Pat'sBlog

Thursday, 5 February 2026

Matrices and Magic Squares

Matrices and Magic Squares

In the last half of January a few years back, John Cook posted a blog about Matrices made up of Magic Squares. He pointed out that if you multiply an odd number of 3 × 3 magic squares together, the result is a magic square. He used the three Spanish Magic Squares above from another of his posts as an example. The conjecture is that it would work for squares of any order, but that may not have been proven yet.

Since -1 is an odd number, it followed that the inverse of a magic square matrix would form a magic square also, so I gave it a go on Wolfram Alpha. The oldest and most common magic square known is the one with integers from 1 to 15 with a total for each row, column, and diagonal of 15 (and five in the center square).

And the inverse came out to be:

If you add up any row, column, or diagonal you should get $ \frac{24}{360} = \frac{1}{15}$ which we might expect, since the product of the inverses has a determinant of one. To make that happen the sequence of numbers 1 to 9 in the original became the sequence from $ \frac{-32}{360}$ and increasing by $ \frac {1}{15} $ each step until it reaches the highest value. The center number, as in any 3x3 magic square must be 1/3 of the total.

If you add up all the numbers in the original magic square, you get 45. If you add up all the numbers in the inverse, you get 1/5, or nine times the center value of 8/360?

If this was consistent in all such inverses of magic square matrices, ... we might expect that in a 5x5 matrix inverse would produce a sum of all the entries that is 1/13? As it turned out, it did. And the sum of each row, column, etc would be 1/65. The center term of the 5x5 should then be 1/5 of 1/65, or 1/325, with the 12 numbers above it increasing by 1/13 each, and the 12 below it decreasing 1/13 each. But when I did the inverse of a 5x5 on Wolfram Alpha, the values were not in the same order as the originals. For example, the smallest number in the standard 3x3, 1, is in the same position as the smallest number in the inverse, -52/360; but when I did the 5x5, the smallest number was NOT in the same spot as the one, and more importantly, their were numbers that repeated.

Even though the method of placing 1/325 in the center square with increments in order as indicated above will produce a magic square with all the same values suggested for rows, columns, totals, etc, it simply is not the inverse of the classic 5x5 magic square. The idea that the inverse would produce a magic square is correct, but not in the classic style in which each value is unique and the numbers all form a sequence. I have not gone on to see if other NxN magic square matrices might have a similar affliction, but would enjoy you sharing your results.

A similar conflict may happen when you cube a magic square matrix. While the 3x3 comes out as expected, the 5x5 has duplicate values in the upper left and lower right corners.

On This Day in Math - February 5

See Events:1897

It is a mathematical fact that the casting of this pebble from my hand alters the center of gravity of the universe.
~Thomas Carlyle

In 2017 on this date was the 5th day of the 2nd month, in 2017 teachers can offer their students, $Sin(2017 \sqrt[5]{2}) = -1 $ (It's not, but it will give that answer on the Ti-84 calculators (mine does at least.) The true answer is

The 36th day of the year; 36 is the smallest non trivial number which is both triangular and square. It's also the largest day number of the year which is both. What's the next? You can find an infinity of them using this beautiful formula from Euler, Hat Tip to Vincent PANTALONI @panlepan

36 is the sum of the first three cubes, $1 ^3 + 2^3 + 3^3 = 36$ The sums of the first n cubes is always a square number. $\sum_{k=1}^n k^3 = (\frac{(n)(n+1)}{2}) ^2$ Note that this sequence and its formula were known to (and possibly discovered by) Nicomachus, 100 CE) (There are only two year days that are square numbers that are the sum of three distinct cubes, can you find the square, and ir's cube partitions)

The sum of the first 36 integers, $\sum_{k=1}^{36} k = 666$ the so called "number of the beast."

And Mario Livio pointed out in a tweet that this is 5/2 in European style dating, and 52 is the maximum number of moves needed to solve the "15" sliding puzzle from any solvable position.

The length of an Inch was decreed by King Edward in 1324 to be “three grains of barley, dry and round, placed end to end lengthwise." Which makes a foot the length of 36 such barleycorns.

The Kiwi's seeds divide the circle into 36 equal sections. Nature's protractor. *Matemolivares@Matemolivares

A special historical tribute to 36: The thirty-six officers problem is a mathematical puzzle proposed by Leonhard Euler in 1782. He asked if it were possible to place officers of six ranks from each of six regiments in a 6x6 square so that no row or column would have an officer of the same rank, or the same regiment. Euler suspected that it could not be done. Euler knew how to construct such squares for nxn when n was odd, or a multiple of four, and he believed that all such squares with n = 4m+2 (6, 10, 14...) were impossible ( Euler didn't say it couldn't be done. He just said that his method does not work for numbers of that form.) Proof that he was right for n=6 took a while. French mathematician (and obviously a very patient man) Gaston Tarry proved it in 1901 by the method of exhaustion. He wrote out each of the 9408 6x6 squares and found that none of them worked. Then in 1959, R.C. Bose and S. S. Shrikhande proved that all the others could be constructed. So the thirty-six square is the only one that can't be done.

Orthogonal Latin squares have been known to predate Euler. As described by Donald Knuth the construction of 4x4 set was published by Jacques Ozanam in 1725 (in Recreation mathematiques et physiques, Vol. IV) as a puzzle involving playing cards. The problem was to take all aces, kings, queens and jacks from a standard deck of cards, and arrange them in a 4x4 grid such that each row and each column contained all four suits as well as one of each face value. This problem has several solutions known back to 1725, but no one could figure out how many in all.

A common variant of this problem was to arrange the 16 cards so that, in addition to the row and column constraints, each diagonal contains all four face values and all four suits as well.

According to Martin Gardner, who featured this variant of the problem in his November 1959 Mathematical Games column, the number of distinct solutions was incorrectly stated to be 72 by Rouse Ball. This mistake persisted for many years until the correct value of 144 was found by Kathleen Ollerenshaw. Notice both 72 and 144 are multiples of 36.

EVENTS

1575 Jan De Groot entered the University of Leiden, in the Netherlands, on its opening day. With Simon Stevin he later performed an experiment proving that bodies of different weights fall the same distance in the same time (published 1586 by Stevin). This anti-Aristotelian experiment anticipated Galileo’s famous, but apocryphal, experiment at the Leaning Tower of Pisa. His son Hugo De Groot was a famous jurist. *VFR Thony Christie pointed out that "The anti-Aristotle tower and ball experiment was first carried out by Johannes Philiponus in 6th century CE". Philiponus proposed a kinetic theory for motion in place of Aristotle's impetus.

1673 Robert Hooke writes in his journal that he had, "Told the Society of Arithmetick engine.‏*@HookesLondon It is said that Newton had this, and other Hooke items, including Hooke's portrait, removed from the Royal Society after Hooke's death but this does not seem to be supported by most math historians

5 Feb 1675 (OS) 15 Feb 1676(NS) Newton wrote Hooke: "What DesCartes did was a good step....If I have seen further it is by standing on ye sholders of Giants." *VFR
The letter is at the Historical Society of Pennsylvania.

1689 The Convention Parliament, with Cambridge U. MP Isaac Newton voting in the majority, declared the throne of England vacant after James II escaped to France with the permission of his Son-in-Law and daughter, William and Mary, who were offered the crown jointly. The only record of a comment by Newton during the Parliament except to ask for a servant to close a drafty window. *Thomas Levenson, Newton and The Counterfeiter.

1772 Laplace presented his ﬁrst probability memoir,, titled "Mémoire sur la probabilité des causes par les événements" (Memoir on the Probability of Causes from Events), to the Académie des Sciences, VFR (sometimes cited in 1774?)

This paper is considered a foundational work in the field of probability theory, as it marked Laplace's early contributions to the subject and introduced important concepts like inverse probability.

A PDF file of S M Stigler's translation is here.

1796 Schiller (1759–1815) wrote to Goethe (1749–1832): “Wo es die Sache leidet, halte ich es immer f¨ur besser, nicht mit dem Anfang anzufangen, der immer das Schwerste ist.” (I always think it better, whenever possible, not to begin at the beginning, as it is always the most difficult part). Although this is advice from one poet to another, it seems to apply to mathematics, especially the foundations of mathematics. Quoted from Numbers (1990) by H.-D. Ebinghaus et al., p. 6. *VFR

1835 A ceremony to honor "The Genius and Discoveries of Sir Isaac Newton" was organized by the citizens of the Lincolnshire, his area of birth, a few years after the centennial of his death. By unanimous choice, the committee selected as the speaker, the 19 yr old George Boole. "All present were struck by the youthful age of the speaker and not a little amazed by both his knowledge of the subject and his confident lecturing style."
*Desmond MacHale, The Life and Work of George Boole

1840 The American Statistical Association held its ﬁrst annual meeting, in Boston. "On November 27, 1839, five men held a meeting in the rooms of the American Education Society at No. 15 Cornhill in Boston, Massachusetts, to organize a statistical society. Its purpose, as stated in the society's first constitution, was to "collect, preserve, and diffuse statistical information in the different departments of human knowledge." Originally called the American Statistical Society, the organization's name was changed to the American Statistical Association (ASA) at its first annual meeting, held in Boston on February 5, 1840. " *Robert L. Mason, ASA: The First 160 Years

The phrase “timing is everything” rings true for the American Statistical Association (ASA), which was formed in November 1839 in Boston—a city that was burgeoning with educational and technical professional opportunities. Back then, annual dues cost $2, and notable figures who joined the society included US President Martin Van Buren and Minister to France Lewis Cass. In a then male-dominated environment, Florence Nightingale—well known for her contributions to the medical field—also became a member and was recognized for using statistical analysis techniques in her data-collection efforts benefitting public health and welfare.

What started with just five founders soon began to attract hundreds of members who were elected, not simply granted voluntary membership. With ties to statistical work of the US government, particularly the Census Bureau, a movement was led by then-ASA President Francis A. Walker (1883–1897) to expand the association’s roots nationwide. ASA leadership chose to drop the exclusive “by invitation only” membership requirement to attract a larger, more diverse group of members and opened the doors for professionals from a variety of fields and business sectors.

The organization began publishing the Journal of the American Statistical Association (JASA) in 1888, when its mission was solidified and membership was growing. And in 1908, the ASA conducted its annual meeting in Atlantic City, New Jersey—stepping away from the traditional stronghold of Boston.

1843 The great comet of 1843, A night-time view showing an eyewitness account of the Great Comet of 1843, painted by the astronomer Charles Piazzi Smyth. The earliest observation occurred on the evening of 5 of February, 1843 and Smyth recorded its appearance at the Royal Observatory, Cape of Good Hope, South Africa between 3 and 6 of March. When at its greatest brilliance, it was visible only from southern latitudes. The view in the painting is probably taken from the Observatory. It shows Table Bay with Table Mountain visible in the background on the left. A large sailing ship sits in the foreground on the right, with other shipping in the distance. One of the great British astronomers, Smyth was 42 years Astronomer Royal for Scotland. *Royal Museums Greenwich

1850 D. D. Parmalee issued a patent (US Patent # 7074) for the ﬁrst key-driven adding machine. *VFR

While this was the first US patent, an earlier key-driven machine had been patented "as early as 1844 by Jean-Baptiste Schwilgue´ (1776– 1856), together with his son Charles. Jean-Baptiste Schwilgue´ was the architect of Strasbourg’s third astronomical clock during the years 1838–1843. He was trained as a clockmaker, but also became professor of mathematics,weights and measures controller, and an industry man, whose particular focus was on improving scales." *Denis Roegel, An Early (1844) Key-Driven Adding Machine, IEEE Annals of the History of Computing, Volume 30, Number 1, January-March 2008, pp. 59-65

In 1897, the Indiana State House legislature presented Bill No.246 which in effect gave 3.2 exactly as the value of pi. It stated, in part, "the ratio of the diameter and circumference [pi] is as five-fourths to four." That is (4 divided by 5/4) = 16/5 = 3.2 exactly. It was introduced by Representative Taylor I. Record, a farmer and lumber merchant, on behalf of a mathematical hobbyist, Dr. Edwin J. Goodwin, M.D. Neither they, nor the House politicians, understood it was mathematically incorrect. That was shortly recognized by Clarence A. Waldo, mathematics professor at Purdue University, who advised the Indiana Senators. They indefinitely postponed the bill on 12 Feb 1897. Pi is, in fact, an irrational number, approx. 3.141592.*TIS

The Committee on Education, reported favorably and following a motion to suspend the rules, the bill passed on February 6, 1897 without a dissenting vote. Although called the "Pi" bill, it did not use the name. The bill also reported that the square root of two would be 10/7. *Wik

1901 Loop-the-loop centrifugal RR (roller coaster) patented by Ed Prescot. (I have also seen the date of patent as August 16, 1898. This date is now the National Roller Coaster Day in the US. ) Prescott,an inventor and mechanic from Arlington, Massachusetts. Prescott’s Loop the Loop coaster, a dual-tracked steel roller coaster, was installed at Coney Island, New York from 1901 to 1910. It seems more people came to look, than to ride.

No more looping roller coasters were built until 1976 when Revolution opened at Six Flags Magic Mountain.*Wik

The vertical loop is not a recent roller coaster innovation. Its origins can be traced back to the 1850s when centrifugal railways were built in France and Great Britain. In 1901 Prescott built the Loop-the-Loop at Coney Island.

*Smithsonian Mag

1920 Discussion on the theory of relativity by J. H. Jeans – a meeting of the Royal Society, *Royal Society Journal, HT Katharina H Mathsbooks

1924 The Royal Greenwich Observatory begins broadcasting the time "pips" on BBC, a series of six short tones broadcast at one-second intervals by many BBC Radio stations. The pips were introduced in 1924 and have been generated by the BBC since 1990. The pips were the idea of the Astronomer Royal, Sir Frank Watson Dyson, and the head of the BBC, John Reith.*Wik
This eight-day wall-mounted astronomical regulator by Edward John Dent & Co was originally made for use in observing the Transit of Venus in 1874. In 1923 it was adapted as the primary standard for the new six-pip time signal. The clock sent electrical impulses down a telephone wire to the BBC for conversion into audio pips for radio broadcasts. It has a zinc tube temperature-compensated pendulum and was corrected from 1929 by the Shortt master clock number 16. The three sets of contacts for closing the six-pip circuit every quarter of an hour can be seen in two of the holes within the seconds dial, and halfway down the pendulum, operated by a roller. This clock was in service for the BBC signal at the Observatory from 1924 to 1949, when it was superseded by a quartz clock. *Royal Observatory Greenwich

1930 You hear all those "Einstein said, " quotes and you wonder which ones are true, knowing most of them are true. And the one about, "Life is like riding a bicycle...", well it is mostly true, but the almost always muck it up a little, like the one in the image below. Einstein wrote it in a letter to his son, Eduard, on February 5, 1930, trying to encourage his son, he wrote "Men are like bicycles, It's only easy to keep your balance when you are on the move".

This letter and one more written to his son on January 24 of the same year, both signed "Papa" , were sold at Christie"s on June 7, 2000 for 4935 GBP.

1958 Kilby Files a Patent for the Integrated Circuit. Jack Kilby of Texas Instruments files a patent application called miniaturized electronic circuits for his work on a multi-transistor device. The patent was only one of 60 that Kilby holds. While Kilby has the earliest patent on the integrated circuit, it was Robert Noyce, later co-founder of Intel, whose parallel work resulted in a practical device. Kilby's device had several transistors connected by flying wires while Noyce devised the idea of interconnection via a layer of metal conductors. Noyce also adapted Jean Hoerni's planar technique for making transistors to the manufacture of more complex circuits. *CHM

*Wik

In 1962, the Sun, the Moon, and the five naked-eye visible planets - Mercury, Venus, Mars, Jupiter, and Saturn - were in conjunction. Though not in a straight line along their orbital paths, as viewed in the sky, they were within 16 degrees of each other (meaning all appeared within a circle just 16 º across). This conjunction coincided with a total solar eclipse, which made viewing Mercury, Venus, Mars, Jupiter, and Saturn possible for a brief period of time from a small stretch of Earth where the eclipse's shadow hit. The five naked-eye visible planets cluster together in the sky within a circle 25 degrees or less in diameter once every 57 years, on average. The next time in the 21st century that this will happen is 8 Sep 2040. *TIS (image...In May of 2011 a planetary conjunction of Mercury, Venus, Mars and Jupiter appeared very close to each other in the sky.) And for St. Valentines day this year (2012) I have ordered up a conjunction with Mercury and Neptune less than 1.5 ^o apart for my beautiful Jeannie, but the rest of you may enjoy it as well.

1974 US Mariner 10 returns 1st close-up photos of Venus' cloud structure2040 The near-Earth asteroid 2011 AG5 currently has an impact probability of 1 in 625 for Feb. 5, 2040, according to Donald Yeomans, head of the Near-Earth Object Observations Program at NASA’s Jet Propulsion Laboratory in Pasadena, California. Made using an ultraviolet filter in its imaging system, the photo has been color-enhanced to bring out Venus's cloudy atmosphere as the human eye would see it. Venus is perpetually blanketed by a thick veil of clouds high in carbon dioxide and its surface temperature approaches 900 degrees Fahrenheit.

Launched on Nov. 3, 1973 atop an Atlas-Centaur rocket, Mariner 10 flew by Venus in 1974.

BIRTHS

1608 Caspar Schott SJ, and Gaspar Schott or Kaspar Schott (February 5 1608 in Königshofen, May 22 1666 in Würzburg) was a scientific author and educator.
Schott attended the Würzburg Jesuit High School and entered the Order in 1627. During his studies in Würzburg one of his teachers was Athanasius Kircher. When the Jesuits fled before the approaching Swedish army in 1631,Schott went to Palermo to complete his studies. He stayed in Sicily 20 years as a teacher of mathematics, philosophy, moral theology at the Jesuit school in Palermo. In 1652 was sent to Rome as support in the scientific work of Kircher. He decided to publish Kircher's work. In 1655, he returned as Professor in the Würzburg school, where he taught mathematics and physics. He was Hofmathematker and confessor of the Elector Johann Philipp von Schönborn who had just purchased the vacuum pump invented by Otto von Guericke and used at Magdeburg.
He corresponded with leading scientists including Otto von Guericke, Christiaan Huygens, and Robert Boyle. The term "technology" was probably invented by Schott in his "Technica curiosa" which inspired Boyle and Hooke's vacuum experiments.
In the posthumously published work Organum mathematicum he describes his Cistula invented by him, a computing device, by Kircher with which you can multiply and divide.

The device described in Schott's book was divided by functionality into 9 main sections, each of which contained approximately 24 rods.

Arithmetic The arithmetic rods included a set of Napier's Bones. They were capable of assisting with the multiplication of multi-digit numbers and producing quotients.

Geometry The rods in this section could aid in determining heights, by use of a geometric square.

Fortifications The rods in this section could aid in determining the design of bulwarks in fortification plans.

ChronologynThe rods in this section could be used to determine the date of Easter and other church holidays which were positioned relative to it. These rods simply contained a table of upcoming dates.

Horography The rods in this section contained information needed to construct sundials.

Astronomy This compartment had tablets which resembled those found in an almanac. For each day of the year, the length of the day and night, the times for sunrise and sunset, and the duration of morning and evening twilight were provided. All the information was based on measurements taken at 48 degrees latitude (Vienna).

Astrology This section had tables describing movements for the visible planets, and the constellation Draco, and also provided astrological interpretations for the 12 zodiac signs.

Cryptography The rods in this section could be used to encrypt and decrypt text using a cyclic transposition cypher, based on a keyword.

Music The rods in this section could be used by non musicians to compose church music. The system used was the same as that used for Kircher's previous device, the Arca Musarithmica. They contained sets of musical phrases which could be combined randomly to set verses to music, producing millions of hymns in 4-part harmony.*Wik

the Organum Mathematicum at the Museo Galileo in Florence, Italy.

1797 Jean-Marie-Constant Duhamel (5 Feb 1797; 29 Apr 1872) French mathematician and physicist who proposed a theory dealing with the transmission of heat in crystal structures based on the work of the French mathematicians Jean-Baptiste-Joseph Fourier and Siméon-Denis Poisson. *TIS

1836 Alexander Stewart Herschel (5 February 1836 – 18 June 1907) was a British astronomer, born in Feldhausen, South Africa.
He was the son of John Herschel and the grandson of William Herschel. Although much less well known than either of them, he did pioneering work in meteor spectroscopy. He also worked on identifying comets as the source of meteor showers. The Herschel graph, the smallest non-Hamiltonian polyhedral graph, is named after Herschel due to his pioneering work on Hamilton's Icosian game. *Wik
The image of the graph at right is from Christian Perfect at the Aperiodical Blog. You can’t draw a path on it that visits each vertex exactly once, but you can make a polyhedron whose vertices and edges correspond with the graph exactly. It’s also bipartite – you can color the vertices using two colors so that edges only connect vertices of different colors.
I think the polyhedron is the only enneahedron (9 faces children) that has all quadrilateral faces. You can see the solid here.

1900 Rosalind Cecilia Hildegard Tanner (née Young) (5 February 1900 – 24 November 1992) was a mathematician and historian of mathematics. She was the eldest daughter of the mathematicians Grace and William Young. She was born and lived in Göttingen in Germany (where her parents worked at the university) until 1908.[2] During her life she used the name Cecily.

Rosalind joined the University of Lausanne in 1917. She also helped her father's research between 1919 and 1921 at the University College Wales in Aberystwyth, and worked with Edward Collingwood, also of Aberystwyth, on a translation of Georges Valiron's course on Integral Functions. She received a L-És-sc (a bachelor's degree) from Lausanne in 1925.

She then studied at Girton College, Cambridge, gaining a PhD in 1929 under the supervision of Professor E. W. Hobson for research on Stieltjes integration. She accepted a teaching post at Imperial College, London where she worked until 1967.

After 1936, most of her research was in the history of mathematics, and she had a particular interest in Thomas Harriot, an Elizabethan mathematician. She set up the Harriot Seminars in Oxford and Durham. Rosalind married William Tanner in 1953; however, he died a few months after their marriage.

In 1972 she and Ivor Grattan-Guinness published a second edition of her parents' book The Theory of Sets of Points, originally published in 1906.

Rosalind Tanner died on 24 November 1992

R. C. H. Young (left, upper) at the ICM 1932

1907 Wilhelm Magnus (February 5, 1907, Berlin, Germany – October 15, 1990, New York City) made important contributions in combinatorial group theory, Lie algebras, mathematical physics, elliptic functions, and the study of tessellations.*Wik

1915 Robert Hofstadter (5 Feb 1915, 17 Nov 1990) American scientist who was a joint recipient of the Nobel Prize for Physics in 1961 for his investigations in which he measured the sizes of the neutron and proton in the nuclei of atoms. He revealed the hitherto unknown structure of these particles and helped create an identifying order for subatomic particles. He also correctly predicted the existence of hte omega-meson and rho-meson. He also studied controlled nuclear fission. Hofstadter was one of the driving forces behind the creation of the Stanford Linear Accelerator. He also made substantial contributions to gamma ray spectroscopy, leading to the use of radioactive tracers to locate tumors and other disorders.*TIS

1932 Lee Aaron Segel ( 5 February 1932 – 31 January 2005) was an Israeli-American applied mathematician. He developed both the Keller-Segel model of chemotaxis, in cell biology, and the Newell-Whitehead-Segel equation, in fluid dynamics. He also co-authored the first simulation model for herbicide resistance evolution. He is also considered one of the forefathers of the field of theoretical immunology.

Segel was active in the Santa Fe Institute, the first of the over 50 research centers which focus, today, on complex physical, computational, biological, and social systems. Segel was also editor-in-chief of the Bulletin of Mathematical Biology from 1986 to 2001 and co-authored the first volume in the SIAM Classics in Applied Mathematics series, created by the Society for Industrial and Applied Mathematics. He migrated between numerous prestigious academic institutions worldwide, culminating at Israel's Weizmann Institute of Science,where he served as dean of the Faculty of Mathematics and Computer Science and chair of the Scientific Council. *Wik

1930 Kazimierz Urbanik (born 5 February 1930 in Krzemieniec - 29 May 2005 in Wrocław ) - Polish mathematician, rector of the University of Wroclaw ( 1975 - 1981 ), Doctor Honoris Causa of the University of Lodz and the Technical University of Wroclaw. He dealt with problems from different fields of mathematics, but his research interests were focused on the theory of probability . He obtained several important results in the theory of stochastic processes , information theory , theoretical physics , universal algebra , topology and measure theory . He published about 180 scientific papers. *Wik

DEATHS

1881 Thomas Carlyle (4 Dec 1795 in Ecclefechan, Dumfriesshire, Scotland - 5 Feb 1881 in Chelsea, London, England) was a Scottish writer who was also interested in mathematics. He translated Legendre's work.*SAU

1939 Gheorghe Ţiţeica ((October 4, 1873–February 5, 1939) publishing as George or Georges Tzitzeica) was a Romanian mathematician with important contributions in geometry. He is recognized as the founder of the Romanian school of differential geometry.*Wik

1865 Benjamin Franklin Finkel (July 5, 1865 – February 5, 1947) was a mathematician and educator most remembered today as the founder of the American Mathematical Monthly magazine. Born in Fairfield County, Ohio and educated in small country schools, Finkel received both bachelor's and master's degrees from Ohio Northern University, then known as Ohio Normal University (1888 and 1891, respectively).

In 1888 he copyrighted A Mathematical Solution Book. The purpose of the book was to provide mathematics teachers a text utilizing a systematic method of problem solving, "The Step Method", representing a chain of reasoning, in logical order, to arrive at the correct result. The first edition was postponed until 1893, due to financial problems of the original publisher. The book's preface stated that the work was based upon eight years of teaching in the public schools. This was followed by following editions in 1897, 1899 and 1902. [The book treats very basic Arithmetic. *PB]

In 1895 he became professor of mathematics and physics at Drury University, then known as Drury College. He was a University Scholar in Mathematics at the University of Chicago from 1895–1896. In 1906 he was awarded a doctorate from the University of Pennsylvania, where he had earlier earned an additional master's degree in 1904 and a Harrison fellow appointment in 1905.

He was a member of the American Mathematical Society, 1891; the London Mathematical Society, 1898; and Circolo Matematico di Palermo, 1902. He retained his professorship at Drury College until his death in 1947. *Wik

1977 Oskar Benjamin Klein (September 15, 1894 – 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

1980 Nachman Aronszajn (26 July 1907, Warsaw, Poland – 5 February 1980 Corvallis, Oregon, U.S) was a Polish American mathematician of Ashkenazi Jewish descent. Aronszajn's main field of study and expertise was mathematical analysis. He also contributed to mathematical logic.
He received his Ph.D. from the University of Warsaw, in 1930, in Poland. Stefan Mazurkiewicz was his thesis advisor. He also received a Ph.D. from Paris University, in 1935; this time Maurice Fréchet was his thesis advisor. He joined the Oklahoma A&M faculty, but moved to the University of Kansas in 1951 with his colleague Ainsley Diamond after Diamond, a quaker, was fired for refusing to sign a newly-instituted loyalty oath. Aronszajn retired in 1977. He was a Summerfield Distinguished Scholar from 1964 to his death.
He introduced, together with Prom Panitchpakdi, the injective metric spaces under the name of "hyperconvex metric spaces". Together with Kennan T. Smith, Aronszajn offered proof of the Aronszajn–Smith theorem. Also, the existence of Aronszajn trees was proven by Aronszajn; Aronszajn lines, also named after him, are the lexicographic orderings of Aronszajn trees.
He also has a fundamental contribution to the theory of reproducing kernel Hilbert space, the Moore–Aronszajn theorem is named after him. *Wik

1988 Dorothy Lewis Bernstein (April 11, 1914 – February 5, 1988) was an American mathematician known for her work in applied mathematics, statistics, computer programming, and her research on the Laplace transform.
Dorothy Bernstein was born in Chicago, the daughter of Russian immigrants to the US. She was a member of the American Mathematical Society and the first woman elected president of the Mathematical Association of America. Due in great part to Bernstein's ability to get grants from the National Science Foundation, Goucher College (where she taught for decades) was the first women's university to use computers in mathematics instruction in the 1960s.*Wik

1997 Frederick Justin Almgren,(3 July 1933 in Birmingham, Alabama, USA - 5 Feb 1997 in Princeton, USA) Almost certainly Almgren's most impressive and important result was only published in 2000, three years after his death. Why was this? The paper was just too long to be accepted by any journal. Brian Cabell White explains the background in a review of the book published in 2000 containing the result:

By the early 1970s, geometric analysts had made spectacular discoveries about the regularity of mass-minimizing hypersurfaces. (Mass is area counting multiplicity, so that if k sheets of a surface overlap, the overlap region is counted k times.) In particular, the singular set of an m-dimensional mass-minimizing hypersurface was known to have dimension at most m - 7. By contrast, for an m-dimensional mass-minimizing surface of codimension greater than one, the singular set was not even known to have m-measure 0. Around 1974, Almgren started on what would become his most massive project, culminating ten years later in a three-volume, 1700-page preprint containing a proof that the singular set not only has m-dimensional measure 0, but in fact has dimension at most (m - 2). This dimension is optimal, since by an earlier result of H Federer there are examples for which the dimension of the singular set is exactly (m - 2). ...

Now, thanks to the efforts of editors Jean Taylor and Vladimir Scheffer, Almgren's three-volume, 1700-page typed preprint has been published as a single, attractively typeset volume of less than 1000 pages.

Fred Almgren received many honours for his outstanding contributions. He was an Alfred P Sloan Fellow in 1968-70, an Exchange Visitor at the Steklov Mathematical Institute in Leningrad in 1970, a John Simon Guggenheim Memorial Fellow in 1974-75, and Earle Raymond Hedrick Lecturer for the Mathematical Association of America in1975. He was elected a fellow of the American Association for the Advancement of Science in 1982, was awarded a medallion by Brown University in 1988:-

... in recognition of distinguished contributions to society through scholarship and professional activity ...

and he received the Class of 55 Public Service Award from Princeton University in 1988:-

... for contributions to society beyond the bounds of occupation.

Among his service we should mention he was an editor of three journals: the Journal of Experimental Mathematics, the Journal of Geometric Algebra, and Differential Geometry and its Applications. He administered the Geometry Supercomputer Project for the Geometry Computing Group and served on the American Mathematical Society Committee on Applications of Mathematics.*SAU

Photograph by Paul Halmos

2003 Werner Romberg (born 16 May 1909 in Berlin; died 5 February 2003 in Heidelberg) was a German mathematician and physicist.

Romberg studied mathematics and physics form 1928 in Heidelberg and Munich and completed his doctorate in 1933 at Munich University under the supervision of Arnold Sommerfeld; his thesis was entitled "Zur Polarisation des Kanalstrahllichtes" ["On the polarisation of channel light beams"]. In Munich he studied mathematics under, among others, Oskar Perron and Constantin Carathéodory. In 1933, as a so-called "half-Jew" in the terminology of the new National Socialist government of Germany, he sought to emigrate to the Soviet Union. From 1934 to 1937 he worked as a theoretical physicist in the university of Dnipro (then Dnipropetrovsk). In 1938 he went, via the Institute for Astrophysics in Prague, to Norway, where he became an assistant to Egil Hylleraas at the University of Oslo. He also briefly worked at the Technical University of Trondheim with Johan Holtsmark, who was building a Van de Graaff generator there. With the German occupation of Norway he fled to Uppsala in Sweden. In 1941 the Nazi German state stripped him of his German citizenship, and in 1943 recognition of his doctorate was revoked. He became a Norwegian citizen in 1947.

After the Second World War, from 1949 to 1968, he was a professor in Trondheim; from 1960 he was head of the applied mathematics department. In Norway he built up his research group in numerical analysis, and part of the introduction of digital computers, such as GIER, the first computer at Trondheim. From 1968 he held the chair for Mathematical Methods in Natural Sciences and Numerics at Heidelberg University. *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

Wednesday, 4 February 2026

On This Day in Math - February 4

Archimedes *http://www.w-volk.de/museum

Technical skill is mastery of complexity while creativity is mastery of simplicity.

~ Sir Erik Christopher Zeeman

The 35th day of the year; There are 35 hexominos, the polyominoes made from 6 squares. *Number Gossip
(I only recently learned that, Although a complete set of 35 hexominoes has a total of 210 squares, which offers several possible rectangular configurations, it is not possible to pack the hexominoies into a rectangle.)

and another gem from Jim, @wilder that is .

For days 34 & 35: 3435 = 3³+4⁴+3³+5⁵ *@wilderlab

The longest open uncrossed (dosn't cross it's own path) knight's path on an 8x8 chessboard is 35 moves. (longest cycle(end where you start) is only 32 moves)

In Base 35 (A=10, B=11, etc) NERD is Prime, $23*35^3+14*35^2+27*35+13 = 1,004,233 $

*Chaw wrote to suggest 36 as a more natural base for letters and numbers combined, and added that "Nerdiest" is prime in that base.

EVENTS

1600 Johannes Kepler arrives at Benatek Castle near Prague, where Tycho Brahe had moved his observatory, and retinue, after his benefactor King Frederick drank himself to death. *Timothy Ferris, Coming of Age in the Milky Way Thony Christie wrote in response to the quote above that, "I suspect Timothy Ferris is making shit up. Frederick didn't drink himself to death." Great to have an accomplished historical scholar on my reading list who can keep me straight. Thanks Thony.

1703 46 of the 47 Ronin commit seppuku (ritual suicide) as recompense for avenging their master's death. . This I mention here because one of the 47, was the greatest Asian mathematician of his age, Shigekiyo Matsumura, who among other things, approximated the value of pi as 3.141592648, which is accurate to eight significant figures..."
More of the story here.

I received a correction from a commenter that "The mathematician's name was Muramatsu Shigekiyo (村松茂清, 1608 – 1695); he was not in the Ako incident, his son in law apparently was one of the 47 samurai, though.

The very kind Arjen Dijksman connected me with Japanese Physicist Tasuo Tabata who gave me some detail. It seems that Matsumura might be more appropriately called Shigekiyo Muramatsu. He did write the sanso, and all the math things described seem to be a modest description of his contributions. However, Professor Tabata tells me that he was NOT one of the 47 Ronin. He is, however, connected to the story. The professor says, "Shigekiyo had only a daughter. Her husband Hidenao and their son Takanao joined the 47 ronin. --"... So now, I guess I'm down to wanting a picture of the 47 Ronin from Sengakuji Temple. And if anyone knows where the grave of Shigekiyo Muramatsu is located, and/or has a picture I would love to have one.

1751 Franklin electrocutes a turkey, opines culinary improvement:

My Respects to Mr. Watson. He desir’d you to enquire what Success we had in our Attempts to kill a Turkey by the Electrical Strokes. Please to acquaint him, that we made several Experiments on Fowls this Winter; That we found two large thin glass Jars, gilt (holding each about 6 Gallons, and taking 2000 Turns of a Globe of 9 Inches Diameter to charge them full, when the Globe works very well, and will charge a common half pint Vial with 50 Turns) were sufficient to kill common Hens outright; but the Turkies, tho’ thrown into violent Convulsions, and then lying as dead for some Minutes, would recover in less than a quarter of an Hour. However, having added Mr. Kinnersley’s Jarrs and mine together, in all 5, tho’ not fully charg’d, we kill’d a Turky with them of about 10 lb.wt. and suppose they would have kill’d a much larger. I conceit that the Birds kill’d in this Manner eat uncommonly tender.

*Franklin papers

1753 Writing about his Experiments and Observations on Electricity made at Philadelphia in America, a work Diderot called the best example of the experimental art with which he was acquainted, Benjamin Franklin (in a letter to John Perkins) boasted that he had “not, with some of our learned moderns, disguised [his] nonsense in Greek, clothed it in algebra, or adorned it with ﬂuxions.” *Thomas L. Hankins, Jean d’Alembert, p 4 (via VFR) (This is in contrast to the quote by Lelande that d'Alembert "had never held a prism in his hand.")

1824, J.W. Goodrich introduced rubber galoshes to the public and little boys and girls discovered the joy of splashing through mud puddles and keeping their shoes dry. *Twisted History (or as they say across the pond, Wellies) I find it a little strange that Macintosh developed his waterproof raincoat in exactly the same year (but don't know what month).

1841 First recorded reference to "Groundhog Day" in America:

When German settlers arrived in the 1700s, they brought a tradition known as Candlemas Day, which has an early origin in the pagan celebration of Imbolc. It came at the mid-point between the Winter Solstice and the Spring Equinox. Superstition held that if the weather was fair, the second half of Winter would be stormy and cold. For the early Christians in Europe, it was the custom on Candlemas Day for clergy to bless candles and distribute them to the people in the dark of Winter. A lighted candle was placed in each window of the home. The day's weather continued to be important. If the sun came out February 2, halfway between Winter and Spring, it meant six more weeks of wintry weather.

The earliest American reference to Groundhog Day can be found at the Pennsylvania Dutch Folklore Center at Franklin and Marshall College:

February 4, 1841 - from Morgantown, Berks County (Pennsylvania) storekeeper James Morris' diary..."Last Tuesday, the 2nd, was Candlemas day, the day on which, according to the Germans, the Groundhog peeps out of his winter quarters and if he sees his shadow he pops back for another six weeks nap, but if the day be cloudy he remains out, as the weather is to be moderate."

According to the old English saying:
If Candlemas be fair and bright,
Winter has another flight.
If Candlemas brings clouds and rain,
Winter will not come again.

*Stormfax.com

In 1868, Charles Darwin began writing his book The Descent of Man and Selection in Relation to Sex. He was now 69 years old, working in his home in Downe, England. *TIS

1883 Feb. 4, 1883: Heard from Mr. Caldecott, who would like to draw for me, but is too deeply engaged to undertake anything at present. I must try to engage him for some future time, and could then feel encouraged to work definitely at a new book. Apparently he never did. Does anyone have information that Dodgson was disappointed with his illustrators? *Lewis Carroll’s Diaries @DodgsonDiaries, *Greg Priest @greg_m_priest

1884 On this day in 1884, the minutes of the Committee on the Course and Statutes of Columbia College record that Winifred Edgerton Merrill was to be allowed to use their telescope:

... access to the Observatory and the use of its instruments ... with the understanding that she will render, from time to time, such assistance in the practical work of the Observatory as may be in her power.

Later Merrill told her son:-

... that a condition of her admission was to dust the astronomical instruments and so comport herself as not to disturb the men students. *SAU (More about her here)

1961 Sputnik 7 launches into Earth orbit. This was the first Soviet attempt at a Venus probe. The probe was successfully launched into Earth orbit with a SL-6/A-2-e (Molniya 8K78) launcher. The launch payload consisted of an Earth orbiting launch platform (Tyazheliy Sputnik 4) and the Venera probe. The fourth stage (a Blok L Zond rocket) was supposed to launch the Venera probe towards a landing on Venus after one Earth orbit but ignition failed, probably due to a fault in the power supply to the guidance system, the PT-200 DC transformer had not been designed to work in a vacuum. *NASA

1967 U.S. launches Lunar Orbiter 3. It was designed primarily to photograph areas of the lunar surface for confirmation of safe landing sites for the Surveyor and Apollo missions. It was also equipped to collect selenodetic, radiation intensity, and micrometeoroid impact data.

1995 The Connect Four game was mathematically solved first by James D. Allen (Oct 1, 1988), and independently by Victor Allis (Oct 16, 1988). First player can force a win. Strongly solved by John Tromp's 8-ply database (Feb 4, 1995). Weakly solved for all boardsizes where width+height is at most 15 (Feb 18, 2006). *Wik

*Gamehouse cafe

BIRTHS

1896 Friedrich (Hermann) Hund (4 Feb 1896 - 31 Mar 1997) was a German physicist known for his work on the electronic structure of atoms and molecules. He introduced a method of using molecular orbitals to determine the electronic structure of molecules and chemical bond formation. His empirical Hund's Rules (1925) for atomic spectra determine the lowest energy level for two electrons having the same n and l quantum numbers in a many-electron atom. The lowest energy state has the maximum multiplicity consistent with the Pauli exclusion principle. The lowest energy state has the maximum total electron orbital angular momentum quantum number, consistent with rule. They are explained by the quantum theory of atoms by calculations involving the repulsion between two electrons. *TIS

1903 Sir Oliver Graham Sutton CBE FRS (4 February 1903 – 26 May 1977) was a Welsh mathematician and meteorologist, notable particularly for theoretical work on atmospheric diffusion, boundary layer turbulence, and for his direction of the UK Meteorological Office.

From 1926 to 1928 he was a lecturer at University College of Wales in Aberystwyth before joining the UK Meteorological Office as an assistant. He was seconded to Shoeburyness to work on the meteorological effects on gunnery practices and then transferred to Porton Down. There he undertook a project on atmospheric turbulence and diffusion which quantified the effect of meteorological conditions on the distribution of gas at ground level, findings which could not be released until after the war. Whilst working at Porton Down he was put in charge of tests related to Operation Vegetarian, which involved the release of anthrax spores over the uninhabited Gruinard Island as part of a biological warfare project.

When the war ended, he was made Chief Superintendent of the Radar Research and Development Establishment, Malvern, a position he held until 1947, when he was appointed Professor of Mathematics at the Royal Military College of Science, Shrivenham, Wiltshire. He was Director-General of the UK Met Office from 1953 to 1965 and Vice-President of the University College of Wales, Aberystwyth from 1967.

He was elected a Fellow of the Royal Society in March 1949. He was awarded CBE in 1950 for his distinguished scientific services to the government.

He was elected president of the Royal Meteorological Society from 1953 to 1955 and awarded their Symons Gold Medal for 1959. He was knighted in 1955.

In 1958 Sutton was invited to co-deliver the Royal Institution Christmas Lecture. In 1968 he was awarded the prestigious International Meteorological Organization Prize from the World Meteorological Organization *Wik

1906 Clyde William Tombaugh (4 Feb 1906 on Ranch near Streator, Illinois - 17 Jan 1997) was an American astronomer who discovered what was then recognized as the planet Pluto, which he photographed on 23 Jan 1930, the only planet discovered in the twentieth century, after a systematic search instigated by the predictions of other astronomers. Tombaugh was 24 years of age when he made this discovery at Lowell Observatory in Flagstaff, Ariz. He also discovered several clusters of stars and galaxies, studied the apparent distribution of extragalactic nebulae, and made observations of the surfaces of Mars, Venus, Jupiter, Saturn, and the Moon.Born of poor farmers, his first telescope was made of parts from worn-out farming equipment. *TIS

From my personal blog after a visit to Mars Hill, Flagstaff, Az. (much material from Wikipedia)

In the late 19th and early 20th century, observers of Mars drew long straight lines that appeared on the surface between 60 degrees north and south of the martian equator. Italian astronomer Giovanni Schiaparelli called these lines canali, which became canals in English. Lowell extended this observation to a theory that Mars had polar ice caps that would melt in the martian spring and fill the canals. He even extended the theory to include intelligent life on Mars that had designed the canals.
Eventually it became clear that there were no martian canals, but Mars hill went on to be the sight where a self educated Kansas schoolboy found his dream of working in astronomy in 1929, when the observatory director, V M Slipher, "handed the job of locating Planet X to Clyde Tombaugh, a 23-year-old Kansas man who had just arrived at the Lowell Observatory after Slipher had been impressed by a sample of his astronomical drawings."
On the nights of Jan 23 and 30th of January, 1830, he found a planet in the images that he thought was the Planet X. "The discovery made front page news around the world. The Lowell Observatory, who had the right to name the new object, received over 1000 suggestions, from "Atlas" to "Zymal". Tombaugh urged Slipher to suggest a name for the new object quickly before someone else did. Name suggestions poured in from all over the world. Constance Lowell proposed Zeus, then Lowell, and finally her own first name. These suggestions were disregarded.
The name "Pluto" was proposed by Venetia Burney (later Venetia Phair), an eleven-year-old schoolgirl in Oxford, England. Venetia was interested in classical mythology as well as astronomy, and considered the name, one of the alternate names of Hades, the Greek god of the Underworld, appropriate for such a presumably dark and cold world. She suggested it in a conversation with her grandfather Falconer Madan, a former librarian of Oxford University's Bodleian Library. Madan passed the name to Professor Herbert Hall Turner, who then cabled it to colleagues in America. The object was officially named on March 24, 1930."
Among the many awards Tombaugh received was a scholarship to the Univ of Kansas, where he would eventually earn a Bachelors and Masters Degree. It is said that the Astronomy Dept head refused to allow him to take the introductory astronomy class because it would be undignified for the discoverer of a planet.
Tombaugh died on January 17, 1997, when he was in Las Cruces, New Mexico, at the age of 90. A small portion of his ashes were placed aboard the New Horizons spacecraft. The container includes the inscription: "Interned (sic) herein are remains of American Clyde W. Tombaugh, discoverer of Pluto and the solar system's 'third zone'. Adelle and Muron's boy, Patricia's husband, Annette and Alden's father, astronomer, teacher, punster, and friend: Clyde W. Tombaugh

1925 Sir Erik Christopher Zeeman FRS (born 4 February 1925 – 13 February 2016), is a Japanese-born British mathematician known for his work in geometric topology and singularity theory. His main contributions to mathematics were in topology, particularly in knot theory, the piecewise linear category, and dynamical systems.
Zeeman is known among the wider scientific public for his contribution to, and spreading awareness of catastrophe theory, which was due initially to another topologist, René Thom, and for his Christmas lectures about mathematics on television in 1978. He was especially active encouraging the application of mathematics, and catastrophe theory in particular, to biology and behavioral sciences.*Wik

1926 Jaroslav Hájek (4 Feb 1926 in Podebrady, Bohemia (now Czech Republic) - 10 June 1974 in Prague, Czechoslovakia) He was among the pioneers of unequal probability sampling. The name "Hájek predictor" now labels his contributions to the use of auxiliary data in estimating population means. In 1967 Hájek published (jointly with Z Sidak) Theory of rank tests but it was a work which had in fact been written four years before in 1963. Their methods use three lemmas of Le Cam in order to treat rank statistics under local alternatives and they established the efficiency of rank tests. *SAU

1927 Rolf William Landauer (4 Feb 1927; 27 Apr 1999) German-born American physicist known for his formulation of Landauer's principle concerning the energy used during a computer's operation. Whenever the machine is resetting for another computation, bits are flushed from the computer's memory, and in that electronic operation, a certain amount of energy is lost. Thus, when information is erased, there is an inevitable "thermodynamic cost of forgetting," which governs the development of more energy-efficient computers. While engineers dealt with practical limitations of compacting ever more circuitry onto tiny chips, Landauer considered the theoretical limit, that if technology improved indefinitely, how soon will it run into the insuperable barriers set by nature?*TIS

1948 Ken Thompson Is Born. Thompson, who with Dennis Ritchie, developed UNIX at AT&T Bell Laboratories, is born. The UNIX operating system combined many of the timesharing and file management features offered by Multics, from which it took its name. (Multics, a projects of the mid - 1960s, represented the first effort at creating a multi-user, multi-tasking operating system.) The UNIX operating system quickly secured a wide following, particularly among engineers and scientists. *CHM

1948 Irena Lasiecka (February 4, 1948 - ) is a Polish-American mathematician, a Distinguished University Professor of mathematics and chair of the mathematics department at the University of Memphis. She is also co-editor-in-chief of two academic journals, Applied Mathematics & Optimization and Evolution Equations & Control Theory.

Lasiecka earned her Ph.D. in 1975 from the University of Warsaw under the supervision of Andrzej Wierzbicki. In 2014, she became a fellow of the American Mathematical Society "for contributions to control theory of partial differential equations, mentorship, and service to professional societies."

Her specific areas of study are partial differential equations and related control theory, non-Linear PDEs, the optimization theory, calculus of variations, and boundary stabilization.

Irena Lasiecka was born and raised in Poland, where she received her initial background in mathematics. She studied math for many years at the University of Warsaw, where she earned her Master of Science degree in applied mathematics in 1972. A few years later, she received her PhD from the same university in the same field of study.

After receiving her PhD, Lasiecka started to transfer her knowledge of Applied Mathematics to others in addition to more personal studying and research. Her first teaching job was at the Polish Academy of Sciences in 1975, and she later ventured to the United States a few years later, teaching at the University of California, Los Angeles. She has been teaching in the US ever since.

Optimization is the mathematical practice of finding the maximum or minimum values for a specific function. It has many real-world uses, and is a common practice for people of many different professions.

The work of Lasiecka involves the optimization differential systems. These involve an optimization problems over functions, with a constraint that relates a function to its derivatives. She has written extensively about this topic in her collaborative work Optimization Methods in Partial Differential Equations.

DEATHS

1615 Giambattista della Porta (1 November 1535 Vico Equense (near Naples), Italy
- 4 February 1615 Naples, Italy) was an Italian scholar who worked on cryptography and also on optics. He claimed to be the inventor of the telescope although he does not appear to have constructed one before Galileo.
In 1563, della Porta published De Furtivis Literarum Notis, a work about cryptography. In it he described the first known digraphic substitution cipher. Charles J. Mendelsohn commented, "He was, in my opinion, the outstanding cryptographer of the Renaissance. Some unknown who worked in a hidden room behind closed doors may possibly have surpassed him in general grasp of the subject, but among those whose work can be studied he towers like a giant."
Della Porta invented a method which allowed him to write secret messages on the inside of eggs. During the Spanish Inquisition, some of his friends were imprisoned. At the gate of the prison, everything was checked except for eggs. Della Porta wrote messages on the egg shell using a mixture made of plant pigments and alum. The ink penetrated the egg shell which is semi-porous. When the egg shell was dry, he boiled the egg in hot water and the ink on the outside of the egg was washed away. When the recipient in prison peeled off the shell, the message was revealed once again on the egg white.

Della Porta was the founder of a scientific society called the Academia Secretorum Naturae (Accademia dei Segreti). This group was more commonly known as the Otiosi, (Men of Leisure). Founded sometime before 1580, the Otiosi were one of the first scientific societies in Europe and their aim was to study the "secrets of nature." Any person applying for membership had to demonstrate they had made a new discovery in the natural sciences.
His private museum was visited by travelers and was one of the earliest examples of natural history museums. It inspired the Jesuit Athanasius Kircher to begin a similar, even more renowned, collection in Rome.
*SAU *Wik

1774 Charles-Marie de La Condamine (27 Jan 1701, 4 Feb 1774) French naturalist and mathematician who became particularly interested in geodesy (earth measurement). He was put in charge by the King of France of an expedition to Ecuador to measure a meridional arc at the equator (1735-43). It was wished to determine whether the Earth was either flattened or elongated at its poles. He then accomplished the first scientific exploration of the Amazon River (1743) on a raft, studying the region, and brought the drug curare to Europe. He also worked on establishment of a universal unit of length, and is credited with developing the idea of vaccination against smallpox, later perfected by Edward Jenner. However, he was almost constantly ill and died in 1773, deaf and completely paralyzed.*TIS

1895 Thomas Penyngton Kirkman FRS (31 March 1806 – 3 February 1895) was a British mathematician. Despite being primarily a churchman, he maintained an active interest in research-level mathematics, and was listed by Alexander Macfarlane as one of ten leading 19th-century British mathematicians. Kirkman's schoolgirl problem, an existence theorem for Steiner triple systems that founded the field of combinatorial design theory, is named after him.
Kirkman's first mathematical publication was in the Cambridge and Dublin Mathematical Journal in 1846, on a problem involving Steiner triple systems that had been published two years earlier in the Lady's and Gentleman's Diary by Wesley S. B. Woolhouse. Despite Kirkman's and Woolhouse's contributions to the problem, Steiner triple systems were named after Jakob Steiner who wrote a later paper in 1853. Kirkman's second research paper paper, in 1848, concerned hypercomplex numbers.
In 1850, Kirkman observed that his 1846 solution to Woolhouse's problem had an additional property, which he set out as a puzzle in the Lady's and Gentleman's Diary:

Fifteen young ladies in a school walk out three abreast for seven days in succession: it is required to arrange them daily, so that no two shall walk twice abreast.

This problem became known as Kirkman's schoolgirl problem, subsequently to become Kirkman's most famous result. He published several additional works on combinatorial design theory in later years. Kirkman also studied the Pascal lines determined by the intersection points of opposite sides of a hexagon inscribed within a conic section. Any six points on a conic may be joined into a hexagon in 60 different ways, forming 60 different Pascal lines. Extending previous work of Steiner, Kirkman showed that these lines intersect in triples to form 60 points (now known as the Kirkman points), so that each line contains three of the points and each point lies on three of the lines. *Wik

1928 Hendrik Antoon Lorentz (18 Jul 1853 - 4 Feb 1928) Dutch physicist who shared (with Pieter Zeeman) the Nobel Prize for Physics in 1902 for his theory of the influence of magnetism upon electromagnetic radiation phenomena. The theory was confirmed by findings of Zeeman and gave rise to Albert Einstein's special theory of relativity. From the start, Lorentz made it his task to extend James Clerk Maxwell's theory of electricity and of light. Already in his doctor's thesis, he treated the reflection and refraction phenomena of light from this new standpoint. His fundamental work in the fields of optics and electricity revolutionized conceptions of the nature of matter. In 1878, he published an essay relating the velocity of light in a medium, to its density and composition. *TIS

*Wik

1974 Satyendra Nath Bose (1 Jan 1894; 4 Feb 1974) Indian physicist and mathematician who collaborated with Albert Einstein to develop a theory of statistical quantum mechanics, now called Bose-Einstein statistics. In his early work in quantum theory (1924), Bose wrote about the Planck black-body radiation law using a quantum statistics of photons, Plank's Law and the Light Quantum Hypothesis. Bose sent his ideas to Einstein, who extended this technique to integral spin particles. Dirac coined the name boson for particles obeying these statistics. Among other things, Bose-Einstein statistics explain how an electric current can flow in superconductors forever, with no loss. Bose also worked on X-ray diffraction, electrical properties of the ionosphere and thermoluminescence. *TIS

2003 Jean Brossel ( 15 August 1918 in Périgueux , France - 4 February 2003 in France)developed with Alfred Kastler the technique of optical pumping at origin of lasers. *Arjen Dijksman ‏@materion

Brossel is known for his work on optical pumping with Alfred Kastler, with whom he founded in 1951 the spectroscopic laboratory at ENS (Laboratoire de Spectroscopie Hertzienne), which now is called the Laboratoire Kastler-Brossel. Brossel was the co-director and then in 1972 after Kastler's resignation the director.

In his hometown of Périgueux a square is named after him. *Wik

2004 Valentina Mikhailovna Borok (9 July 1931, Kharkiv, Ukraine, USSR–4 February 2004, Haifa, Israel) was a Soviet Ukrainian mathematician. She is mainly known for her work on partial differential equations.

Valentina Borok had a talent for math even in her high school years. So in 1949, with the advice of her high school teachers Borok started to study Mathematics at Kyiv State University. There she met Yakov Zhitomirskii, who would be her husband until her death. During her stay at Kyiv State University, Borok, along with her future husband, started her research in the field of mathematics under the supervision of the mathematics department supervisor, Georgii Shilov. Her undergraduate thesis on distribution theory and the applications to the theory of systems of linear partial differential equations was found to be extraordinary and was published in a top Russian journal. This thesis was later selected in 1957 to be part of the first volumes of American Mathematical Society translations.*Wik

2010 Daniel Jay Rudolph (Oct 3, 1949–Feb 4, 2010) was a mathematician who was considered a leader in ergodic theory and dynamical systems. He studied at Caltech and Stanford and taught postgraduate mathematics at Stanford University, the University of Maryland and Colorado State University, being appointed to the Albert C. Yates Endowed Chair in Mathematics at Colorado State in 2005. He jointly developed a theory of restricted orbit equivalence which unified several other theories. He founded and directed an intense preparation course for graduate math studies and began a Math circle for middle-school children. Early in life he was a modern dancer. He died in 2010 from amyotrophic lateral sclerosis, a degenerative motor neuron disease.

He founded and directed the SPIRAL program at Maryland, an intensive six-week preparation for graduate studies in mathematical sciences. It was acknowledged by the American Mathematical Society with an award for "Mathematics Programs That Make a Difference" in 2008. *Wik

2018 Alan Baker FRS (19 August 1939 – 4 February 2018) was an English mathematician, known for his work on effective methods in number theory, in particular those arising from transcendental number theory.

His interests were in number theory, transcendence, linear forms in logarithms, effective methods, Diophantine geometry and Diophantine analysis.

Baker generalised the Gelfond–Schneider theorem, which itself is a solution to Hilbert's seventh problem.

In 2012 he became a fellow of the American Mathematical Society. He has also been made a foreign fellow of the National Academy of Sciences, India.

2025 William Browder (January 6, 1934 – February 4, 2025) was an American mathematician, who specialized in algebraic topology, differential topology and differential geometry. He served as president of the American Mathematical Society from 1989 to 1991.

William Browder was born in Harlem, New York City on January 6, 1934, the son of Raisa (née Berkmann), a Russian Jewish woman from Saint Petersburg, and American Communist Party leader Earl Browder, from Wichita, Kansas. His father had moved to the Soviet Union in 1927, where he met and married Raisa. Their first two sons, Felix and Andrew, were born in Moscow in 1931. William attended local public schools in Yonkers for early schooling and graduated from the Massachusetts Institute of Technology with a B.S. degree in 1954. He was a instructor at the University of Rochester from 1957 to 1958 and at Cornell University from 1958 until 1963. In August 1957, his original thesis fell apart when his advisor, John Coleman Moore, found an issue with the idea. However, William came up with a new idea which was titled Homology of Loop Spaces. He received his Ph.D. from Princeton University in 1958, using the dissertation.

From 1964 onwards, Browder was a professor at Princeton University; he was chair of the mathematics department at Princeton from 1971 to 1973. He was editor of the journal Annals of Mathematics from 1969 to 1981, and president of the American Mathematical Society from 1989 to 1991.

Browder was elected to the United States National Academy of Sciences in 1980, the American Academy of Arts and Sciences in 1984, and the Finnish Society of Sciences and Letters in 1990. In 1994, a conference was held at Princeton in celebration of his 60th birthday. A conference was held at Princeton on the occasion of his retirement in 2012. Browder advised 30 Ph.D. students in his career as well as multiple undergraduate students. *Wik

An Oft-told story about him at Princeton is:

As a young faculty member at Princeton in the early 1960s, Browder quickly developed a reputation for intellectual intensity and uncompromising standards. One story often told by his former students concerns a graduate seminar where a student proudly presented what seemed to be a new result in homotopy theory.

The student finished the talk to polite applause. After a short pause, Browder quietly said something like:

“Yes, that’s interesting. But it isn’t a theorem yet.”

When the student asked what was missing, Browder pointed to a subtle gap—an implicit assumption about a map being smoothable that looked completely harmless, and that everyone else in the room had missed. Browder then sketched, on the spot, a counterexample showing that the argument failed unless an additional condition was imposed.

What impressed people was not just that he found the gap, but how quickly he located it, and how deeply it cut into the foundations of the argument. The student later said that moment permanently changed how he read papers and wrote proofs. *PB notes