of 200,000 people. With a cat, a dog, and a caged pigeon, he rose into the air with only a partially filled bag and then set down at Welham Green, to release the cat, which seems to have become airsick. He then continued to Standon Green End. A stone marks the event in Welham Green :

"NEAR THIS SPOT AT 3.30 IN THE
AFTERNOON OF SEPTEMBER 15TH
1784 VINCENZO LUNDARDI THE
ITALIAN BALLOONIST MADE HIS
FIRST LANDING WHILST ON HIS
PIONEER FLIGHT IN THE ENGLISH
ATMOSPHERE.
HAVING HANDED OUT A CAT AND DOG
THE PARTNERS OF HIS FLIGHT FROM
LONDON HE RE-ASCENDED AND
CONTINUED NORTH EASTWARD."

The 24 mile flight brought Lunardi fame and began the ballooning fad that inspired fashions of the day—Lunardi skirts were decorated with balloon styles, and in Scotland, the Lunardi Bonnet was named after him (balloon-shaped and standing some 600 mm tall), and is even mentioned by Scotland's national poet, Robert Burns (1759–96), in his poem 'To a Louse', written about a young woman called Jenny, who had a louse scampering in her Lunardi bonnet, *Wik





1788 Thomas Paine writes to Thomas Jefferson to discuss shapes for Iron Bridges:


Whether I shall set off a catenarian Arch or an Arch of a Circle I have not yet determined, but I mean to set off both and take my choice. There is one objection against a Catenarian Arch, which is, that the Iron tubes being all cast in one form will not exactly fit every part of it. An Arch of a Circle may be sett off to any extent by calculating the Ordinates, at equal distances on the diameter. In this case, the Radius will always be the Hypotenuse, the portion of the diameter be the Base, and the Ordinate the perpendicular or the Ordinate may be found by Trigonometry in which the Base, the Hypotenuse and right angle will be always given.,


Jefferson's reply of Dec 23, 1788 is cited by OED as the first use of "catenary".  *Jeff Miller

In 1803 Paine was the first person to receive a patent for an Iron Bridge. His design was poor, as might be expected with no education or training in the craft. and no Payne bridge ever crossed any stream or river, and the first iron bridge would not be built in America for half a century.  

in 1839 cast Iron bridge was completed over the Dublaps Creek, at the town of Brownsville, Pa.  The bridge still stands today.  

A plaque attached to its railing commemorates the bridge.

*Pa Center for the Book



1846 George Boole, age 30, applied for a professorship at “any of her Majesty’s colleges, now in the course of being established in Ireland.” Although he had “never studied at a college” he had been a teacher for 15 years and was “familiar with the elementary and the practical as well as the higher Mathematics.” Although he was self taught, the testimonies of DeMorgan, Cayley, and William Thomson showed that he was an accomplished mathematician. In August 1849, he was appointed the first professor of mathematics at Queen’s College Cork. The reason for the long delay is unclear. *MacHale, George Boole, His Life and Work, pp. 75-84

*Wik



1855 J J Sylvester commenced his duties as professor of mathematics and lecturer in natural philosophy at the Royal Military Academy, Woolwich, and one of the richest research periods of his life began. [Osiris, 1(1936), 101] *VFR

The Woolwich academy initially refused to pay Sylvester his full pension, and only relented after a prolonged public controversy, during which Sylvester took his case to the letters page of The Times.

In 1872, he finally received his B.A. and M.A. from Cambridge, having been denied the degrees due to his being a Jew.

In 1876 Sylvester again crossed the Atlantic Ocean to become the inaugural professor of mathematics at the new Johns Hopkins University in Baltimore, Maryland. His salary was $5,000 (quite generous for the time), which he demanded be paid in gold. After negotiation, agreement was reached on a salary that was not paid in gold.

In 1877, he was elected as a member to the American Philosophical Society.

In 1878 he founded the American Journal of Mathematics. The only other mathematical journal in the US at that time was the Analyst, which eventually became the Annals of Mathematics.




1947 The world's oldest computing society, the Association for Computing Machinery, is founded. With more than 80,000 members today, ACM organizes conference and educational workshops to exchange information on technology.*CHM

*CHM



2017 The Cassini space probe, launched in 1997, was named after Giovanni Cassini and became the first probe to orbit Saturn. For over a decade the probe sent back vital information about Saturn and its moons, expanding our knowledge of the planet, its moons and rings. Fittingly, it crashed into the planet on the day following the anniversary of the death of the astronomer for whom it was named. Earth received @CassiniSaturn’s final signal at 7:55am ET. Cassini is now part of the planet it studied *NASA





BIRTHS



973 Al-Biruni (15 Sept 973, 13 Dec 1048) is one of the major figures of Islamic mathematics. He contributed to astronomy, mathematics, physics, medicine and history. *SAU




1736 Jean-Sylvain Bailly (15 Sep 1736; 12 Nov 1793) French astronomer who computed an orbit for Halley's Comet (1759) and studied the four satellites of Jupiter then known. He was the first Mayor of Paris (1789-91). He was executed by guillotine in Paris during the French Revolution.*TIS
Bailly published his Essay on the theory of the satellites of Jupiter in 1766, an expansion of a presentation he had made to the Academy in 1763. It was followed up in 1771 by a noteworthy dissertation, On the inequalities of light of the satellites of Jupiter. and in 1778, he was elected a foreign member of the Royal Swedish Academy of Sciences. *Wik

Titlepages of two of Jean-Sylvain Bailly’s history of astronomy publications (Linda Hall Library)



1852 Edward Bouchet (15 Sept 1852, New Haven, Conn – 28 Oct 1918, New Haven, Conn) was the first African-American to earn a Ph.D. in Physics from an American university and the first African-American to graduate from Yale University in 1874. He completed his dissertation in Yale's Ph.D. program in 1876 becoming the first African-American to receive a Ph.D. (in any subject). His area of study was Physics. Bouchet was also the first African-American to be elected to Phi Beta Kappa.
Bouchet was also among 20 Americans (of any race) to receive a Ph.D. in physics and was the sixth to earn a Ph. D. in physics from Yale.
Edward Bouchet was born in New Haven, Connecticut. At that time there were only three schools in New Haven open to black children. Bouchet was enrolled in the Artisan Street Colored School with only one teacher, who nurtured Bouchet's academic abilities. He attended the New Haven High School from 1866–1868 and then Hopkins School from 1868-1870 where he was named valedictorian (after graduating first in his class).
Bouchet was unable to find a university teaching position after college, most likely due racial discrimination. Bouchet moved to Philadelphia in 1876 and took a position at the Institute for Colored Youth (ICY). He taught physics and chemistry at the ICY for 26 years. The ICY was later renamed Cheyney University. He resigned in 1902 at the height of the W. E. B. Du Bois-Booker T. Washington controversy over the need for an industrial vs. collegiate education for blacks.
Bouchet spent the next 14 years holding a variety of jobs around the country. Between 1905 and 1908, Bouchet was director of academics at St. Paul's Normal and Industrial School in Lawrenceville, Virginia (presently, St. Paul's College). He was then principal and teacher at Lincoln High School in Gallipolis, Ohio from 1908 to 1913. He joined the faculty of Bishop College in Marshall, Texas in 1913. Illness finally forced him to retire in 1916 and he moved back to New Haven. He died there, in his childhood home, in 1918, at age of 66. He had never married and had no children.*Wik



1857  Anna Winlock (15 Sept 1857– 4 Jan 1904) was an American astronomer and human computer, one of the first members of female computer group known as "the Harvard Computers." She made the most complete catalog of stars near the north and south poles of her era. She is also remembered for her calculations and studies of asteroids. In particular, she did calculations on 433 Eros and 475 Ocllo.

Winlock attended the Cambridge, Ma. Schools as a child and began to develop an interest in both mathematics and the Greek language. By age 10, Anna had watched her father go from Superintendent at the American Nautical Almanac Office in Cambridge, Massachusetts, to the Director of the Harvard College Observatory as well as a professor of Astronomy at the main Harvard College. Upon her graduation she received a letter from her principal expressing his appreciation for her Greek and of her character. Her father influenced her interest in astronomy. When she was twelve, she attended a solar eclipse expedition with her father in his home state of Kentucky. In June 1875, Joseph died shortly after Winlock had graduated from secondary school. Winlock quickly followed in her father's footsteps becoming one of the first female paid staff members of the Harvard College Observatory. *Wik



1883 Esteban Terrades i Illa (15 September 1883;Barcelona,-  9 May 1950,Madrid,) was a Spanish mathematician, scientist and engineer. He researched and taught widely in the fields of mathematics and the physical sciences, working not only in his native Catalonia, but also in the rest of Spain and in South America. He was also active as a consultant in the Spanish aeronautics, electric power, telephone and railway industries. *Wik



1886 Paul Pierre Lévy (15 Sep 1886; 15 Dec 1971) was a French mining engineer and mathematician. He contributed to probability, functional analysis, partial differential equations and series. He also studied geometry. In 1926 he extended Laplace transforms to broader function classes. He undertook a large-scale work on generalised differential equations in functional derivatives.*TIS




1894 Oskar Benjamin Klein (September 15, 1894 (or 1893?) – February 5, 1977) was a Swedish theoretical physicist. Klein retired as professor emeritus in 1962. He was awarded the Max Planck medal in 1959. He is credited for inventing the idea, part of Kaluza–Klein theory, that extra dimensions may be physically real but curled up and very small, an idea essential to string theory / M-theory. *Wik



1901 Luigi Fantappiè (15 September 1901 – 28 July 1956) was an Italian mathematician, known for work in mathematical analysis and for creating the theory of analytic functionals: he was a student and follower of Vito Volterra. Later in life he proposed scientific theories of sweeping scope.

In 1942 he put forth a unified theory of physics and biology, and the syntropy concept. In 1952 he started to work on a unified physical theory called projective relativity, for which, he asserted, special relativity was a limiting case. Giuseppe Arcidiacono worked with him on this theory.*Wik




1923 Georg Kreisel FRS (September 15, 1923 – March 1, 2015) is an Austrian-born mathematical logician who has studied and worked in Great Britain and America. Kreisel came from a Jewish background; his family sent him to England before the Anschluss, where he studied mathematics at Trinity College, Cambridge and then, during World War II, worked on military subjects. After the war he returned to Cambridge and received his doctorate. He taught at the University of Reading until 1954 and then worked at the Institute for Advanced Study from 1955 to 1957. Subsequently he taught at Stanford University and the University of Paris. Kreisel was appointed a professor at Stanford University in 1962 and remained on the faculty there until he retired in 1985.
Kreisel worked in various areas of logic, and especially in proof theory, where he is known for his so-called "unwinding" program, whose aim was to extract constructive content from superficially non-constructive proofs.*Wik




1926 Jean-Pierre Serre (15 September 1926 - ) born in Bages, France. In 1954 he received a Fields Medal for his work on the homotopy groups of spheres. He also received the Wolf Prize in 2000 and the inaugural Abel Prize in 2003. He reformulated some of the main results of complex variable theory in terms of sheaves. See International Mathematical Congresses. An Illustrated History, 1893–1986, edited by Donald J. Albers, G. L. Alexanderson and Constance Reid. Today will be his 100th birthday




1929 Murray Gell-Mann (September 15, 1929 – May 24, 2019).  American theoretical physicist who predicted the existence of quarks. He was awarded the 1969 Nobel Prize for Physics for his contributions to particle physics. His first major contribution to high-energy physics was made in 1953, when he demonstrated how some puzzling features of hadrons (particles responsive to the strong force) could be explained by a new quantum number, which he called “strangeness”. In 1964, he (and Yuval Ne'eman) proposed the eightfold way to define the structure of particles. This led to Gell-Mann's postulate of the quark, a name he coined (from a word in James Joyce's Finnegan's Wake).*TIS






DEATHS

1883 physicist J. Plateau (14 October 1801 – 15 September 1883)  Plateau’s problem asks for the minimal surface through a given curve in three dimensions. A minimal surface is the surface through the curve with the least area. Mathematically the problem is still unsolved, but physical solutions are easy: dip a curved wire in a soap solution. The “soap bubble” that results is the minimal surface for that curve. *VFR
In 1829 Joseph Plateau submitted his doctoral thesis to his mentor Adolphe Quetelet for advice. It contained only 27 pages, but formulated a great number of fundamental conclusions. It contained the first results of his research into the effect of colors on the retina (duration, intensity and color), his mathematical research into the intersections of revolving curves (locus), the observation of the distortion of moving images, and the reconstruction of distorted images through counter revolving

discs Prior to going blind was the first person to demonstrate the illusion of a moving image. To do this he used counter rotating disks with repeating drawn images in small increments of motion on one and regularly spaced slits in the other. He called this device of 1832 the phenakistoscope.
Plateau has often been termed a "martyr for science". . In many (popular) publications the blindness of Plateau is ascribed to his experiment of 1829 in which he looked directly into the sun for 25 seconds. Recent research definitely refutes this. The exact date of the blindness is difficult to formulate simply. It was a gradual process during the year 1843 and early 1844. Plateau publishes two papers in which he painstakingly describes the scientific observations of his own blindness. After 40 years of blindness he still has subjective visual sensations. For his experiments, as well as for the related deskwork colleagues and family help him. *Wik


1898 William Seward Burroughs (born 28 Jan 1855, 15 Sep 1898) American inventor who invented the world's first commercially viable recording adding machine and pioneer of its manufacture. He was inspired by his experience in his beginning career as a bank clerk. On 10 Jan 1885 he submitted his first patent (issued 399,116 on 21 Aug 1888) for his mechanical “calculating machine.” Burroughs co-founded  the American Arithmometer Co in 1886 to develop and market the machine. The manufacture of the first machines was contracted out, and their durability was unsatisfactory. He continued to refine his design for accuracy and reliability, receiving more patents in 1892, and began selling the much-improved model for $475 each. By 1895, 284 machines had been sold, mostly to banks, and 1500 by 1900. The company later became Burroughs Corporation (1905) and eventually Unisys. *TIS





1947 Annie Scott Dill Maunder (née Russell) FRAS (14 April 1868 – 15 September 1947)
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

On the far side of the Moon lies the Maunder crater, named after two British astronomers - Annie and Walter Maunder.
Annie worked alongside her husband at the end of the 19th Century, recording the dark spots that pepper the Sun.
The name Maunder is still known in scientific circles, yet Annie has somehow slipped from history.
"I think the name Maunder is there and we have all rather forgotten that that's two people," says Dr Sue Bowler, editor of the Royal Astronomical Society magazine, Astronomy and Geophysics.
"She was acknowledged on papers, she published in her own name as well as with her husband, she wrote books, she was clearly doing a lot of work but she also clearly kept to the conventions of the day, I think." *By Helen Briggs BBC News
She is known to have worked closely with her husband on the study of sunspots, and she is often credited with discovering the butterfly pattern. *LH







1962  William W(eber) Coblentz   (20 Nov 1873, 15 Sep 1962) was an American physicist and astronomer whose work lay primarily in infrared spectroscopy. In 1905 he founded the radiometry section of the National Bureau of Standards, which he headed for 40 years. Coblentz measured the infrared radiation from stars, planets, and nebulae and was the first to determine accurately the constants of blackbody radiation, thus confirming Planck's law.*TIS



2003 Alexander Ivanovich Skopin (Александр Иванович Скопин) (22 October, 1927–15 September, 2003) was a Russian mathematician known for his contributions to abstract algebra.

Skopin's student work was in abstract algebra, and concerned upper central series of groups and extensions of fields. In the 1970s, Skopin received a second doctorate concerning the application of computer algebra systems to group theory. From that point onward he used computational methods extensively in his research, which focussed on lower central series of Burnside groups. He related this problem to problems in other areas of mathematics including linear algebra and topological sorting of graphs.




2015 Malcolm John Williamson (Nov 2, 1950 - Sept 15, 2015) discovered in 1974 what is now known as Diffie-Hellman key exchange.  He was then working at GCHQ.
Williamson studied at Manchester Grammar School, winning first prize in the 1968 British Mathematical Olympiad. He also won a Silver prize at the 1967 International Mathematical Olympiad in Cetinje, Yugoslavia and a Gold prize at the 1968 International Mathematical Olympiad in Moscow. He read mathematics at Trinity College, Cambridge, graduating in 1971. After a year at Liverpool University, he joined GCHQ, and worked there until 1982.
From 1985 to 1989 Williamson worked at Nicolet Instruments in Madison, Wisconsin where he was the primary author on two digital hearing aid patents. *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

Sunday, 13 September 2026

On This Day in Math - September 14

 



Mathematicians have tried in vain to this day to discover some order in the sequence of prime numbers, and we have reason to believe that it is a mystery into which the human mind will never penetrate.
~Leonhard Euler


The 257th day of the year; 257 is a prime number of the form 223+1 and therefore a Fermat prime. It is currently the second largest known Fermat prime.

257 is the third consecutive number (255,256,257) for which the regular n-gon is constructible with straightedge and compass. The 255th day of the year; 255= 28-1 is the product of three distinct Fermat Primes, 3*5*17, 256=28 is a power of two, and 257 is a Fermat Prime *HT to Don S. McDonald ‏@McDONewt  (Goldbach used the fact that all Fermat Numbers are 2 + product of all smaller Fermat Primes to prove that no two Fermat Numbers share a common prime divisor)

257 = 44 + 1 It is the largest known prime of the form nn + 1. *Prime Curios

More than 90% of all positive integers are composite numbers that have a lowest prime factor of 257 or less.

2257 - 1 is the largest number in Mersenne's list of primes in the preface to his Cogitata Physica-Mathematica (1644), it later turned out to be Composite. * Dan Garbowitz ‏@DGoneseventh

Ones and zeros, 257 written in different bases, 1000000012, 100014   10116





EVENTS


In 1716, Boston Light, the first lighthouse in America was first lighted just before sunset. Located on Little Brewster Island to mark the entrance to Boston, Massachusetts, harbour, has guided ships since then. Building it was authorized 23 Jul 1715 by the Boston Light Bill. In the 1600s, treacherous rocks caused countless loss of lives. False signal fires lit in the wrong places by “wreckers” lured ships aground to plunder. Boston Light was blown up by the British in 1776, but rebuilt in 1783 by Governor John Hancock. The lighthouse is also the last remaining manned station in the U.S.




1752 The first day of the Gregorian calendar in Britain and its colonies. The dates 3 to 13 September did not exist in England in 1752 due to the conversion to the Gregorian calendar. Poor Richard’s Almanac for 1752 carried the catchy heading, “September hath XIX days.” Benjamin Franklin wrote Much of Europe made the change in 1582, and since 1600 was a leap year under the Gregorian but not the Julian calendar, England had to omit eleven days, not ten. *VFR England and the American Colonies dropped the Roman era Julian Calendar, which had become 10 days out of synchrony with the solar cycle, and adopted the Gregorian Calendar. People rioted in the streets thinking the government stole 11 days of their lives. The Act also rectified other dating anomalies, such as changing the start of the legal year from 25 March to 1 January (except in Scotland where they had changed the New Year to Jan 1 in 1600.)  

Benjamin Franklin, who was then 46, didn't think about losing 10 days. He looked on the bright side, and advised his readers to do the same. He gave the following advice to readers of his newspaper, Poor Richard's Almanac: Do not to look upon the loss of 10 days with wonder or scorn. Do not regret the removal of 10 days from the calendar. All those who love sleep can console themselves by thinking about how wonderful it will be to go to bed on the second of the month and to sleep until the morning of the 14th.
 
Instituted by Pope Gregory XIII in 1582, the calendar has 365 days with an extra day every four years (the leap year) except in years divisible by 100 but not divisible by 400. Thus, the calendar year has an average length of 365.2422 days. It moved the day's date up from September 3rd to September 14th. Some other countries, including Russia, did not change until the twentieth century.*TIS
In 1755 William Hogarth’s satirical print, “An Election Entertainment,” was published. It contains a Tory sign bearing the inscription “Give us our eleven days.” (out the window).  Despite thousands of tales of ignorant peasants protests and riots, there seems to be no true records of such an event. Historian Robert Poole  has written, "the riots, like the Snarks, are universally known, but defy detection."

*HT toGianluca Spizzo who noted: "… two centuries later!
Voltaire wrote on this his famous wit, that Protestants preferred to disagree with the Sun than agree with the Pope… "





1792 
In a letter from Bernardino Ferrari to Sebastiano Canterzani describes the interest created by Galvani's "Frog" experiment. Writing from Milan he said "Now here the experiments are also repeated in ladies’ salons, and they furnish a good spectacle to all. " *Walter Bernardi, The Controversy on Animal Electricity (web post)




1814 Francis Scott Key wrote “The Star-Spangled Banner.” Actually he wrote a poem called "Defence of Fort McHenry" . The Poem was written by the 35-year-old lawyer and amateur poet after witnessing the bombardment of Fort McHenry by the British Royal Navy ships in Chesapeake Bay during the Battle of Fort McHenry in the War of 1812. The tune was actually a popular British tune written for a mens social club in London which had become popular in the US too. It became the official National Anthem on March 3, 1931 when President Hoover signed a Congressional resolution to that effect. Mathematics??? umm, OK, the song has a range of 1 1/2 octaves, so the highest note has a frequency that is the square root of eight times the lowest note. *wik (by the way all you patriotic types, sing the second verse)


Fort Meade, near Sturgis, South Dakota is often called the “birthplace” of the national anthem.   In 1892  Colonel Caleb H. Carlton, commander of the 8th Cavalry at Fort Meade, decided that the United States ought to have a national song that would be treated with the dignity accorded to national anthems in other countries.

According to Carlton's later account, he and his wife had discussed the subject. His wife, Sadie Carlton, suggested The Star-Spangled Banner. Carlton agreed because of the extraordinary circumstances under which Francis Scott Key had written it in 1814 and because of its association with the American flag.
 Carlton then ordered that The Star-Spangled Banner be played at the daily retreat ceremony, when the flag was lowered, and required those present to stand and show respect. He also had it played at parades and concerts. 
Carlton didn't simply establish the practice at Fort Meade and leave it there.
He actively promoted the idea elsewhere. He told visiting South Dakota Governor Charles Sheldon about the custom. He subsequently discussed it with Pennsylvania officials and, most importantly, communicated with Secretary of War Daniel S. Lamont.
Carlton later recalled that Lamont subsequently issued an order requiring "The Star-Spangled Banner" to be played at every Army post at evening retreat.*HT to Dr David M Grabitske for giving me the note about Ft Mead.




1858 
 The Donati Comet was first seen and named after its discoverer, Giovanni Battista Donati, at Florence earlier in the year. It was the second-brightest comet of the nineteenth century It reached perihelion on 30 Sep 1858.  On Sep 14th, the night before his third debate with Stephen Douglas, Abraham Lincoln sat on the porch of the Jonesboro, Illinois hotel and viewed the comet with a friend.  On Sept. 27,  It became the first comet to be photographed. The English photographer Warren De La Rue captured the comet on a collodion plate using a telescope at the Royal Observatory, Greenwich.


1959 Bank of America accepts the ERMA (Electronic Recording Method of Accounting) system. This revolutionary system digitized checking for the Bank of America by creating a computer-readable font. A special scanner read account numbers preprinted on checks in magnetic ink. The system was developed at the Stanford Research Institute in Menlo Park, California.*CHM
An early check, demonstrating the features developed by SRI: account numbers and Magnetic Ink Character Recognition.



1959 Life Magazine cover story is picture of the first seven Nasa Astronauts.


2015 Einstein was right, when large Gravitational events happen in space, they produce a gravitational wave pulsing through the universe at the speed of light. The Laser Interferometer Gravitational-Wave Observatories (LIGO) recorded the first evidence on this date of a gravitational wave which had resulted from a merging of a pair of black holes each of about 30 solar masses which had merged about 1.3 billion light years ago. As of December of 2018, LIGO has recorded eleven gravitational wave events, ten from mergers of black holes, and one from a collision of two neutron stars. *Wik, *The Perfectionists, Simon Winchester.





BIRTHS


1648 Caspar (or Kaspar) Neumann (14 September 1648 – 27 January 1715) was a German professor and clergyman from Breslau with a special interest in mortality rates. His collection and publication of the births and deaths in Breslaw were the foundation of E. Halley's, An Estimate of the Degrees of the Mortality of Mankind, drawn from curious Tables of the Births and Funerals at the City of Breslaw; with an Attempt to ascertain the Price of Annuities upon Lives presented to the Royal Society. Halley noted that no similar records existed of sufficient quantity in an area where the population was stable.
He first did an apprenticeship as a pharmacist. He finished his higher school education at Breslau's Maria-Magdalen grammar school. In 1667 he became a student of theology at the university of Jena, and on Nov. 30, 1673 was ordained as a priest, having been requested as a traveling chaplain for Prince Christian, the son of Ernest I, Duke of Saxe-Gotha. On his return home, following a two-year journey through west­ern Ger­ma­ny, Switz­er­land, north­ern It­a­ly, and south­ern France, he became a court-chaplain at Altenburg, and married the daughter of J. J. Rabe, physician in ordinary to the prince of Saxe-Friedenstein. In 1678 he was made the deacon of St. Maria-Magdalen in Breslau and became pastor in 1689. *Wik He was a student of Erhard Weigel



1713 Johann Kies (September 14, 1713—July 29, 1781) a German astronomer and mathematician. Born in Tübingen, Kies worked in Berlin in 1751 alongside Jérôme Lalande in order to make observations on the lunar parallax in concert with those of Nicolas Louis de Lacaille at the Cape of Good Hope.
From 1742 to 1754, at the recommendation of the mathematician Leonhard Euler, he was made professor of mathematics at Berlin's Academy of Sciences and astronomer at its observatory.
He subsequently taught also at the Collegium of Tübingen. From 1754 to 1755, Kies served as director of the Astronomisches Rechen-Institut in Heidelberg.
Kies was one of the first to propagate Newton's discoveries in Germany, and dedicated two of his works to the Englishman: De viribus centralibus (Tübingen, 1758) and De lege gravitatis (Tübingen, 1773). Kies is also the author of a work on lunar influences: De influxu lunae in partes terrae mobiles (Tübingen, 1769). He wrote many other works, both in French and in Latin, on astronomy.
Kies corresponded with Euler from 1747 to 1767. Their correspondence consists of 8 letters, all of which were written by Kies.
The crater Kies on the Moon is named in his honor. *TIA



1769 (Baron) Friedrich Wilhelm Heinrich Alexander von Humboldt (14 Sep 1769; 6 May 1859) was a German natural scientist, archeologist, explorer and geographer, who made two major expeditions to Latin America (1799-1804) and to Asia (1829). During the first, equipped with the best scientific instruments, he surveyed and collected geological, zoological, botanical, and ethnographic specimens, including over 60,000 rare or new tropical plants. He charted and made observations on a cold ocean current along the Peruvian coast, now named, the Humboldt Current. In geology, he made pioneering observations of stratigraphy, structure and geomorphology; he understood the connections between volcanism and earthquakes. Humboldt named the Jurassic System. *TIS
Basalt prisms at Santa María Regla, Mexico by Alexander von Humboldt, *Wik 




1837 Nicolai Vasilievich Bugaev (14 Sept 1837 , 11 June 1903) His research was mainly on analysis and number theory. Bugaev gave proofs of theorems stated without proof by Liouville. He wrote on algebraic integrals of certain differential equations. His work in Moscow was to lead to the creation of the Moscow school of the theory of functions of a real variable in 1911, eight years after his death by Egorov, one of his students. Sonin was another of Bugaev's pupils who went on to make a major contribution to mathematics.
Bugaev's most important work in number theory was based on an analogy between some operations in number theory and the operations such as differentiation and integration in analysis. Bugaev built a systematic theory of discontinuous functions which he called arithmology. *SAU



1858 Henry Burchard Fine (September 14, 1858 – December 22, 1928) born in Chambersburg, Pennsylvania. Fine began his time as a Princeton undergraduate studying Greek and Latin, but a mathematics tutor, George B. Halstead, convinced him to switch his considerable talents to mathematics. He ranked highest academically in his Class of 1880 for all four years, during which he caught the attention of President James McCosh. As a result, Fine was among a small group of highly talented undergraduates whom McCosh invited to his house for informal seminars and nurtured as future faculty.

After graduation, Fine remained at Princeton (then called the College of New Jersey) for a year of post-graduate work followed by three more years as a tutor. Then, as Germany was the leading center of mathematics scholarship, he went to the University of Leipzig to study mathematics with Felix Klein under whom he earned his PhD in one year.The mathematics building at Princeton is named in his honor. (Fine Hall is the tallest building on the campus)







1887 Karl Taylor Compton (14 Sep 1887; 22 Jun 1954) American educator and physicist who directed development of radar during WW II. His research included the passage of photoelectrons through metals, ionization and the motion of electrons in gases, fluorescence, the theory of the electric arc, and collisions of electrons and atoms. In 1933, President Roosevelt asked him to chair the new Scientific Advisory Board. When the National Defense Research Committee was formed in 1940, he was chief of Division D (detection: radar, fire control, etc.) In 1941, he was in charge of those divisions concerned with radar within the new Office of Scientific Research and Development (OSRD). Afterwards he was cited for personally shortening the duration of the war. (Brother of Arthur H. Compton, American Physicist and Nobel Laureate.)*TIS In the famous photo of physicists in the Solvay Conference, Compton is one of only two Americans Present.
He was president of the Massachusetts Institute of Technology (MIT) from 1930 to 1948.




1891 Ivan Matveevich Vinogradov (14 Sept 1891 , 20 March 1983) Vinogradov used trigonometric series to attack deep problems in analytic number theory.
In analytic number theory, Vinogradov's method refers to his main problem-solving technique, applied to central questions involving the estimation of exponential sums. In its most basic form, it is used to estimate sums over prime numbers, or Weyl sums. It is a reduction from a complicated sum to a number of smaller sums which are then simplified. He also used this technique on the Dirichlet divisor problem, allowing him to estimate the number of integer points under an arbitrary curve. This was an improvement on the work of Georgy Voronoy.

In 1918 Vinogradov proved the Pólya–Vinogradov inequality for character sums.
Vinogradov served as director of the Mathematical Institute for 49 years. For his long service he was twice awarded the order of The Hero of the Socialist Labour. The house where he was born was converted into his memorial – a unique honour among Russian mathematicians. As the head of a leading mathematical institute, Vinogradov enjoyed significant influence in the Academy of Sciences and was regarded as an informal leader of Soviet mathematicians, not always in a positive way: his anti-Semitic feelings led him to hinder the careers of many prominent Soviet mathematicians. *Wik




1906 Franz Rellich (September 14, 1906–September 25, 1955) was an Austrian-Italian mathematician. He made important contributions in mathematical physics, in particular for the foundations of quantum mechanics and for the theory of partial differential equations
Among Rellich's most important mathematical contributions are his work in the perturbation theory of linear operators on Hilbert spaces. Although the origins and applications of the problem are in quantum mechanics, Rellich's approach was completely abstract.

Rellich successfully worked on many partial differential equations with degeneracies. For instance, he showed that in the elliptic case, the Monge-Ampère differential equation, while not necessarily uniquely soluble, can have at most two solutions.

Particularly relevant to physics was Rellich's mathematical clarification of the outgoing Sommerfeld conditions.
.*Wik 




1914 Robert Sinclair Dietz (14 Sep 1914; 19 May 1995) was an American geophysicist and oceanographer who set forth a theory (1961) of seafloor spreading (a term he coined), in which new crustal material continually upswells from the Earth's depths along the mid-ocean ridges and spreads outward at a rate of several inches per year. While a student Dietz identified the Kentland structure in Indiana as a meteoric impact site. His professors steered him toward marine geology. He became the founder and director of the Sea Floor Studies Section at the Naval Electronics Laboratory (1946-1963). He also achieved prominence by studying meteorite craters, both on Earth and on the moon and arguing that these impact craters were common. He died of a heart attack.*TIS
 While at the Scripps Institution of Oceanography he observed the nature of the Emperor chain of seamounts that extended from the northwest end of the Hawaiian Island–Midway chain and speculated over lunch with Robert Fisher in 1953 that something must be carrying these old volcanic mountains northward like a conveyor belt.  





1920 Alberto Pedro Calderón (September 14, 1920- April 16, 1998) was one of the leading mathematicians of the 20th century. He was born in Mendoza, Argentina. His name is associated with the University of Buenos Aires, but first and foremost with the University of Chicago, where Calderón and his mentor, the distinguished analyst Antoni Zygmund, started one of the longest (more than 30 years) and most productive collaborations in mathematical history. Together they developed the ground-breaking theory of singular integral operators, thus creating the "Chicago School of (hard) Analysis" (sometimes simply known as the "Calderón-Zygmund School"); this has been one of the most influential movements in pure mathematics, but with remarkable applications to science and engineering as well. Calderón’s work, characterized by great originality, elegance and power reshaped the landscape of mathematical analysis and ranged over a wide variety of topics: from singular integral operators to partial differential equations, from interpolation theory to Cauchy integrals on Lipschitz curves, from ergodic theory to inverse problems in electrical prospection. Calderón’s work has also had a powerful impact on practical applications including signal processing, geophysics, and tomography. *Wik



1926 Hans-Joachim Bremermann​ (14 September, 1926 - 21 February, 1996) was a German-American mathematician and biophysicist. He worked on computer science and evolution, introducing new ideas of how mating generates new gene combinations. Bremermann's limit, named after him, is the maximum computational speed of a self-contained system in the material universe.
 Bremermann's limit, named after him, is the maximum computational speed of a self-contained system in the material universe.
Bremermann came to the United States in 1952 and held a research associate position at Stanford University. In 1953, he was appointed a research fellow at Harvard University. He returned to Münster for 1954–55.

After returning to the United States, he was a mathematics researcher at the Institute for Advanced Study in Princeton (1955–57), and then appointed assistant professor at the University of Washington, Seattle (1957–58). He then spent another year researching at Princeton (1958–59), this time in physics.

In 1959, he became an associate professor of mathematics at University of California, Berkeley, where he remained for the rest of his career, being promoted to full professor in 1966. He held chairs at Berkeley in mathematics and biophysics. By the 1960s, his work had turned towards the theory of computation and evolutionary biology, in which he studied complexity theory, genetic search algorithms, and pattern recognition.

In 1978 he gave the "What Physicists Do" series of lectures at Sonoma State University, discussing physical limitations to mathematical understanding of physical and biological systems. He continued work in mathematical biology through the 1980s, developing mathematical models of parasites and disease, neural networks, and AIDS epidemiology and pathology. He retired from the University of California in 1991.*Wik



1936 Leone Minna Burton (née Gold; 14 September 1936 – 1 December 2007) was a professor of education in mathematics and science, working in London teacher education colleges in the 1970s, the Open University in the 1980s and, from 1992, the University of Birmingham. At the South Bank Polytechnic (now London South Bank University), she helped establish the first MSc in Mathematics Education in the UK. After retiring in 2001 she became Honorary Professor at King's College London, and Visiting Fellow in the Cambridge University Faculty of Education. She was noted for her influence as a researcher and doctoral supervisor, setting up national and international research networks in the developing area of mathematics education.
Leone Burton's contribution to mathematics education focused on researching the practices of working mathematicians and arguing their relevance for school teaching and learning. This research is included in what is now termed the field of ethnomathematics which examines how mathematics is related to the culture in which it is developed. At the Open University, Burton collaborated in creating innovative courses in teacher education, Developing Mathematical Thinking, that emphasized the role of problem solving in mathematics and argued that teachers should be aware of mathematical reasoning as well as mathematical content. A subsequent publication, Thinking Mathematically, written in 1982 with Mason and Stacey, brought these ideas to an international teacher audience focusing on teachers' own knowledge of using and applying mathematics.

From 1984 to 1988 Burton was international convenor for the International Organization of Women and Mathematics Education and visiting professor at institutions in Asia. She played a major role in shifting teachers’ perceptions in relation to girls and mathematics in the UK and other places around the world. Burton founded the monograph series International Perspective on Mathematics Education with the Greenwood Publishing group in 2001 which published three monographs between 2002 and 2006. This monograph series was subsequently renamed International Perspectives on Mathematics Education: Cognition, Equity and Society in honor of her pioneering work on equity and gender issues in mathematics education, edited by Bharath Sriraman, and published by Information Age Publishing.

Her final book, Mathematicians as Enquirers, used interviews to characterize the ways professional mathematicians learn, including enquiry, visualization and collaboration. This research showed that the ways mathematicians learn are consistent with principles recognized in mathematics education research as suitable for school learning.






DEATHS

1638 Pierre Vernier (19 Aug 1584, 14 Sep 1638) French mathematician who developed the vernier scale, which enabled instruments to make more accurate linear or angular measurements. He first described it in a work entitled La construction, l'usage et les propriétés du cadran nouveau (1631)*. It consists of a small graduated scale or arc made to slide along a larger fixed scale or arc to enable determining the increment between two graduations of the larger scale. The ten divisions of the smaller, vernier scale are equal to nine of the fixed scale. For example, calipers with a larger scale graduated in tenths of inches can be read by use of the vernier scale to within one-hundredths of an inch. Vernier scales are also used on sextants and mercury
column barometers.*TIS
The vernier scale was invented in its modern form in 1631 by Vernier), but its use was described in detail in English in Navigatio Britannica (1750) by John Barrow, the mathematician and historian. In some languages, this device is called a nonius. It was also commonly called a nonius in English until the end of the 18th century. Nonius is the Latin name of the Portuguese astronomer and mathematician Pedro Nunes (1502–1578) who in 1542 invented a related but different system for taking fine measurements on the astrolabe (nonius) that was a precursor to the vernier. The French astronomer Jérôme Lalande (1732-1807) popularized the name of the instrument as a "vernier" in his book on astronomy (1764) *Wik

1712 Giovanni Domenico Cassini (8 Jun 1625, 14 Sep 1712) Italian-French astronomer who discovered (1675) the dark gap subdividing Saturn's rings into two parts, now known as Cassini's Division. He stated that Saturn's ring, believed by Huygens to be a single body, was actually composed of small particles. Cassini also discovered four of Saturn's moons: Iapetus (Sep 1671), Rhea (1672) and on 21 Mar 1684,* Tethys and Dione. He compiled new tables (1662) on the annual motion of the Sun. He observed shadows of four Galilean satellites on Jupiter (1664), and measured its rotation period by studying the bands and spots on its surface. He determined the period of rotation of Mars (1666), and attempted the same for Venus. His son Jacques was also an astronomer.*TIS (There were four consecutive Cassini generations to hold the post at the French Observatory. After Giovanni came Giovanni's son Jacques, then his grandson César-François Cassini de Thury, and finally his great grandson Jean-Dominique Cassini, Conte de Cassini.)
The Cassini spaceprobe, launched in 1997, was named after him and became the fourth to visit Saturn and the first to orbit the planet. It met it's end falling into the atmosphere of Saturn on the 15 September, 2017.




1835 The Rt. Rev. John Mortimer Brinkley D.D. (ca. 1763 (Baptized 31 Jan,1763, Woodbridge, Suffolk – 14 September 1835, Dublin) was the first Royal Astronomer of Ireland and later Bishop of Cloyne.
He graduated B.A. in 1788 as senior wrangler and Smith's Prizeman, was elected a fellow of the college and was awarded M.A. in 1791. He was ordained at Lincoln Cathedral in the same year, and in 1792 became the second Andrews Professor of Astronomy in the University of Dublin, which carried the new title of Royal Astronomer of Ireland. Together with John Law, Bishop of Elphin, he drafted the chapter on "Astronomy" in William Paley's Natural Theology. His main work concerned stellar astronomy and he published his Elements of Plane Astronomy in 1808. In 1822 he was elected a Foreign Honorary Member of the American Academy of Arts and Sciences. He was awarded the Copley Medal by the Royal Society in 1824. Brinkley's observations that several stars shifted their apparent place in the sky in the course of a year were disproved at Greenwich by his contemporary John Pond, the Astronomer Royal. In 1826, he was appointed Bishop of Cloyne in County Cork, a position he held for the remaining nine years of his life. Brinkley was elected President of the Royal Astronomical Society in 1831, serving in that position for two years.
He died in 1835 at Leeson Street, Dublin and was buried in Trinity College chapel. He was succeeded at Dunsink Observatory by Sir William Rowan Hamilton. *Wik



1882 Georges Leclanché  9 October 1839 – 14 September 1882 ) French engineer who invented the wet cell Leclanché battery (1866), ancestor of the familiar carbon-zinc dry cell batteries used to power portable electric lights and electronic devices. His wet cell, provided an e.m.f. of about 1.5 volts. A porous pot containing manganese dioxide and a carbon rod as current collector was immersed in an electrolyte of ammonium chloride solution with a negative terminal of zinc metal. From 1867, Leclanché gave full-time attention to his invention, which was adopted the following year by the Belgian telegraph service. He opened a factory to manufacture the battery. In 1881, J.A. Thiebaut had the idea of packing the chemicals in a zinc cup. Carl Gassner made the first commercially successful "dry" cell.*TIS




1912 Georg Landsberg (30 Jan 1865 , 14 Sept 1912) studied the theory of functions of two variables and also the theory of higher dimensional curves. In particular he studied the role of these curves in the calculus of variations and in mechanics.
He worked with ideas related to those of Weierstrass, Riemann and Heinrich Weber on theta functions and Gaussian sums. His most important work, however was his contribution to the development of the theory of algebraic functions of a single variable. Here he studied the Riemann-Roch theorem.
He was able to combine Riemann's function theoretic approach with the Italian geometric approach and with the Weierstrass arithmetical approach. His arithmetic setting of this result led eventually to the modern abstract theory of algebraic functions.
One of his most important works was Theorie der algebraischen Funktionen einer Varaiblen (Leipzig, 1902) which he wrote jointly with Kurt Hensel. This work remained the standard text on the subject for many years. *SAU



1916 Pierre-Maurice-Marie Duhem (10 Jun 1861, 14 Sep 1916) was a French physicist, philosopher of science and mathematician who emphasized a history of modern science based on evolutionary metaphysical concepts. He had a wide variety of mathematical interests from mechanics and physics to philosophy and the history of mathematics. Duhem studied magnetism following the work of Gibbs and Helmholtz and also worked on thermodynamics and hydrodynamics producing over 400 papers. He maintained that the role of theory in science is to systematize relationships rather than to interpret new phenomena.*TIS

Kai Wenz reached out and sent a link to point out one of Duhem's big contributions to thermodynamics.  My thanks to Kai for sharing, and please enjoy:   https://www.linkedin.com/posts/kai-wenz_equations-physics-thermodynamics-activity-7342461354475241472-Rrhc?utm_source=share&utm_medium=member_android&rcm=ACoAAD7cn3wBl6ENNa5xUGyD1St4HSISx-8nfLA




1925 Charles Tweedie (27 June 1868 , 14 Sept 1925) studied at Edinburgh, Göttingen and Berlin. He returned to Edinburgh as assistant to Prof. George Chrystal. In the autumn of 1892 he became an assistant in the mathematics department at the University of Edinburgh under Professor Chrystal and became an official soon after, as Chrystal's right-hand man.
He served as a Schools Inspector and published works on the History of Mathematics. He became President of the EMS in 1903 and an honorary member in 1915. *SAU



1926 Johan Ludvig Emil Dreyer (13 Feb 1852, 14 Sep 1926) Danish astronomer who compiled the New General Catalog of Nebulae and Clusters of Stars, (NGC) in 1888. When he became Director of the Armagh Observatory in 1882, financially it was destitute, with no prospect of replacing its aging instruments. Though Dreyer obtained a new 10-inch refractor by Grubb, the lack of funding for an assistant, precluded him from a continuation of traditional positional astronomy. Instead he concentrated on the compilation of observations made earlier. The NGC he listed 7840 objects and in its supplements (1895, 1908) he added a further 5386 objects. It still remains one of the standard reference catalogs.*TIS




1932 Ernest Julius Wilczynski (13 Nov 1876 , 14 Sept 1932) began his research career as a mathematical astronomer. This interest lasted until he was appointed to Berkeley. By that time he had published over a dozen papers in astronomy, but his interests moved towards differential equations which arose in his study of the dynamics of astronomical objects. From there his interests became pure mathematical interests in differential equations. However, Wilczynski's main work was in projective differential geometry and ruler surfaces. He extended Halphen's work, devised new methods and extended the theory of curves to surfaces.*SAU



1973 Eleanor Pairman Brown (8 June 1896, 14 Sept 1973) graduated from Edinburgh. She went to London where she worked with Karl Pearson and then went to the USA where she gained a doctorate from Radcliffe College ( only the third woman to receive a doctorate in math from Radcliffe College in Massachusetts )   *SAU 
Eleanor Pairman graduated with an MA in 1917 with first class honors in mathematics and natural philosophy, after which she was awarded a three-year Vans Dunlop scholarship which permitted her to continue her studies at any university. Pairman read two papers at meetings of the Edinburgh Mathematical Society early in 1918.

In 1918 Pairman joined the staff of Karl Pearson's Department of Applied Statistics, which comprised the Biometric Laboratory and Francis Galton Laboratory for National Eugenics, at University College London. Pairman's role in the Galton Laboratory was that of a human computer. She was referenced as one of a number of women contributors in the 1917 Galton Laboratory publication A study of the long bones of the English skeleton Part I, co-authored by Julia Bell and Karl Pearson and which sought to identify "racial differences in man".

In 1919, Pairman co-authored with Karl Pearson the paper "On Corrections for the Moment-Coefficients of Limited Range Frequency Distributions When there are Finite or Infinite Ordinates and Any Slopes at the Terminals of the Range" published in the journal Biometrika.  

One of her instructors, Cargill G. Knott, wrote a letter of recommendation saying: "With fitting opportunity she has every promise of a distinguished and useful career." Pairman arrived in New York on 12 October 1919 and went on to Cambridge, Massachusetts to study at Radcliffe College, an all-women's college closely associated with the all-male Harvard College. There she studied under George David Birkhoff. Her thesis was titled 'Expansion Theorems for Solution of a Fredholm's Linear Homogeneous Integral Equation of the Second Kind with Kernel of Special Non-Symmetric Type' and was awarded a PhD in 1922. When she received her doctorate she was only the third woman to be awarded a PhD in mathematics from Radcliffe College. In that same year she married a fellow grad student, Bancroft Brown.

The couple moved to Hanover, N.H. in 1922 so Bancroft could assume a teaching position at Dartmouth College, which, at the time, was a men's school with an all-male faculty but occasionally admitting women as graduate students. Later, Pairman published a joint paper with Rudolph E. Langer in 1927.

About 1950, Pairman started focusing on teaching mathematics to blind students, learning Braille and learning how to make diagrams using her sewing machine and other household items. Her daughter Margaret later wrote, “Geometry was a particular problem, because you really need diagrams. Braille is done on paper like thin cardstock. So she rounded up all kinds of household implements like pinking shears and pastry wheels and such and created diagrams that could be felt with the fingers, like the Braille symbols. Apparently nobody had ever done this before."





2011 Rudolf Ludwig Mössbauer (31 Jan 1929 - 14 September 2011) German physicist and co-winner (with American Robert Hofstadter) of the Nobel Prize for Physics in 1961 for his researches concerning the resonance absorption of gamma-rays and his discovery in this connection of the Mössbauer effect. The Mössbauer effect occurs when gamma rays emitted from nuclei of radioactive isotopes have an unvarying wavelength and frequency. This occurs if the emitting nuclei are tightly held in a crystal. Normally, the energy of the gamma rays would be changed because of the recoil of the radiating nucleus. Mössbauer's discoveries helped to prove Einstein's general theory of relativity. His discoveries are also used to measure the magnetic field of atomic nuclei and to study other properties of solid materials. *TIS
Rudolf Mössbauer was an excellent teacher. He gave highly specialized lectures on numerous courses, including Neutrino Physics, Neutrino Oscillations, The Unification of the Electromagnetic and Weak Interactions and The Interaction of Photons and Neutrons With Matter. In 1984, he gave undergraduate lectures to 350 people taking the physics course. He told his students: “Explain it! The most important thing is, that you are able to explain it! You will have exams, there you have to explain it. Eventually, you pass them, you get your diploma and you think, that's it! – No, the whole life is an exam, you'll have to write applications, you'll have to discuss with peers... So learn to explain it! You can train this by explaining to another student, a colleague. If they are not available, explain it to your mother – or to your cat!” *Wik




2018  Branko Grünbaum ( October 2, 1929  in Osijek , Croatia ; September 14, 2018 in Seattle , Washington) was an Israeli mathematician of Yugoslavian descent who worked on discrete geometry.
A scholarship allowed Grünbaum to spend from September 1958 to June 1960 at the Institute for Advanced Study at Princeton, USA. Branko and Zdenka, with their son Ram, sailed on the T.S.S. Olympia arriving in New York on 5 September 1958 having left Lisbon exactly one month earlier. From New York they travelled by train to Princeton. After two years at Princeton, they spent one year in Seattle at the University of Washington where their second son Daniel Grünbaum was born on 2 November 1960. The family had spent the summer of 1960 at the University of California, Los Angeles, living during this time in Santa Monica. While in Seattle, Grünbaum accepted a position at the Hebrew University in Jerusalem.

There now arose a complication with his marriage. Branko and Zdenka's Orthodox Jewish marriage had been annulled because Branko's mother was not Jewish. In the City of Seattle, on 5 September 1961, Branko Grünbaum and Zdenka Bienenstock were married by a Justice of the Peace at 9:30 a.m. just before they left the United States for Jerusalem. Back at the Hebrew University his career went extremely well and he was promoted to Associate Professor in 1964. By this time he had over fifty publications and, let us note at this point, that he carried on with a remarkably high publication rate throughout his life; MathSciNet list 271 publications in total.

Grünbaum now felt slightly uneasy in Israel since, despite having a Jewish father, he had been declared a non-Jew since his mother was not Jewish. This eventually contributed to his decision to leave Israel and emigrate to North America. In 1965 he went to Michigan State University to spend a sabbatical year. While there he learnt of another marriage being annulled in similar circumstances to his own and the Israeli immigrant from the mixed marriage had her passport and citizenship revoked; this tipped the balance. It was not an easy decision, however, since Zdenka had been half way through her Ph.D. studies in Chemistry when they left Israel and she would have liked to have returned to complete the degree. Grünbaum had two possible places in North America which were particularly attractive because of his interest in geometry, the University of Toronto where Donald Coxeter was a professor, and the University of Washington in Seattle where he could work with Victor Klee. He chose the University of Washington where he was appointed to a full professorship in 1966 and remained there for the rest of his career until he retired in 2001. *SAU






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