Sunday, 22 February 2026

The 3x3 Magic Square, More Magical than You Thought!



I just came across an older article from the Journal of Recreational Mathematics about the 3x3 Magic square that reminded me of some beautiful relations in the square, and showed me a few I had never seen. The article is by Owen O'Shea and is titled "SOME WORDS ON THE LO SHU". If you want to search out the whole thing (well worth the read) it is in Volume 35(1) starting on page 23.

The Lo Shu Square ( literally: Luo (River) Book/Scroll) is the unique normal magic square of order three. Except for rotations or reflections it is the only order three magic square that can be formed with the digits 1-9. Chinese legends concerning the pre-historic Emperor Yu tell of the Lo Shu: In ancient China there was a huge deluge: the people offered sacrifices to the god of one of the flooding rivers, the Luo river, to try to calm his anger. A magical turtle emerged from the water with the curious and decidedly unnatural (for a turtle shell) Lo Shu pattern on its shell: circular dots giving unary (base 1) representations of the integers one through nine are arranged in a three-by-three grid. The representation in the more common Arabic Numerals looks like this:



The odd and even numbers alternate in the periphery of the Lo Shu pattern; the 4 even numbers are at the four corners, and the 5 odd numbers (outnumbering the even numbers by one) form a cross in the center of the square. The sums in each of the 3 rows, in each of the 3 columns, and in both diagonals, are all 15 (the number of days in each of the 24 cycles of the Chinese solar year.

Beyond the basics of the magic square, O'Shea points out several other interesting relations.  First, the sum  squares of the numbers in the top and bottom row are equal.  42 + 92 + 22 = 82 + 12 + 62 = 101.  You can do the same thing with the two outside columns, 42 + 32 + 82 = 22 + 72 + 62 = 89.  Go ahead, try the two diagonals, you now you are dying to know. 

So what about the middle row and column?  Well, the middle column is special; Because north is placed at the bottom of maps in China, the 3x3 magic square having number 1 at the bottom and 9 at the top is used in preference to the other rotations/reflections. As seen in the "Later Heaven" arrangement, 1 and 9 correspond with ☵ Kǎn 水 "Water" and ☲ Lí 火 "Fire" respectively. In the "Early Heaven" arrangement, they would correspond with ☷ Kūn 地 "Earth" and ☰ Qián 天 "Heaven" respectively. The 951 does have a nice numerical representation in the number. If you  read the rows or columns as three digit numbers, you might notice that 492 – 357 + 816 = 951 and that 294 – 753 + 618 = 159. Kind of a transition from Heaven to Earth and back again.
An original O'Shea contribution is his discovery that, "Ignoring the middle column, form two-digit numbers with the other columns as follows: 42 + 37 + 86. These numbers sum to 165. Their sum of their
reversals, 68 + 73 + 24, is also 165. The same is true of 84 + 19 + 62 and their reversals, 26 + 91 + 48. Curiously, the sum of the squares of the odd digits, 1, 3, 5, 7, and 9, also equals 165."

If we go back to considering the rows as a three digit number, the square of each row numeral is the same as the square of their reversal:  4922 + 3572 + 8162 = 6182 + 7532 + 2942. Of course that would be really impressive if it worked with the columns too... I mean, awesome impressive... ahh go on, try it.

The article goes on with several dozen interesting numerical relations, and if that's your thing, you should seek it out.  I'll leave you with one last beauty:
There is a not too well know problem in math called the Tarry-Escott problem  which asks if there are sets of integers with the same order (same number in each set) so that the integers in each set have the same sum, the same sum of squares, etc.up to and including the same sum of kth powers.
Remarkably, the pattern in the lo shu gives a solution to the Tarry-Escott problem. Starting at the top left and reading around the outside you get the four three digit numbers, 492 ,276 , 618 , 834 .  Now read them going the other way round, 438, 816, 672, 294.    Now add up the numbers in each set.  Add up their squares..... their cubes?

Historically, The magic squares appeared first in China.   In 500

BCE, and 300 BCE, the river map is mentioned, but no explicit magic
square is given. In 80 AD Ta Tai Li Chi gives the first clear reference to a
magic square. In 570 AD Shuzun gives an actual description of a magic
square of 3. Not until 1275 do we hear of the Chinese making squares of
order larger than 3. *Mark Swaney

India seems to have developed magic squares, favoring 4x4 squares, as early as the first century AD.  Larger 5x5 and 6x6 first appeared in Islamic works in the 10th century.  

Fran Swetz in his Legacy of the Lo Shu, mentions Tibet and Japan in a section on "Who else Knew Aboutn  Magic Squares.  And in the section on "Who didn't Know About Magic Squares"  he lists Babylonia, Egypt and Greece.

Magic squares came first to Western Europe around the niddle of the 15th Century.  Luca Paccioli, in particular had a collection of magic squares and expanded on the work of Ahmid al-Buni of Algeria, who wrote many mystical writings in the 12th and 13th Centuries. He was also a talented mathematician.  


See more about Magic squares :

A Unique approach for Odd Order Magic Squares






On This Day in Math - February 22

    


Illustration from "On the forms of plane quartics", by Ruth Gentry




Suppose a contradiction were to be found in the axioms of set theory. Do you seriously believe that a bridge would fall down?
~Frank P. Ramsey


The 53rd day of the year; the month and day are both prime a total of 53 times in every leap year, but not today.

If you reverse the digits of 53 you get its hexadecimal representation; no other two digit number has this quality.

The sum of the first 53 primes is 5830, which is divisible by 53. It is the last year day for which n divides the sum of the first n primes.

53 is the smallest prime p such that 1p1 (ie, 1531) , 3p3, 7p7 and 9p9 are all prime.(Can you find the 2nd smallest?)   Raj Madhuram suggested 2477 is the second smallest of these, and offered the wonderful term, "Sandwich Primes."  




EVENTS

1535 On this day the contestants, Tartaglia and Fiore, were to deliver the answer to the 30 questions they were asking of their opponent to a notary. I assume the contest went on the same day, and it may not have taken long. Thony Christie at the Renaissance Mathematicus described it this way, "Tartaglia sat down and almost instantly gave the correct answers to Fiore’s entire list, who was completely unable to solve a single one of Tartaglia’s questions. This whitewash made Tartaglia a star amongst the reckoning masters." In Mario Livio's "The Equation That Couldn't be Solved" he says that Tartaglia finished all 30 of Fiore's questions in less than two hours. All 30 of Fiore's questions were of the form ax3 + bx = c, and Tartaglia had discovered a general solution for that type of cubic only eight days before the contest. 

Statue of Tartaglia in Brescia



1630 Popcorn was introduced to the English colonists at their first Thanksgiving dinner on this date (admit it, you thought it was in November) by Quadequina, brother of Massasoit. As his contribution to the dinner he offered a deerskin bag containing several bushels of “popped” corn. *Kane, Famous First Facts, p. 481 Popcorn is a type of corn with smaller kernels than regular corn, and when heated over a flame, it "pops" into the snack we know it as today. Native Americans were growing it for more than a thousand years before the arrival of European explorers. In 1964, scientists digging in southern Mexico found a small cob of popcorn discovered to be 7,000 years old. (don't you wonder if they tried to pop some of it?) Today, the United States grows nearly all of the world's popcorn. *TIS

During the Great Depression, popcorn was fairly inexpensive at 5–10 cents a bag and became popular. Thus, while other businesses failed, the popcorn business thrived and became a source of income for many struggling farmers, including the Redenbacher family, namesake of the Orville Redenbacher's popcorn brand. During World War II, sugar rations diminished candy production, and Americans compensated by eating three times as much popcorn as they had before.

An early popcorn machine in a street cart, invented in the 1880s by Charles Cretors in Chicago.




1726 This Arabic work, Risālah fī al-ʻamal bi'l-asṭurlāb (Treatise concerning the use of the astrolabe, Oriental MS Plimpton 284), by Ḥaydar ibn 'Abd al-Raḥmān Jazarī, was signed by the scribe, ʻAbd Allāh al-Bukhārī, on 22 February 1726. It may have come from what is now Iraq. Several undated manuscript copies of this work about the astrolabe are extant, though nothing is known about its author. In this copy, the ten chapters of the treatise are followed by a concise commentary. The page layout of the opening pages shows that the scribe expected the addition of an illuminated headpiece, because the work begins mid-page with the invocation of God (basmala). The manuscript’s wide margins were purposefully designed to provide the reader with sufficient space for their own notes and comments. *MAA Mathematical Treasures




1805 Francois Arago picked to head the completion of the measurement of the Paris Meridian. He was a 19yr old student at the Ecole Polytechnique. He was nominated by his professor, Dennis Poisson and appointed on Feb 2, 1805 to finish the work began by Mechain and Delambre. He would leave for Spain on Sept 3 of the following year *Amir D Aczel, Pendulum, pg 75-78  Wilpedia describes the ensuing adventure this way:

Arago and Biot left Paris in 1806 and began operations along the mountains of Spain. Biot returned to Paris after they had determined the latitude of Formentera, the southernmost point to which they were to carry the survey.[4] Arago continued the work until 1809, his purpose being to measure a meridian arc in order to determine the exact length of a metre.

After Biot's departure, the political ferment caused by the entrance of the French into Spain extended to the Balearic Islands, and the population suspected Arago's movements and his lighting of fires on the top of Mount Galatzó (Catalan: Mola de l'Esclop) as the activities of a spy for the invading army. Their reaction was such that he was obliged to give himself up for imprisonment in the fortress of Bellver in June 1808. On 28 July he escaped from the island in a fishing-boat, and after an adventurous voyage he reached Algiers on 3 August. From there he obtained a passage in a vessel bound for Marseille, but on 16 August, just as the vessel was nearing Marseille, it fell into the hands of a Spanish corsair. With the rest the crew, Arago was taken to Roses, and imprisoned first in a windmill, and afterwards in a fortress, until the town fell into the hands of the French, when the prisoners were transferred to Palamos.

After three months' imprisonment, Arago and the others were released on the demand of the dey of Algiers, and again set sail for Marseille on 28 November, but then within sight of their port they were driven back by a northerly wind to Bougie on the coast of Africa. Transport to Algiers by sea from this place would have occasioned a weary delay of three months; Arago, therefore, set out over land, guided by a Muslim priest, and reached it on Christmas Day. After six months in Algiers he once again, on 21 June 1809, set sail for Marseille, where he had to undergo a monotonous and inhospitable quarantine in the lazaretto, before his difficulties were over. The first letter he received, while in the lazaretto, was from Alexander von Humboldt; and this was the origin of a connection which, in Arago's words, "lasted over forty years without a single cloud ever having troubled it."

Arago had succeeded in preserving the records of his survey; and his first act on his return home was to deposit them in the Bureau des Longitudes at Paris. As a reward for his adventurous conduct in the cause of science, he was elected a member of the French Academy of Sciences, at the remarkably early age of twenty-three, and before the close of 1809 he was chosen by the council of the École Polytechnique to succeed Gaspard Monge in the chair of analytical geometry.




1876 The Johns Hopkins University Founded... commonly referred to as Johns Hopkins, JHU, or simply Hopkins, is a private research university based in Baltimore, Maryland, United States. Johns Hopkins maintains campuses in Maryland, Washington, D.C., Italy, China, and Singapore.
The university was founded on January 22, 1876 and named for its benefactor, the philanthropist Johns Hopkins. Daniel Coit Gilman was inaugurated as first president on February 22, 1876. On his death in 1873, Johns Hopkins, a Quaker entrepreneur and childless bachelor, bequeathed $7 million to fund a hospital and university in Baltimore, Maryland. At that time this fortune, generated primarily from the Baltimore and Ohio Railroad, was the largest philanthropic gift in the history of the United States.*Wik


1877 J. J. Sylvester, at a commencement address at Johns Hopkins, gave his view on the relation between teaching and research: “An eloquent mathematician must, from the nature of things, ever remain as rare a phenomenon as a talking fish, and it is certain that the more anyone gives himself up to the study of oratorial effect, the less he will find himself in a fit state of mind to mathematicize.” See Midonick, The Treasury of Mathematics, p. 768. *VFR


1880 American Poet Sidney Lanier (1842–1922) read his “Ode to The Johns Hopkins University”, which indicated the original faculty was “Led by the soaring-genius’d Sylvester.” [Osiris, 1(1936), p. 112] *VFR


1926 At its fiftieth anniversary celebration, Johns Hopkins University awarded a long overdue doctorate to Christine Ladd-Franklin. Now a sprightly 79, she attended the ceremonies to collect her degree 44 years late. [New York Times, 23 February 1926, p. 12. Thanks to Judy Green. Also see Rossiter, Women Scientists in America, p. 46.] *VFR She applied to Johns Hopkins University as a graduate student, a university not traditionally open to women. A fellow contributor to the publication, Educational Times, who was familiar with her work, James J. Sylvester, noticed her name on a list of applicants and urged the university to admit her. In 1878, she was accepted on the terms that she would only attend his lectures.




1965 Rwanda, in central Africa, issued a series of stamps honoring the National University of Rwanda at Butare. Included in the picture is a radical sign, in fact, this is the only stamp which includes a radical sign, a symbol which originated in Germany. 
[Scott #84, 88] *VFR







2016 JAVIER CILLERUELO AND FLORIAN LUCA  proved that for any base greater than 4 EVERY POSITIVE INTEGER IS A SUM OF THREE PALINDROMES )  Nice that it happened on a palindrome month/day  2-22.  


BIRTHS

1785 Jean-Charles-Athanase Peltier (22 Feb 1785; 27 Oct 1845 at age 60)
French physicist who discovered the Peltier effect (1834), that at the junction of two dissimilar metals an electric current will produce heat or cold, depending on the direction of current flow. In 1812, Peltier received an inheritance sufficient to retire from clockmaking and pursue a diverse interest in phrenology, anatomy, microscopy and meteorology. Peltier made a thermoelectric thermoscope to measure temperature distribution along a series of thermocouple circuits, from which he discovered the Peltier effect. Lenz succeeded in freezing water by this method. Its importance was not fully recognized until the later thermodynamic work of Kelvin. The effect is now used in devices for measuring temperature and non-compressor cooling units. *TIS




1796 (Lambert) Adolphe (Jacques) Quetelet (22 Feb 1796, 17 Feb 1874 at age 78) was a Belgian mathematician, astronomer, statistician, and sociologist known for his pioneering application of statistics and the theory of probability to social phenomena, especially crime. At an observatory in Brussels that he established in 1833 at the request of the Belgian government, he worked on statistical, geophysical, and meteorological data, studied meteor showers and established methods for the comparison and evaluation of the data. In Sur l'homme et le developpement de ses facultés, essai d'une physique sociale (1835) Quetelet presented his conception of the average man as the central value about which measurements of a human trait are grouped according to the normal curve. *TIS Quetelet created the Body Mass Index in a paper in 1832.  It was known as the Quetelet Index until it was termed the Body Mass Index in 1972 by Ancel Keys.
Statue of Quetelet in Bruxelles


1817 Carl Borchardt (22 Feb 1817 in Berlin, Germany - 27 June 1880 in Rudersdorf (near Berlin), Germany) was a German mathematician who worked in a variety of areas in analysis. He edited Crelle's Journal for more than 30 years. (At that time it was called Borchardt's Journal)*SAU  

He did research in the area of the arithmetic-geometric mean, continuing work by Gauss and Lagrange. He generalised the results of Kummer on diagonalising symmetric matrices, using determinants and Sturm functions. *Wik



1824 Pierre (-Jules-César) Janssen (22 Feb 1824, 23 Dec 1907) was a French astronomer who in 1868 devised a method for observing solar prominences without an eclipse (an idea reached by Englishman Joseph Norman Lockyer). Janssen observed the total Sun eclipse in India (1868). Using a spectroscope, he proved that the solar prominences are gaseous, and identified the chromosphere as a gaseous envelope of the Sun. He noted an unknown yellow spectral line in the Sun in 1868, and told Lockyer (who subsequently recognized it as a new element he named helium, from Greek "helios" for sun). Janssen was the first to note the granular appearance of the Sun, regularly photographed it, and published a substantial solar atlas with 6000 photographs (1904). *TIS

By incredible chance, both letters arrived at he French Academy on the same day, and so they are considered co-discoverers.




1849 Nikolay Yakovlevich Sonin (February 22, 1849 – February 27, 1915) was a Russian mathematician.
Sonin worked on special functions, in particular cylindrical functions. He also worked on the Euler–Maclaurin summation formula. Other topics Sonin studied include Bernoulli polynomials and approximate computation of definite integrals, continuing Chebyshev's work on numerical integration. Together with Andrey Markov, Sonin prepared a two volume edition of Chebyshev's works in French and Russian. He died in St. Petersburg.*Wik




1856 Micaiah John Muller Hill born. He worked in hydrodynamics, on the three-body problem, and has a differential equation named after him. *VFR He was Vice-Chancellor of the University of London from 1909 to 1911. His books on Euclids fifth and sixth books, and on the Theory of Proportion are available on the internet.


1857 Heinrich Rudolf Hertz (22 Feb 1857, 1 Jan 1894) was a German physicist who was the first to broadcast and receive radio waves. He studied under Kirchhoff and Helmholtz in Berlin, and became professor at Bonn in 1889. His main work was on electromagnetic waves (1887). Hertz generated electric waves by means of the oscillatory discharge of a condenser through a loop provided with a spark gap, and then detecting them with a similar type of circuit. Hertz's condenser was a pair of metal rods, placed end to end with a small gap for a spark between them. Hertz was also the first to discover the photoelectric effect. The unit of frequency - one cycle per second - is named after him. Hertz died of blood poisoning in 1894 at the age of 37. *TIS

Hertz's 1887 apparatus for generating and detecting radio waves: a spark-gap transmitter (left) consisting of a dipole antenna with a spark gap (S) powered by high voltage pulses from a Ruhmkorff coil (T), and a receiver (right) consisting of a loop antenna and spark gap.




1862 Ruth Gentry (February 22, 1862 - October 15, 1917) grew up in Indiana and received her A.B. degree at Indiana State Normal (now Indiana State University) in 1880. After ten years of teaching at preparatory schools, she earned a degree in mathematics from the University of Michigan in 1890. She spent the following year as a Fellow in Mathematics at Bryn Mawr, then became the first mathematician and the second recipient of the Association of College Alumnae European Fellowship, which she used in 1891-92 to attend lectures at the University of Berlin (but was not allowed to enroll for a degree). After a further semester attending mathematics lectures at the Sorbonne in Paris, Gentry returned to Bryn Mawr to become one of Charlotte Scott's first two graduate students. She received her Ph.D. in 1896 on the topic "On the Forms of Plane Quartic Curves." As she writes at the beginning of this thesis:
"Many papers dealing with curves of the fourth order, or Quartic Curves, are to be found in the various mathematical periodicals; but these leave the actual appearance of the curve as a whole so largely to the reader's imagination that it is here proposed to give a complete enumeration of the fundamental forms of Plane Quartic Curves as they appear when projected so as to cut the line infinity the least possible number of times, together with evidence that the forms presented can exist."
Gentry taught at Vassar College from 1896 until 1902, where she was the first mathematics faculty member to hold a Ph.D. degree. She was promoted to associate professor in 1900, but left Vassar two years later to become the associate principal and head of the mathematics department at a private school in Pittsburgh, Pennsylvania, a position she held until 1905. After that she spent some time as a volunteer nurse and traveled in the United States and Europe, but she became increasingly ill and died at the age of 55. She was a member of the American Mathematical Society from 1894 until her death in 1917 in Indianapolis, Indiana. *Agnes Scott College web page




1903 Frank Plumpton Ramsey (22 Feb 1903, 19 Jan 1930) English mathematician, logician and philosopher who died at age 26, but had already made significant contributions to logic, philosophy of mathematics, philosophy of language and decision theory. He remains noted for his Ramsey Theory, a mathematical study of combinatorial objects in which a certain degree of order must occur as the scale of the object becomes large. This theory spans various fields of mathematics, including combinatorics, geometry, and number theory. His papers show he was also a remarkably creative and subtle philosopher. *TIS His father Arthur, also a mathematician, was President of Magdalene College. His brother, Michael Ramsey, later became Archbishop of Canterbury. Suffering from chronic liver problems, Ramsey contracted jaundice after an abdominal operation and died on 19 January 1930 at Guy's Hospital in London at the age of 26. He is buried at the Parish of the Ascension Burial Ground in Cambridge, UK.*Wik




1928 BASIC co-inventor Thomas Kurtz is born. With John Kemeny, Kurtz developed the easy-to-learn programming language for his students at Dartmouth College in the early 1960s. He said: "If Fortran is the lingua franca ... BASIC is the lingua playpen." *CHM





DEATHS

1512 Amerigo Vespucci (9 Mar 1451, 22 Feb 1512 at age 60)Spanish astronomer whose name was given to the New World - America - because it was he and not Columbus, who realized and announced that Columbus had discovered a new continent. *TIS


1687 Francesco Lana de Terzi (Brescia, Lombardy 1631 – 22 February 1687 Brescia, Lombardy) was an Italian Jesuit, mathematician, naturalist and aeronautics pioneer. Having been professor of physics and mathematics at Brescia, he first sketched the concept for a vacuum airship and has been referred to as the Father of Aeronautics for his pioneering efforts, turning the aeronautics field into a science by establishing "a theory of aerial navigation verified by mathematical accuracy". He also developed the idea that developed into Braille. *Wik

His airship, inspired by Otto von Guericke's Magdeburg experiments with evacuated copper spheres, was totally impractical, but then many of his proposed machines involved perpetual motion.  But on the plus side, his idea was to use a real gondola, making this a true air-ship.


1941 Dayton Clarence Miller (13 Mar 1866, 22 Feb 1941 at age 74)American physicist. Author of The Science of Musical Sounds (1916). Miller's collection of nearly 1,650 flutes and other instruments, and other materials mostly related to the flute, is now at the Library of Congress. To provide a mechanical means of recording sound waves photographically, he invented the phonodeik (1908). He became expert in architectural ecoustics. During WW I, he was consulted concerning using his photodeik to help locate enemy guns. Miller spent considerable research effort on repeating the Michelson and Morley experiment, proposed by Maxwell, to detect a stationary aether. He spent some time working with Morley (1902-4), then more time at Mt. Wilson, recording results favoring the presence of the aether.*TIS



1975 Oskar Perron ( 7 May 1880 in Frankenthal, Pfalz, Germany - 22 Feb 1975 in Munich, Germany)was a German mathematician best known for the Perron paradox:
Suppose the largest natural number is N. Then if N is greater than 1 we have N^2 greater than N contradicting the definition. His publications cover a wide range of mathematical topics. His work in analysis is certainly remembered through the Perron integral. However he also worked on differential equations, matrices and other topics in algebra, continued fractions, geometry and number theory. *SAU

*Wik



1984 Maxwell Herman Alexander "Max" Newman, FRS (7 February 1897 – 22 February 1984) was a British mathematician and codebreaker. After WWII he continued to do research on combinatorial topology during a period when England was a major center of activity, notably Cambridge under the leadership of Christopher Zeeman. Newman made important contributions leading to an invitation to present his work at the 1962 International Congress of Mathematicians in Stockholm at the age of 65, and proved a Generalized Poincaré conjecture for topological manifolds in 1966. He died in Cambridge.*Wik



1985 Ernests Fogels (12 October 1910 – 22 February 1985) was a Latvian mathematician who specialized in number theory. Fogels discovered new proofs of the Gauss-Dirichlet formula on the number of classes of positively definite quadratic forms and of the de la Vallée-Poussin formula for the asymptotic location of prime numbers in an arithmetic progression.
Fogels retired in 1966 but continued his scientific work with research on the Hecke's L-functions, prime ideals and the Riemann hypothesis until his death on 22 February 1985 in Latvia.




2011 Frank Featherstone Bonsall FRS (31 March 1920, Crouch End, London – 22 February 2011, Harrogate) was a British mathematician.

Bonsall was born on 31 March 1920, the youngest son of Wilfred C Bonsall and Sarah Frank. His older brother was Arthur Bonsall. He married Gillian Patrick, a Somerville graduate, in 1947. Bonsall and his wife were keen hill-walkers. He wrote two articles for The Scottish Mountaineering Club on the definition of a Munro. After his retirement, Bonsall and his wife moved to Harrogate.

Bonsall graduated from Bishop's Stortford College in 1938, and studied at Merton College, Oxford. He served in World War II, in the Corps of Royal Engineers, and in India from 1944 to 1946.

He lectured at the University of Edinburgh from 1947 to 1948; was visiting associate professor at Oklahoma State University from 1950 to 1951; taught at Newcastle University, with Werner Wolfgang Rogosinski in the 1950s. He taught at the University of Edinburgh, from 1963 to 1984. In 1963, a second chair in Mathematics was established (the Maclaurin chair). Bonsall took up the chair in 1965, but spent the following year as a visiting professor at Yale. In 1966, he was awarded the London Mathematical Society's Berwick Prize.

Despite not himself having a PhD, Bonsall supervised many PhD candidates who knew him affectionately as "FFB".  *Wik



2018 Richard E. Taylor (2 November 1929 – 22 February 2018) Canadian physicist who in 1990 shared the Nobel Prize for Physics with Jerome Friedman and Henry Kendall for his collaboration in pioneering investigations concerning deep inelastic scattering of electrons on protons and bound neutrons, which have been of essential importance for the development of the quark model in particle physics. The team performed a series of experiments that confirmed the hypothesis that protons and neutrons are made up of quarks. This discovery was crucial to the formulation of the currently accepted theoretical description of matter and its interactions, known as the standard model. *TIS





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

Saturday, 21 February 2026

On This Day in Math - February 21

   

Durer Perspective



My mother said, "Even you, Paul, can be in only one place at one time." Maybe soon I will be relieved of this disadvantage. Maybe, once I've left, I'll be able to be in many places at the same time. Maybe then I'll be able to collaborate with Archimedes and Euclid.
~Paul Erdos

The 52nd day of the year; The month and day are simultaneously prime a total of 52 times in a non-leap year. *Tanya Khovanova, Number Gossip How many times in a leap year ?

52 is also the maximum number of moves needed to solve the 15 puzzle from the worst possible start. *Mario Livio



52 is the number of 8-digit primes (on a calculator) that remain prime if viewed upside down, in a mirror, or upside down in a mirror. *Prime Curios

There are 52 letters in the names of the cards in a standard deck: ACE KING QUEEN JACK TEN
(This also works in Spanish. any other languages for which this is true?) *Futility Closet    (One correspondent suggested his names for cards in Spanish have 54 letters.  Any good Spanish speakers care to comment?)



EVENTS

1632 Galileo's epic Dialogue on the Two Chief World Systems is Published in Florence. After receiving, what Galileo viewed as permission to write about "the systems of the world" from the new pope, Urban VIII. Greeted with Praise from scholars across Europe, it would eventually be Galileo's downfall. *Brody & Brody, The Science Class You Wish You Had



1699 Newton elected the second foreign member of the French Academy. See January 28, 1699. [American Journal of Physics, 34(1966), 22] *VFR Thony Christie points out in a comment (below) that "Newton was appointed foreign associate of the Académie Royale des Sciences along with four others so to claim he was the second is more than somewhat dubious." (My Thanks)


1727/8 Isaac Greenwood began his “Publick” lectures at Harvard as the first Hollis Professor of Mathematics and Natural Philosophy. The lectures were open to the entire university. [I. B. Cohen, Some Early Tools of American Science, p. 35.] *VFR

A list of Hollis Professors up to 2025:

Isaac Greenwood (1727–1737)

John Winthrop (1737–1779)

Samuel Williams (1779–1789)

Samuel Webber (1789–1806)

John Farrar (1807–1838)

Joseph Lovering (1838–1888)

Benjamin Osgood Peirce (1888–1914)

Wallace Clement Sabine (1914–1919)

vacant (January 1919–September 1921)

Theodore Lyman (1921–1926)

Percy Williams Bridgman (1926–1950)

John Hasbrouck Van Vleck (1951–1969)

Andrew Gleason (1969–1992)

Bertrand Halperin (1992–2018)

Cumrun Vafa (2018–present)






1811, as Humphry Davy read a paper to the Royal Society, he introduced the name "chlorine" from the Greek word for "green," for the bright yellow green gas chemists then knew as oxymuriatic gas. In his paper, On a Combination of Oxymuriatic Gas and Oxygene Gas, Davy reported on his numerous experiments with oxymuratic gas, which appeared to have many of the reactive properties of oxygen. Hydrochloric acid was then known as muriatic acid, and when chlorine was first obtained from a reaction with the acid, the yellow green gas had been thought to be a compound containing oxygen. Later, Davy's careful work would show that the chlorine gas was in fact an element, unable to be decomposed into any simpler substances. *TIS

The element was first studied in detail in 1774 by Swedish chemist Carl Wilhelm Scheele, and he is credited with the discovery. Scheele produced chlorine by reacting MnO2 (as the mineral pyrolusite) with HCl:

4 HCl + MnO_2 → MnCl_2 + 2 H_2O + Cl_2

Scheele observed several of the properties of chlorine: the bleaching effect on litmus, the deadly effect on insects, the yellow-green color, and the smell similar to aqua regia.[14] He called it "dephlogisticated muriatic acid air" since it is a gas (then called "airs") and it came from hydrochloric acid (then known as "muriatic acid"). He failed to establish chlorine as an element. *Wik

Carl Wilhelm Scheele



1831 Michael Faraday in a letter to William Whewell regarding a recent publication by Whewell (Journal of the Royal Institution of England (1831), 437-453.), “Your remarks upon chemical notation with the variety of systems which have arisen, had almost stirred me up to regret publicly that such hindrances to the progress of science should exist. I cannot help thinking it a most unfortunate thing that men who as experimentalists, philosophers are the most fitted to advance the general cause of science; knowledge should by promulgation of their own theoretical views under the form of nomenclature, notation, or scale, actually retard its progress. *Isaac Todhunter, William Whewell, (1876), Vol. 1., 307.

Faraday, *Wik



1845 The ship Charles Heddle sailed north from Mauritius and encountered a terrible storm. Striking sails and scudding before the wind they proceeded four times around the center in clockwise loops hundreds of miles wide. After six days a clearing sky allowed the Captain to take a reading and realize that as they circled, they had also been driven back nearly to their starting point. Reading the log of the Charles Heddle and other reports of this storm, Henry Piddington coined the word cyclone, from the Greek for "coils of a snake,". After he used the term in his "The Sailor's Horn-Book for the Law of Storms" it became a common term.




1880 Noyes Chapman had applied for a patent on his "Block Solitaire Puzzle" (the 15 puzzle above in number facts) on February 21, 1880. However, that patent was rejected, likely because it was not sufficiently different from the August 20, 1878 "Puzzle-Blocks" patent (US 207124) granted to Ernest U. Kinsey 
His was a 6x6 square with letters, blanks and symbols.




1908 Birth date of Dr. Irving Joshua Matrix, the greatest numerologist who (n)ever lived. At the age of seven he astonished his minister Father when he pointed out that 8 is the holiest number of all: “The other numbers with holes are 0, 6, and 9, and sometimes 4, but 8 has two holes, therefore it is the holiest.” Martin Gardner first drew attention to Dr. Matrix in his January 1960 column “Mathematical Games,” in Scientific American. For more details, see The Incredible Dr. Matrix, by Martin Gardner [p. 3-4]. *VFR





1953, Francis Crick and James Watson reached their conclusion about the double helix structure of the DNA molecule. They made their first announcement on Feb 28, and their paper, A Structure for Deoxyribose Nucleic Acid, was published in the 25 Apr 1953 issue of journal Nature. *TIS

1958: The Peace symbol is designed and completed by Gerald Holtom #OTD.
*History Time

1996 Cox Enterprises announces it was buying a one-third interest in Digital Domain, a computer-generated special effects company, in order to heighten the use of special effects in media. The deal reflected "another step in the rapid convergence of various computer, software, entertainment and media companies," The New York Times wrote. *CHM

2012 The engineering profession's highest honors for 2012, presented by the National Academy of Engineering (NAE), recognize ground-breaking contributions to the development of the modern liquid crystal display and achievements that led to a curriculum that encourages engineering leadership. The awards, announced today, will be presented at a gala dinner event in Washington, DC on February 21, 2012.
George H. Heilmeier, Wolfgang Helfrich, Martin Schadt, and T. Peter Brody will receive the Charles Stark Draper Prize a $500,000 annual award that honors engineers whose accomplishments have significantly benefited society "for the engineering development of the Liquid Crystal Display (LCD) that is utilized in billions of consumer devices." *AAAS/Science Newsletter, January 19, 2012
The Draper prize is named for Charles Stark Draper, the "father of inertial navigation", an MIT professor and founder of Draper Laboratory.
The Priza was first presented in 1989 to Jack S. Kilby and Robert N. Noyce for their independent development of the monolithic integrated circuit.





BIRTHS

1591 Girard Desargues (21 Feb 1591 in Lyon, France - ? Sept 1661 in Lyon, France) He did noted work in projective geometry. *VFR Desargues' most important work, the one in which he invented his new form of geometry, has the title Rough draft for an essay on the results of taking plane sections of a cone (Brouillon project d'une atteinte aux evenemens des rencontres du Cone avec un Plan). A small number of copies was printed in Paris in 1639. Only one is now known to survive, and until this was rediscovered, in 1951, Desargues' work was known only through a manuscript copy made by Philippe de la Hire (1640 - 1718). The book is short, but very dense. It begins with pencils of lines and ranges of points on a line, considers involutions of six points (Desargues does not use or define a cross ratio), gives a rigorous treatment of cases involving 'infinite' distances, and then moves on to conics, showing that they can be discussed in terms of properties that are invariant under projection. We are given a unified theory of conics.
Desargues' famous 'perspective theorem' - that when two triangles are in perspective the meets of corresponding sides are colinear - was first published in 1648, in a work on perspective by Abraham Bosse. *SAU


1764 Ruan Yuan (Chinese characters: 阮元) (21 Feb 1764 in Yangzhou, Jiangsu province, China - 27 Nov 1849 in Yangzhou, Jiangsu province, China), was a scholar official in the Qing Dynasty in Imperial China. He won jinshi (high) honors in the imperial examinations in 1789 and was subsequently appointed to the Hanlin Academy. He was famous for his work Biographies of Astronomers and Mathematicians and for his editing the Shi san jing zhu shu (Commentaries and Notes on the Thirteen Classics) for the Qing emperor.*Wik



1788 Francis Ronalds (21 February 1788 – 8 August 1873) came from a family of cheese purveyors, a profession he adopted for some years (while considering changing his name to Wensleydale).  But around 1810, he abruptly shifted his attention to electricity (this was 10 years after Volta's battery had opened up a new world for electrical investigators).  Ronalds invented a slew of ingenious electrical devices, including an electrograph that would measure the electricity in the atmosphere.  He also started collecting books and pamphlets on electricity, a collection that would grow into a sizable library.

In 1816, Ronalds built a working telegraph in the garden of the family house in Hammersmith in west London.  Part of it was underground, but above ground he strung out 8 miles of insulated wire in ribbon-candy fashion, with clocks at each end whose faces contained letters instead of numbers; the electrical signals in some way synchronized the clocks and spelled out a message.  Apparently, the device worked; he gave a demonstration on 5 August, 1816 for the Admiralty, offering it to them gratis, but the Secretary of the Admiralty, John Barrow, rejected it as an unnecessary invention, preferring the semaphore telegraph then in use.  Two years later, Barrow distinguished himself by sending out the first ships in search of a Northwest Passage, but he has never quite lived down the ignominy of rejecting the electrical telegraph as useless.  It would be 20 more years before England re-entered the telegraph business, and by that time, they were well behind the Americans.  Many today regard Ronalds as the true inventor of the telegraph, and there was considerable scholarly commotion in his behalf in 2016, the bicentennial of his invention.

Ronalds continued to invent and collect books throughout a very long life (he died in 1873, at age 85).  In the 1840s, with the invention of photography, he found a way to continuously photograph a full 24 hours of readings of his electrograph (second image).  His Library grew to accommodate 2000 books and 4000 pamphlets; after his death, it was deposited with the Institution of Engineering and Technology in London, and finally donated to that institution in 1976.

Ronalds published a book on his telegraph, Descriptions of an Electrical Telegraph, and of some other Electrical Apparatus (1823).  This work is surprisingly not in our collections, a deficiency we will try to remedy in the near future.  Ironically, we just last week acquired the principal book on semaphore telegraphy, the system that Barrow preferred to Ronalds’ electrical telegraph.

As a final note, the Ronalds house in Hammersmith, where his telegraph was first laid out, was acquired in the 1870s by designer William Morris, and is today known as Kelmscott House.  There is a plaque on the wall that commemorates Ronalds' garden telegraph (first image).  The only surviving portrait of Ronalds, painted not long before his death, is in the National Portrait Gallery, London (third image). *Linda Hall Org

*Wik





1849 Édouard Gaston (Daniel) Deville (21 Feb 1849; 21 Sep 1924 at age 75)
was a French-Canadian surveyor was a French-born Canadian surveyor of Canadian lands (1875-1924) who perfected the first practical method of photogrammetry, or the making of maps based on photography. His system used projective grids of images taken from photographs made with a camera and theodolite mounted on the same tripod. Photographs were taken from different locations, at precise predetermined angles, with measured elevations. Each photograph slightly overlapped the preceding one. With enough photographs and points of intersection, a map could be prepared, including contour lines. He also invented (1896) the first stereoscopic plotting instrument called the Stereo-Planigraph, though its complexity resulted in little use. *TIS




1965 Frances Evelyn Cave-Browne-Cave FRAS (21 February 1876–30 March 1965) was an English mathematician and educator.

Frances Cave-Browne-Cave was the daughter of Sir Thomas Cave-Browne-Cave and Blanche Matilda Mary Ann Milton. She was educated at home in Streatham Common with her sisters and entered Girton College, Cambridge, with her elder sister Beatrice Mabel Cave-Browne-Cave in 1895. She obtained a first-class degree and she would have been Fifth Wrangler in 1898 if she had been a man(Immediately behind G H Hardy.). She took Part II of the Mathematical Tripos in 1899.

Like her sister, she was usually known by the single surname Cave professionally. Along with Beatrice, she worked with Karl Pearson at University College London. Her work was funded by the first research grant offered at Girton: an Old Students' Research Studentship from Girton, provided by Florence Margaret Durham.Her research in the field of meteorology produced two publications in the Proceedings of the Royal Society which discussed barometric measurements, and was read to the British Association at Cambridge in 1904.

In 1903, Cave returned to Girton as a fellow. She prioritised teaching over research, and focused on developing the weakest students because she felt that was where the biggest difference could be made. She became the director of studies in 1918. She was on the executive council of the college and was largely responsible for drafting the charter of incorporation granted in 1924. On the 11 November 1921 she was elected a Fellow of the Royal Astronomical Society. Cave was made honorary fellow of Girton in 1942.

Cave received an MA from Trinity College, Dublin, in 1907 (since the rules of Cambridge University did not then permit women to take degrees) and from Cambridge in 1926.

Cave retired to Southampton in 1936. She died in Shedfield in a nursing home on 30 March 1965




1915 Evgeny Mikhailovich Lifshitz FRS (February 21, 1915 – October 29, 1985) was a leading Soviet physicist of Jewish origin and the brother of physicist Ilya Mikhailovich Lifshitz. (Some commonly encountered alternative transliterations of his names include Yevgeny or Evgenii and Lifshits or Lifschitz.) Lifshitz is well known in general relativity for coauthoring the BKL conjecture concerning the nature of a generic curvature singularity. As of 2006, this is widely regarded as one of the most important open problems in the subject of classical gravitation.
With Lev Landau, Lifshitz co-authored Course of Theoretical Physics, an ambitious series of physics textbooks, in which the two aimed to provide a graduate-level introduction to the entire field of physics. These books are still considered invaluable and continue to be widely used. Landau's wife strongly criticized his scientific abilities, hinting at how much of their joint work was done by Lifshitz and how much by Landau. Despite the sniping, he is well known for many invaluable contributions, in particular to quantum electrodynamics, where he calculated the Casimir force in an arbitrary macroscopic configuration of metals and dielectrics.*Wik
Offer Pade' added that The Course of Theoretical Physics is a ten-volume series of books covering theoretical physics that was initiated by Lev Landau and written in collaboration with his student Evgeny Lifshitz starting in the late 1930s. It is said that Landau composed much of the series in his head while in an NKVD prison in 1938–1939. (Wikipedia)
I have used several of the book in the series and found them excellent.




Landau(L) with Lifshitz(R) 




1984  Hannah Fry (born 21 February 1984-) is a British mathematician, author and broadcaster. She is Professor of the Public Understanding of Mathematics at the University of Cambridge, a fellow of Queens' College, Cambridge, and president of the Institute of Mathematics and its Applications. She was previously a professor at University College London.

Her work has included studies of patterns of human behaviour, such as interpersonal relationships and dating, and how mathematics can apply to them, the mathematics behind pandemics, and scientific explanations of modern appliances. She has had a particular focus on helping the public to improve their mathematical skills. Fry gave the Royal Institution Christmas Lectures in 2019 and has presented several television and radio programmes for the BBC, including The Secret Genius of Modern Life. She has received several awards for her work in mathematics, including the Asimov Prize and David Attenborough Award. *Wik

When Fry was a student at University College London, she was once invited to give a short public talk about her research on the mathematics of human behavior — specifically, how mathematical models can describe how people move through cities. She realized, though, that the audience would not be mathematicians. So instead of diving into equations, she brought along a bag of toy cars and began explaining how traffic patterns, crowd movements, and even riots could be understood through the same mathematical lens.

Her playful approach — literally rolling cars across a table to illustrate differential equations — so impressed the audience (and her department) that it launched her public-speaking career. That talk eventually led to her first BBC appearance, and she has said that it taught her one of her main lessons as a science communicator:
“If people can see the math in the world around them, they’ll fall in love with it — even if they think they hate equations.”






DEATHS

1900 Charles Piazzi Smyth FRSE FRS FRAS FRSSA (3 January 1819, Naples, Italy – 21 February 1900), was Astronomer Royal for Scotland from 1846 to 1888, well known for many innovations in astronomy and his pyramidological and metrological studies of the Great Pyramid of Giza. *Wik

1901 George Francis Fitzgerald (3 Aug 1851, 21 Feb 1901 at age 49) Irish physicist whose suggestion of a way to produce waves helped lay a foundation for wireless telegraphy. He also first developed a theory, independently discovered by Hendrik Lorentz, that a material object moving through an electromagnetic field would exhibit a contraction of its length in the direction of motion. This is now known as the Lorentz-FitzGerald contraction, which Einstein used in his own special theory of relativity. He also was first to propose the structure of comets as a head made of large stones, but a tail make of such smaller stones (less than 1-cm diam.) that the pressure of light radiation from the sun could deflect them. FitzGerald also studied electrolysis as well as electromagnetic radiation.*TIS
In his letter to Science dated May 2, 1889, which was quite brief, FitzGerald proposed that the best way to explain the null result of the Michelson-Morley experiment was to assume that the length of an object was not a constant, but that objects moving through the ether with a velocity v were contracted by a factor of v^2/c^2, where c is the speed of light. *Linda Hall Org




1912  Émile Michel Hyacinthe Lemoine (22 Nov 1840 in Quimper, France - 21 Feb 1912 in Paris, France) Lemoine work in mathematics was mainly on geometry. He founded a new study of properties of a triangle in a paper of 1873 where he studied the point of intersection of the symmedians of a triangle. He had been a founder member of the Association Française pour l'Avancement des Sciences and it was at a meeting of the Association in 1873 in Lyon that he presented his work on the symmedians.
A symmedian of a triangle from vertex A is obtained by reflecting the median from A in the bisector of the angle A. He proved that the symmedians are concurrent, the point where they meet now being called the Lemoine point. Among other results on symmedians in Lemoine's 1873 paper is the result that the symmedian from the vertex A cuts the side BC of the triangle in the ratio of the squares of the sides AC and AB. He also proved that if parallels are drawn through the Lemoine point parallel to the three sides of the triangle then the six points lie on a circle, now called the Lemoine circle. Its centre is at the mid-point of the line joining the Lemoine point to the circumcentre of the triangle. Lemoine gave up active mathematical research in 1895 but continued to support the subject. He had helped to found a mathematical journal, L'intermédiaire des mathématiciens., in 1894 and he became its first editor, a role he held for many years. *SAU   His mathematical recreation books are still popular in France.
Lemoine has been described by Nathan Altshiller Court as a co-founder (along with Henri Brocard and Joseph Neuberg) of modern triangle geometry, a term used by William Gallatly, among others. In this context, "modern" is used to refer to geometry developed from the late 18th century onward. Such geometry relies on the abstraction of figures in the plane rather than analytic methods used earlier involving specific angle measures and distances. The geometry focuses on topics such as collinearity, concurrency, and concyclicity, as they do not involve the measures listed previously.
The Lemoine point; L. The black lines are medians, the dotted lines are angle bisectors and the red lines are the symmedians (the reflections of the black lines in the dotted lines).





1912 Osborne Reynolds (23 Aug 1842 in Belfast, Ireland - 21 Feb 1912 in Watchet, Somerset, England) was an Irish mathematician best known for introducing the Reynolds number classifying fluid flow.*SAU
 British innovator in the understanding of fluid dynamics. Separately, his studies of heat transfer between solids and fluids brought improvements in boiler and condenser design. He spent his entire career at what is now the University of Manchester. *Wik




1926 Heike Kamerlingh Onnes (21 Sep 1853, 21 Feb 1926 at age 72)Dutch physicist who was awarded the 1913 Nobel Prize for Physics for his work on low-temperature physics in which he liquified hydrogen and helium. From his studies of the resistance of metals at low temperatures, he discovered superconductivity (a state in which certain metals exhibit almost no electrical resistance at a temperature near absolute zero).*TIS




1932 James Mercer FRS (15 January 1883 – 21 February 1932) was a mathematician, born in Bootle, close to Liverpool, England. He was educated at University of Manchester, and then University of Cambridge. He became a Fellow, saw active service at the Battle of Jutland in World War I, and after decades of suffering ill health died in London, England.
He proved Mercer's theorem, which states that positive definite kernels can be expressed as a dot product in a high-dimensional space. This theorem is the basis of the kernel trick (applied by Aizerman), which allows linear algorithms to be easily converted into non-linear algorithms. *Wik




1938 George Ellery Hale (29 Jun 1868, 21 Feb 1938 at age 69). U S astronomer known for his development of important astronomical instruments. To expand solar observations and promote astrophysical studies he founded Mt. Wilson Observatory (Dec 1904). He discovered that sunspots were regions of relatively low temperatures and high magnetic fields. Hale hired Harlow Shapley and Edwin Hubble as soon as they finished their doctorates, and he encouraged research in galactic and extragalactic astronomy as well as solar and stellar astrophysics. Hale planned and tirelessly raised funds for the 200-inch reflecting telescope at the Palomar Mountain Observatory completed in 1948, after his death, and named for him—the Hale telescope. *TIS
Originally, the Hale Telescope was going to use a primary mirror of fused quartz manufactured by General Electric, but instead the primary mirror was cast in 1934 at Corning Glass Works in New York State using Corning's then new material called Pyrex (borosilicate glass). Pyrex was chosen for its low expansion qualities so the large mirror would not distort the images produced when it changed shape due to temperature variations (a problem that plagued earlier large telescopes).
The 5 meter (16 ft. 8 in.) mirror in December 1945 at the Caltech Optical Shop when grinding resumed following World War 2. The honeycomb support structure on the back of the mirror is visible through the surface.*Wik

Gavin Putland added , "Hale co-invented the spectroheliograph."





1962 Julio Rey Pastor (14 August 1888 – 21 February 1962) was a Spanish mathematician and historian of science. Rey proposed the creation of a "seminar in mathematics to arouse the research spirit of our school children.” His proposal was accepted and in 1915 the JAE created the Mathematics Laboratory and Seminar, an important institution for the development of research on this field in Spain.
In 1951, he was appointed director of the Instituto Jorge Juan de Matemáticas in the CSIC. His plans in Spain included two projects: the creation, within the CSIC, of an Institute of Applied Mathematics, and the foundation of a Seminar on the History of Science at the university. *Wik




1993 Inge Lehmann  (13 May 1888 – 21 February 1993) was a Danish seismologist and geophysicist. In 1936, she discovered that the Earth has a solid inner core inside a molten outer core. Before that, seismologists believed Earth's core to be a single molten sphere, being unable, however, to explain careful measurements of seismic waves from earthquakes, which were inconsistent with this idea. Lehmann analysed the seismic wave measurements and concluded that Earth must have a solid inner core and a molten outer core to produce seismic waves that matched the measurements. Other seismologists tested and then accepted Lehmann's explanation. Lehmann was also one of the longest-lived scientists, having lived for over 104 years 

Lehmann's parents enrolled both her and her sister at Fællesskolen in 1904, a liberal and progressive school that offered the same curriculum to both boys and girls, a practice uncommon at the time. This school was led by Hanna Adler, Niels Bohr's aunt, a pioneering woman scholar and firm believer in gender equality. A year after earning her degree, Adler launched her school, inspired by innovative teaching practices in the US.*Wik 

Lehmann Memorial





1996 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



2009 Ilya Piatetski-Shapiro (30 March 1929 – 21 February 2009) was a Russian-Jewish mathematician. During a career that spanned 60 years he made major contributions to applied science as well as theoretical mathematics. In the last forty years his research focused on pure mathematics; in particular, analytic number theory, group representations and algebraic geometry. His main contribution and impact was in the area of automorphic forms and L-functions.
For the last 30 years of his life he suffered from Parkinson's disease. However, with the help of his wife Edith, he was able to continue to work and do mathematics at the highest level, even when he was barely able to walk and speak.*Wik



2012 Vera Nikolaevna Kublanovskaya (née Totubalina; November 21, 1920 – February 21, 2012) was a Russian mathematician noted for her work on developing computational methods for solving spectral problems of algebra. She proposed the QR algorithm for computing eigenvalues and eigenvectors in 1961, which has been named as one of the ten most important algorithms of the twentieth century. This algorithm was proposed independently by the English computer scientist John G.F. Francis in 1961.
Kublanovskaya was born in November 1920 in Krokhona, a village near Belozersk in Vologda Oblast, Russian Soviet Federative Socialist Republic. She was born in a farming and fishing family as one of nine siblings. She died at the age of 91 years old in February 2012. 

Kublanovskaya started her tertiary education in 1939 at the Gertzen Pedagogical Institute in Leningrad.[4] There, she was encouraged to pursue a career in mathematics. She moved on to study mathematics at Leningrad State University in 1945 and graduated in 1948. Following her graduation, she joined the Leningrad Branch of the Steklov Mathematical Institute of the USSR Academy of Sciences. She remained there for 64 years of her life.

In 1955, she got her first doctorate degree on the application of analytic continuation to numeric methods. In 1972 she obtained a secondary doctorate on the use of orthogonal transformations to solve algebraic problems.
In October 1985, she was awarded an honorary doctorate at Umeå University, Sweden, with which she has collaborated.
During her first PhD, she joined Leonid Kantorovich's group that was working on developing a universal computer language in the USSR. Her task was to select and classify matrix operations that are useful in numerical linear algebra. *Wik

*SAU



2025   Ioan Mackenzie James FRS (23 May 1928 – 21 February 2025) was a British mathematician working in the field of topology, particularly in homotopy theory.

James was born in Croydon, Surrey, England, and was educated at St Paul's School, London and Queen's College, Oxford. In 1953 he earned a D. Phil. from the University of Oxford for his thesis entitled Some problems in algebraic topology, written under the direction of J. H. C. Whitehead.

In 1957 he was appointed reader in pure mathematics, a post which he held until 1969. From 1959 until 1969 he was a senior research fellow at St John's College, Oxford. He held the Savilian Chair of Geometry at the University of Oxford from 1970 to 1995. He was a professor emeritus, and later an honorary fellow of St John's.

He was elected a Fellow of the Royal Society in 1968. In 1978 the London Mathematical Society awarded him the Senior Whitehead Prize, which was established in honor of his doctoral supervisor, Whitehead. In 1984 he became President of the London Mathematical Society.

James married Rosemary Stewart, a writer and researcher in business management and healthcare management, in 1961. She died in 2015, aged 90. James died on 21 February 2025, aged 96.






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