On This Day in Math - June 7

  

Go down deep enough into anything 

and you will find mathematics.

~Dean Schlicter

I often quoted a similar idea to my students;
"In any endeavor, at the top of the heap, the bottom line, is math."

The 158th day of the year; 158 is the smallest number such that sum of the number plus its reverse is a non-palindromic prime: 158 + 851 = 1009 and 1009 is a non-palindromic prime. *Number Gossip (What's the next one?)

Middle school # 158 in Bayside, Queens, New York, is called Marie Curie Middle School.

158 is a number in the Perrin sequence, but lovingly called the "skiponacci" sequence after its resemblance to the Fibonacci sequence. Defined by a(n) = a(n-2) + a(n-3) with a(0) = 3, a(1) = 0, a(2) = 2. The pattern starts 3, 0, 2, 3, 2, 5, 5, 7, 10, 12, 17,...     This sequence was mentioned implicitly by Édouard Lucas (1876). In 1899, the same sequence was mentioned explicitly by François Olivier Raoul Perrin

More recently..Inspired by the physical distancing imposed by the covid epidemic , Vincent Vatter asked himself the question of the number of ways to place guests around a table with n chairs so that two guests have at least one free chair between them and that no more guests can be added without violating this condition (therefore no more than two free chairs between two guests). For example, for 𝑛=6, there are five solutions, three with two guests separated by two chairs and two with three guests separated by one chair.

He showed that the number of solutions for n ⩾ 2  is equal to the Perrin number  𝑃𝑛

158 is the sum of the first nine Mersenne prime exponents. *Wik

158 in base 7 is the first three digits of Pi, 314

The decimal expansion of 100! (the product of the first 100 natural numbers) has 158 digits.

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EVENTS

1634  In a letter which he wrote at Dover in England to Mersenne on 7 June 1634, Bernard Frenicle de Bessy describes an experiment to study the trajectory of a body released from the top of the mast of a moving ship. The data which he presents in the letter is quite accurate. Again on a more applied mathematical topic, Frenicle wrote an article which makes comments on Galileo's Dialogue. *SAU

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1713 Johan Bernoulli (I) writes to Leibniz from Basil to stir the pot in the great calculus dispute. "...my nephew (Nikolaus) brought from Paris a single copy of the Commercium Epistolicum... sent from London for distribution to the learned.... you are at once accused by a tribunal consisting,..., of the participants and witnesses themselves.. documents against you are produced, sentence is passed; you lose the case, you are condemned." *The Correspondence of Isaac Newton (Thony Christie points out that this was about "At the same time as Newton was making him a member of the Royal Society <= Embarrassing!" )

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1742, the German mathematician Christian Goldbach originally of Brandenburg-Prussia wrote a letter to Leonhard Euler (letter XLIII) in which he proposed the following conjecture:
“Every integer which can be written as the sum of two primes, can also be written as the sum of as many primes as one wishes, until all terms are units.”
He then proposed a second conjecture in the margin of his letter:
“Every integer greater than 2 can be written as the sum of three primes.”
He considered 1 to be a prime number, a convention subsequently abandoned. Today the conjecture is usually stated as "Every even integer greater than 2 can be expressed as the sum of two primes." The two conjectures are now known to be equivalent, but this did not seem to be an issue at the time. A modern version of Goldbach's marginal conjecture is:
Every integer greater than 5 can be written as the sum of three primes.
*Wik

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1753  the British Museum was founded, the world's oldest public national museum, when King George II gave his royal assent to an Act of Parliament to accept the collection of Sir Hans Sloane, a London-based physician, following his death. In his will, he had offered the British nation the collection he built over his lifetime: 71,000 objects, mostly plant and animal specimens. In return, he asked a sum of £20,000 for his heirs (which today would be more than £2,000,000). The museum opened to the public 15 Jan 1759 at Bloomsbury. Its current buildings there date from the mid-19th century. The natural history collection moved to its own museum in 1881. The British Museum set up a laboratory in 1920 for scientific study of objects. *TIS A description of how to attain entry and museum protocol from Nicholson's Journal@ Wm_Nicholson

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1759 Benjamin Franklin writes to William Heberden, 7 June 1759 On the electical effects of heated Tourmaline crystals. Tourmaline crystals, brought to Europe from the East by the Dutch early in the eighteenth century, began to attract the attention of electrical scientists when they found that, if heated, they had the power of attracting and repelling ashes and other light substances. Franklin’s letter is the earliest known report on such investigations in England. Since it was not published for ten years, however, or read to the Royal Society, his friends John Canton and Benjamin Wilson, accounts of whose experiments became public later in 1759, gained general priority among English investigators of the subject. *Franklin Papers, Natl.Archives  (Tourmaline was sometimes called the "Ceylonese Magnet" because it could attract and then repel hot ashes due to its pyroelectric properties.)

Tourmalines were used by chemists in the 19th century to polarize light by shining rays onto a cut and polished surface of the gem

*Wik

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1886 Just two-and-a-half years after Winifred Edgerton entered Columbia, she completed her thesis. At the Board of Trustees meeting that day the following motion was made and passed unanimously: “That in consideration of the extraordinary excellence of the scientific work done by Miss Winifred Edgerton, as attested by the Professors who have had the superintendence of her course in practical Astronomy, and the Pure Mathematics in the Graduate Department, the degree of Doctor of Philosophy can be conferred upon Miss Edgerton cum laude”
Winifred Edgerton thus became the first American woman to receive her Ph.D. in mathematics and the first woman to graduate from Columbia University.*Susan E. Kelly and Sarah A. Rozner *AMS Notices,Volume 59, Number 4

Winifred Edgerton Merrill made a vast impact on the male orientated world of mathematics. She left behind the Victorian ideal that a wellborn woman should stay at home, and went about continuing her education in mathematics to Ph.D. level. This was a fantastic achievement and Merrill became the first American woman to obtain a Ph.D. in mathematics. Her determination to obtain graduate education is an example that many have followed since.  *SAU

*SAU

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1906 The New York Times reported on an early implementation of what might be considered speed bumps in the U.S. town of Chatham, New Jersey, which planned to raise its crosswalks five inches above the road level: "This scheme of stopping automobile speeding has been discussed by different municipalities, but Chatham is the first place to put it in practice". The average automobile's top speed at the time was around 30 miles per hour (48 km/h) The more conventional speed bumps you are familiar with today seem to have been invented by Arthur Holly Compton, a physicist and winner of the Nobel Prize in physics in 1927. He created his "traffic control bumps," in 1953 after noticing the speed at which motorists passed Brookings Hall at Washington University in St. Louis, Missouri, where he was chancellor. *Wik with HT to arclight ‏@arclight

English Road Sign

(My favorite UK road sign said "Cat's Eyes Removed Ahead".  I was confused about the true meaning for months)

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1914   the Alliance was the first vessel to pass through the Panama Canal.*TIS  (I can't find conformation of this quote, but two I did find.)

The Alexandre La Valley, an old French crane boat, reached the Pacific Ocean and became the first self-propelled vessel to cross the Panama Canal. The crane moved through the waterway during the final stages of construction, which would end later that year.  

The S.S. Cristobal became the first passenger vessel to cross the entirety of the Panama Canal on August 3.  

S. S. Cristobal *Grand Circle Cruise Line

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1958 France issued a stamp with a portrait of Denis Diderot (1713–1784). [Scott #B 323].

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2007 You hear all those "Einstein said",  quotes and you wonder which ones are true, knowing most of them are not.  And the one about, "Life is like riding a bicycle...", well it is mostly true, but they 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.  

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BIRTHS

1761 John Rennie (7 June 1761 – 4 October 1821) Scottish engineer and architect who designed London Bridge. After working as a millwright with Andrew Meikle he studied at Edinburgh University (1780-83). He was employed by Boulton & Watt for five years In 1791, he moved to London and started his own engineering company. Over the next few years he became famous as a bridge-builder, including Leeds Bridge, Southwark Bridge and Waterloo Bridge. He was also designed and built docks at Hull, Liverpool, Greenock and Leith and improving the harbours and dockyards at Portsmouth, Chatham and Plymouth. His last project was London Bridge, though he died in 1821 before it was finished. The bridge was completed by his son, Sir John Rennie.*TIS  This bridge was 1831–1967

*Cornell Library

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1862 Philipp Eduard Anton von Lenard (7 June 1862 – 20 May 1947), was a German physicist and the winner of the Nobel Prize for Physics in 1905 for his research on cathode rays and the discovery of many of their properties. He was a nationalist and anti-Semite; as an active proponent of the Nazi ideology, he had supported Adolf Hitler in the 1920s and was an important role model for the "Deutsche Physik" movement during the Nazi period.
Lenard is remembered today as a strong German nationalist who despised "English physics", which he considered to have stolen its ideas from Germany. He joined the National Socialist Party before it became politically necessary or popular to do so. During the Nazi regime, he was the outspoken proponent of the idea that Germany should rely on "Deutsche Physik" and ignore what he considered the fallacious and deliberately misleading ideas of "Jewish physics", by which he meant chiefly the theories of Albert Einstein, including "the Jewish fraud" of relativity. An advisor to Adolf Hitler, Lenard became Chief of Aryan physics under the Nazis. *Wik

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1863  Edward Burr Van Vleck   (June 7, 1863, Middletown, Connecticut – June 3, 1943, Madison, Wisconsin) The son of astronomer John Monroe Van Vleck, he graduated from Wesleyan University in 1884, attended Johns Hopkins in 1885-87, and studied at Göttingen (Ph.D., 1893). He was assistant professor and professor at Wesleyan (1895-1906), and after 1906 a professor at the University of Wisconsin–Madison, where the mathematics building is named after him. In 1913 he became president of the American Mathematical Society, of whose Transactions he had been first associate editor (1902-05) and then editor (1905-10). He was the author of Theory of Divergent Series and Algebraic Continued Fractions (1903), and of several monographs in mathematical journals. His son, John Hasbrouck van Vleck, was a notable physicist who received the Nobel Prize in 1977.
Edward van Vleck was also an important art collector, particularly in the medium of Japanese woodblock prints (principally Ukiyo-e), known as Van Vleck Collection. He began collecting around 1909, but became a serious collector in the late 1920s, when he acquired approximately 4,000 prints that had been owned by Frank Lloyd Wright. His collection, one of the largest in the world outside the Library of Congress, features more than 2,000 prints by Utagawa Hiroshige as well as many prints by Hokusai, and fine examples of shin hanga made well into the 20th century. His collection now resides at the Chazen Museum of Art in Madison, Wisconsin.*Wik

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1868 Sir John Sealy Edward Townsend (7 Jun 1868, 16 Feb 1957 at age 88) British physicist who pioneered in the study of electrical conduction in gases. In 1898 he made the first direct measurement of the unit electrical charge (e). As a postgraduate, he was a research student of J. J. Thomson. In 1897, Townsend developed the falling-drop method for measuring e, using saturated clouds of charged water droplets (extended by Robert Millikan's highly accurate oil-drop method). He was first to explain how electric discharges pass through gases (Electricity in Gases, 1915) whereby motion of electrons in an electric field releases more electrons by collision. These in turn collide releasing even more electrons in a multiplication of charges known as an avalanche. *TIS

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1877 Charles Barkla (7 June 1877 to 23 October 1944) was an influential English physicist who became professor of Natural Philosophy in Edinburgh. He was awarded the Nobel Prize for Physics in 1917 for his work on X-ray spectroscopy.

In 1899 Barkla was admitted to Trinity College, Cambridge, with an 1851 Research Fellowship from the Royal Commission for the Exhibition of 1851,[5] to work in the Cavendish Laboratory under the physicist J. J. Thomson (discoverer of the electron). During his first two years at Cambridge, under the directions of Thomson, Barkla studied the velocity of electromagnetic waves along wires of different widths and materials.

After a year and a half at Trinity College, Cambridge, his love of music led him to transfer to King's College, Cambridge, in order to sing in their chapel choir. Barkla's voice was of remarkable beauty and his solo performances were always fully attended.[6] He completed his Bachelor of Arts degree in 1903, and then his Master of Arts degree in 1907.[7] He married Mary Esther Cowell in the same year,[8] with whom he had two sons and one daughter.

In 1913, after having worked at the Universities of Cambridge, Liverpool, and King's College London, Barkla was appointed as a Professor of Natural Philosophy at the University of Edinburgh in 1913, a position that he held until his death.

Barkla made significant progress in developing and refining the laws of X-ray scattering, X-ray spectroscopy, the principles governing the transmission of X-rays through matter, and especially the principles of the excitation of secondary X-rays. For his discovery of the characteristic X-rays of elements, Barkla was awarded the Nobel Prize in Physics in 1917. He was also awarded the Hughes Medal of the British Royal Society that same year.

Barkla proposed the J-phenomenon as a hypothetical form of X-ray behaviour similar to X-ray fluorescence but other scientists were not persuaded that this was a different mechanism from other known effects such as Compton scattering and so the theory was not successful.

From 1922 to 1938 he lived at Hermitage of Braid in south-west Edinburgh.

He died in Edinburgh on 23 October 1944.

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1890 Werner Schmeidler (7 June 1890 - 1 April 1969. He worked in analysis and applied mathematics.*SAU  He studied mathematics in Göttingen.  From 1939 he was Professor at the Technical University of Berlin , where he held the Chair of Pure and Applied Mathematics until the summer semester 1958. *Wik

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1896 Robert Sunderson Mulliken (June 7, 1896 – October 31, 1986),  primarily responsible for the early development of molecular orbital theory, i.e. the elaboration of the molecular orbital method of computing the structure of molecules. Dr. Mulliken received the Nobel Prize for chemistry in 1966. He received the Priestley Medal in 1983. *Wik

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1924 Donald Watts Davies, CBE FRS (7 June 1924 – 28 May 2000) was a Welsh computer scientist who was employed at the UK National Physical Laboratory (NPL).

In 1965 he conceived of packet switching, which is today the dominant basis for data communications in computer networks worldwide. Davies proposed a commercial national data network in the United Kingdom and designed and built the local-area NPL network to demonstrate the technology. Many of the wide-area packet-switched networks built in the 1970s were similar "in nearly all respects" to his original 1965 design. The ARPANET project credited Davies for his influence, which was key to the development of the Internet.

Davies' work was independent of the work of Paul Baran in the United States who had a similar idea in the early 1960s, and who also provided input to the ARPANET project, after his work was highlighted by Davies' team.

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1926 John Cedric Shepherdson, FBA (7 June 1926 – 8 January 2015) was a British logician who was Henry Overton Wills Professor of Mathematics at the University of Bristol from 1976 to 1991.

Shepherdson was born in Huddersfield on 7 June 1926, the son of Arnold Shepherdson, a chemist, and his wife Elsie, née Aspinall. He attended Manchester Grammar School on a scholarship; excelling in mathematics, in 1943 he secured a state scholarship and an open scholarship to Trinity College, Cambridge, where he read mathematics. He graduated with a first-class degree in 1946.

Shepherdson was appointed to an assistant lectureship at the University of Bristol in 1946. He spent the rest of his career at the university, being promoted to lecturer in 1949, reader in 1955 and professor in 1964, before he was finally Henry Overton Wills Professor of Mathematics from 1977 until he retired in 1991. He was elected a fellow of the British Academy in 1990.

Shepherdson was a keen climber and skier. His wife, Margaret, née Smith, a biochemist and academic whom he had married in 1955, died in 2014. Shepherdson died on 8 January 2015.

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1928  Bernard Flood Burke (June 7, 1928 – August 5, 2018) was an American astronomer. He co-discovered radio emission from Jupiter, and was part of the team that discovered the first Einstein ring in 1988.

Burke studied for an undergraduate physics degree at Massachusetts Institute of Technology (MIT), graduating in 1950, before going on to study for a PhD in physics, graduating again from MIT in 1953.

From 1953 until 1965, he was employed to carry out radio astronomy research by Carnegie Institution of Washington, where he also headed the Radio Astronomy Section from 1962 until 1965. Burke became a faculty member of the Physics department at MIT and later was the William A. M. Burden Professor of Astrophysics, Emeritus. He was a principal investigator of the Kavli Institute for Astrophysics and Space Research at MIT.

He served on the National Science Foundation Astronomy Advisory Panel between 1958 and 1963, and the National Radio Astronomy Observatory Visiting Committee in 1958–1962. He was a Trustee for Associated Universities, Inc. between 1972 and 1990. He was also a member of Planetary Systems Working Group and the Towards Other Planetary Systems Scientific Working Group, and he was on advisory councils and committees for the National Research Council, the National Academy of Sciences, the National Science Board, the Keck Telescope, the Naval Studies Board and the Space Science Board.

He was Councilor and later President of the American Astronomical Society in 1971–74 and 1986–88. He was a member of the National Science Foundation Astronomy Advisory Panel in 1958–63 *Wik

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DEATHS

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1624  Giuseppe Biancani  (8 March, 1566-7 June,1624)was an Italian Jesuit astronomer and mathematician who made observations of the moon and planets with the newly invented telescope.

Giuseppe Biancani's name also appears in its Latin version of Josephus Blancanus; in fact his books were published under this Latin version of his name. He entered the novitiate of the Society of Jesus (the Jesuit Order) on 4 October 1592. He studied mathematics, taught by the famous Christopher Clavius at the Jesuit Collegio Romano in Rome. Between 1596 and 1599, he was studying at the Jesuit College in Padua. Galileo had been appointed professor of mathematics at the University of Padua, the university of the Republic of Venice, in 1592 and Biancani became acquainted with him during his years in Padua. This friendship was an important one for Biancani, who later found himself in a difficult position pulled between the views of his Jesuit order and the revolutionary new ideas being argued by Galileo. In a letter he wrote on 14 June 1611, he referred to his friendship with Galileo:-

"I love and admire Galileo, not only for his rare learning and invention, but also for the old friendship that I had with him in Padua, where I was overcome by his courtesy and affection, which bound me to him."

It is also worth recounting the tensions in Padua during the years that Biancani studied there. The Jesuit College, established in Padua in 1542, had become an important educational establishment by 1590 offering a three-year philosophy degree; logic was taught in year one, natural philosophy and physical science in year two, and metaphysics and natural philosophy in year three. However, the university students objected to the Jesuit College and the Venetian Senate became involved in the argument in December 1591. The Jesuit College was accused of being a rival university to the University of Padua, something which was illegal by Venetian law. As a result of the dispute, it was forbidden from teaching students other than Jesuits. Much of the argument, which continued during the years that Biancani studied there, was centred around the teachings of Aristotle; the Jesuit teachers were accused of not teaching directly from Aristotle but rather using modern texts. Clearly this influenced Biancani who, a few years later in 1615, published a text Aristotelis loca mathematica ex universis ipsius operibus collecta et explicata  in which he treated the mathematical parts of Aristotle's writings. *SAU

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1787  Joseph Ritter von Fraunhofer (6 March 1787 – 7 June 1826) was a German physicist and optical lens manufacturer. He made optical glass, an achromatic telescope, and objective lenses. He also invented the spectroscope and developed diffraction grating. In 1814, he discovered and studied the dark absorption lines in the spectrum of the sun now known as Fraunhofer lines. *Wik

The Great Dorpat Refractor built by Joseph Fraunhofer and completed in 1824 was the first modern, achromatic, refracting telescope. At the start of the 19th century, progress in astronomy was stifled by the lack of astronomical quality telescopes of sufficient aperture and manageability. There were long-focus, nonachromatic refractors, reflectors with speculum metal mirrors, and achromatic refractors of small aperture and mediocre design. Contributing to the construction and success of the Great Dorpat Refractor were P. L. Guinand's development of a process for making large disks of homogenous flint glass, Fraunhofer's improvement of the design and fabrication of the optical and mechanical components of the telescope, and F. G. W. Struve's skilled and dedicated use of the telescope and its accessories. The successors of the Great Dorpat Refractor were the giant refractors which were the mainstay of astronomy in the 19th century and which were not displaced until the early 20th century when the age of the giant reflectors began.*Astrophysics Data System

Illustration of solar spectrum drawn and colored by Joseph von Fraunhofer with dark lines named after him (1987 DBP's stamp on 200th anniversary of birthday of Fraunhofer):

Fraunhofer demonstrating the spectroscope:

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1843 Alexis Bouvard (27 June 1767 – 7 June 1843) French astronomer and director of the Paris Observatory, who is noted for discovering eight comets and writing Tables astronomiques of Jupiter and Saturn (1808) and of Uranus (1821). Bouvard's tables accurately predicted orbital locations of Jupiter and Saturn, but his tables for Uranus failed, leading him to hypothesize that irregularities were caused by an unknown perturbing body. This spurred observations leading to the discovery of Neptune by Adams and Leverrier.*TIS

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1907 Edward John Routh FRS (20 January 1831–7 June 1907), was an English mathematician, noted as the outstanding coach of students preparing for the Mathematical Tripos examination of the University of Cambridge in its heyday in the middle of the nineteenth century. He also did much to systematize the mathematical theory of mechanics and created several ideas critical to the development of modern control systems theory.*Wik

Routh's theorem, is first given by him in his Treatise on Analytical Statics with Numerous Examples, 1891.   Routh's theorem determines the ratio of areas between a given triangle and a triangle formed by the pairwise intersections of three cevians. The problem and solution had appeared  with a proof in Solutions of the Cambridge Senate-house Problems and Riders for the Year 1878, i.e., the mathematical tripos of that year,

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1954 Alan Turing (23 June 1912 – 7 June 1954), died by committing suicide because he was persecuted by the British Government for his homosexuality. *VFR Alan Mathison Turing, OBE, FRS (play /ˈtjʊərɪŋ/ tewr-ing; 23 June 1912 – 7 June 1954), was an English mathematician, logician, cryptanalyst and computer scientist. He was highly influential in the development of computer science, providing a formalization of the concepts of "algorithm" and "computation" with the Turing machine, which played a significant role in the creation of the modern computer. Turing is widely considered to be the father of computer science and artificial intelligence.
Turing's homosexuality resulted in a criminal prosecution in 1952, when homosexual acts were still illegal in the United Kingdom. On 10 September 2009, following an Internet campaign, British Prime Minister Gordon Brown made an official public apology on behalf of the British government for the way in which Turing was treated after the war.
My favorite Turing story is this: When he was found, he had a half eaten apple by his bed, which may have been the delivery mechanism for the poison. Some suggest he chose this method because it was a re-enactment of a scene from the 1937 film Snow White, his favorite fairy tale. Years later, to honor Turing, the developers of Apple Computers used the symbol of an apple with a bite out for their logo. The last part, about the Apple logo, seems not to be true, but it is a great story, and a good excuse to tell students about the work of Turing.. so I do.*Wik

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2004  Joseph Doob (February 27, 1910–June 7, 2004) was an American mathematician who worked in probability and measure theory. *SAU  After writing a series of papers on the foundations of probability and stochastic processes including martingales, Markov processes, and stationary processes, Doob realized that there was a real need for a book showing what is known about the various types of stochastic processes. So he wrote his famous "Stochastic Processes" book. It was published in 1953 and soon became one of the most influential books in the development of modern probability theory. *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

A Unique approach for Odd Order Magic Squares

  



Lo Shu Magic Square







I have been interested in Math History and Recreation Math for a really long time,  (yes, I'm that old), so when I came across a new approach on twitter that I had never seen, I was a little surprised.  When I read that it was about 400 years old, I was even more surprised (and no, I'm not THAT old).

I've written about Magic Squares over the years, from the earliest known 3x3 supposedly found on the back of a turtle in Chinese Mythology, called the Lo Shu Square ( literally: Luo (River) Book/Scroll)  and about the magic square on the Passion Facade on the Sagrada Familia Cathedral in Barcelona and then about  a magic square relationship to Matrices I just learned this year (2018) from John D. Cook's blog.

I usually not surprised in finding out new relationships in magic squares, but part of what surprised me this time, was that it was a method created by Claude Gaspard Bachet de Méziriac, Who I've read a lot about, and written a little about, and was aware that he worked with recreational math and number theory. He published a Latin translation of the Greek text of Diophantus’s Arithmetica in 1621. This is the translation that Fermat made his famous margin note that became the famous Fermat's Last Theorem. He asked the first ferrying problem: Three jealous husbands and their wives wish to cross a river in a boat that will only hold two persons, in such a manner as to never leave a woman in the company of a man unless her husband is present.

So, anyway, if I'm not the only person in the world who never saw it before, here is a really unique method of constructing nXn magic Squares when n is odd. which I found on a animated tweet created in Geogebra by Jason-Automaths@palajsn, and thanks to Vincent Pantaloni for sharing.

You start by constructing a Diamond stack of squares with 1 square in the first row, three squares in the second, etc. until you get to 2n-1 squares for the desired nXn desired, then descending back down to one. Here is the example for the 7x7 square.





Then you start at the 1'st diagonal down the right side and write the numbers in order, 1 to 7. Skip to the third diagonal and do the next 7 digits. Continue in like fashion and you get something like this.






Now here is the slickest little move imaginable, you take the pyramid of six numbers above the the top row of seven squares, and move it down until the number one is just below the center square (25 in this case)...






Make a similar translation of the pyramids on the other three sides across to the similar position on the other side of the center square, and you have a magic square.









The first known magic square was the Lo Shu, shown above. If you learned the quick method I did for odd squares, you start at the bottom center with one (apparently the Chinese put North on their calendars at the bottom, and that was an influence on the future evolution of magic squares). Then you just number up and right (or down and right) on the diagonal (as if the edges were connected right and left, top and bottom like a torus). Each time you come to a multiple of n, you drop down one and continue. Notice this works the same way, except that the diagonals go down and right, and at ever multiple of n, you drop down two rows, instead of one.

Addendum:::  Grand Valley Mathematics Department professor Dr. John Golden teaches math classes for future teachers. He has been sending thought provoking posts and comments  for about 15 years.  This time he connected me to a spreadsheet he made to try out variations on your own.  You can find it here.

This Day in Math - June 6

  

Map of 2012 Transit of Venus visibility *Eclipse Maps

No mathematician can be

a complete mathematician unless

he is also something of a poet.

~Karl Weierstrass

The 157th day of the year; 2¹⁵⁷ is the smallest "apocalyptic number," i.e., a number of the form 2ⁿ that contains '666'. *Prime Curios (Can you find an apocalyptic number of the form 3ⁿ)

157 is prime and it's reverse, 751 is also prime. 157 is also the middle value in a sexy triplet (three primes successively differing by six; 151, 157, 163). 751 is also a sexy prime with 757.

157 is also the largest solution I know for a prime, p, such that \( \frac{p^p-p!}{p} \) is prime.

The number 157 in base ten is equal to \(31_{[52]}\), but don't worry if you get that backwards,
\(52_{[31]}\) is also equal to 157 in decimal. Can you find other examples of reversible numeral/base that give the same decimal value?

157 is a prime which is the arithmetic average of the squares of four consecutive primes, (7^2 + 11^2 + 13^2 + 17^2)/4 = 157.  There are only two such year days that meet this definition. and this is the smaller.  

And from Fermat's Library @fermatslibrary In 1993 Don Zagier found the smallest rational right triangle with area 157. He used sophisticated techniques using elliptic curves paired with a lot of computational power. If he could do that, certainly you ought to be able to find the smallest rational right triangle with area of 1.... (OK trick question, ask your teacher to explain)

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EVENTS

1647  Fermat writes to Digby to repeat challenges he had set in January.  1) Find a cube that when added to the sum of its aliquot parts is a square.   2)  Find a square that when increased by the sum of its aliquot parts is a cube.  He added that \(7^3\) is not the only solution.  Can you solve either, or both?

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In 1799, the first definitive prototype meter bars (mètre des Archives) and kilograms were constructed in platinum. This followed the legal definition of the metric system by the French National Assembly on 7 Apr 1795, that was itself established during the famous measurements of the Earth's meridian between Dunkerque and Barcelona. The use of a metal bar to define the standard meter continued until replaced in 1960 by a definition based upon a number of wavelengths of light from a certain spectroscopic light source.*TIS

A copy of the "provisional" meter installed 1796–1797, located in the wall of a building, 36 rue de Vaugirard, Paris. These meters were based on the "provisional" meter, because the expedition to re-determine the meter was not completed until 1798.

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1902 Scottish chemist professor James Dewar exhibits air in the solid state and a jet of liquid air rising six feet above it with beautiful effects, before the Prince and Princess of Wales. *Great Geek Manual

James Dewar lecturing at the Royal Institution, painting by Henry J. Brooks, 1904 (Royal Institution)

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1942, the first parachute jump in the U.S. using a nylon parachute was made by Adeline Gray. Cotton had been superseded by silk cloth as a higher-strength, lower-weight parachute fabric. Oriental high-volume sources of the silkworm product were cut off during WWII. Fortunately, nylon, a newly invented synthetic substitute produced by the DuPont Co was available, as exhibited at the 1939 World's Fair. Nylon parachutes had been tested with dead weights, but the military needed a live trial to confirm personnel use. Gray, a parachute rigger at the Pioneer Parachute Company volunteered. She jumped from an aircraft flying from Brainard Field, Hartford, Conn. convincing an audience of 50 critical army and navy observers.

Gray rigging a parachute

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1944, Supreme Allied Commander General Dwight D. Eisenhower gives the go-ahead for largest amphibious military operation in history: Operation Overlord, code named D-Day, the Allied invasion of northern France.

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1984 Sweden issued a series of stamps celebrating the centenary of their Patent System. One shows a tetrahedral container patented in 1948. [Scott #1501]. *VFR 

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1984 Tetris is a Soviet tile-matching puzzle video game originally designed and programmed by Alexey Pajitnov. It was released on June 6, 1984. A nice post with ten things you did't know about about Tetris is at this blog from Wallifaction, a very good history blog by Adam Richter

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2012 Last Chance. The most recent transit of Venus when observed from Earth took place on June 8, 2004. The event received significant attention, since it was the first Venus transit to take place after the invention of broadcast media. No human alive at the time had witnessed a previous Venus transit, since the previous Venus transit took place on December 6, 1882. The next transit of Venus will occur on June 5–June 6 in 2012. After 2012, the next transits of Venus will be in December 2117 and December 2125.

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BIRTHS

1436 Johann Mueller (6 June 1436 – 6 July 1476) , AKA Johannes Regiomontanus after the Latinization of his hometown, Konigsburg. He is the founder of trigonometry as an independent science. The spherical law of sines was first presented by Johann Muller, in his De Triangulis Omnimodis in 1464. This was the first book devoted wholly to trigonometry (a word not then invented). David E. Smith suggests that the theorem was Muller's creation.
The ideas behind the law of sines, like those of the law of cosines, predate the word sine by over a thousand years. Theorems in Euclid on lengths of chords are essentially the same ideas we now call the law of sines. What we now call the law of sines for plane triangles was known to Ptolemy. By the tenth century Abu'l Wefa had clearly expounded the spherical law of sines. It seems that the term "law of sines" was applied sometime near 1850, but I am unsure of the origin of the phrase.

"In Jan 1472 he made observations of a comet which were accurate enough to allow it to be identified with Halley's comet 210 years later (being three returns of the 70 year period comet). He also observed several eclipses of the Moon. His interest in the motion of the Moon led him to make the important observation that the method of lunar distances could be used to determine longitude at sea. However, instruments of the time lacked the necessary accuracy to use the method at sea. " *TIS {There is a nice blog at The Renaissance Mathematicus about the important role Regiomontanus played in scientific publishing.}

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1553 Bernardino Baldi (6 June 1553 – 10 October 1617) was an Italian mathematician and writer.
Baldi descended from a noble family from Urbino, Marche, where he was born. He pursued his studies at Padua, and is said to have spoken about sixteen languages during his lifetime, though according to Tiraboschi the inscription on his tomb limits the number to twelve.
The appearance of the plague at Padua forced him to return to his native city. Shortly afterwards he was called to act as tutor to Ferrante Gonzaga, from whom he received the rich abbey of Guastalla. The oldest biography of Nicolaus Copernicus was completed on 7 October 1588 by him. He held office as abbot for 25 years, and then returned once again to Urbino. In 1612 he was employed by the duke as his envoy to Venice. Baldi died at Urbino on 12 October 1617.
He is said to have written upwards of a hundred different works, the chief part of which have remained unpublished. His various works show his abilities as a theologian, mathematician, geographer, antiquary, historian and poet. One of these has been recently found and is now at the Univ. of Oklahoma.
"Baldi is known to have written a treatise on sun dials and timekeeping. However, this treatise was never published and, since 1783, it has been considered lost. Now we are happy to announce that it has been recently acquired by the History of Science Collections, digitized in high resolution, and made available for study in the Collections’ Online Galleries." The Cronica dei Matematici (published at Urbino in 1707) is an abridgment of a larger work on which he had written for twelve years, and was intended to contain the lives of more than two hundred mathematicians. His life has been written of by Affò, Mazzucchelli and others. *Wik

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1580 Govaert Wendelen (6 June 1580 – 24 October 1667) was a Flemish astronomer who was born in Herk-de-Stad. He is also known by the Latin name Vendelinus. His name is sometimes given as Godefroy Wendelin; his first name spelt Godefroid or Gottfried.
Around 1630 he measured the distance between the Earth and the Sun using the method of Aristarchus of Samos. The value he calculated was 60% of the true value (243 times the distance to the Moon; the true value is about 384 times; Aristarchus calculated about 20 times).
In 1643 he recognized that Kepler's third law applied to the satellites of Jupiter.
Wendelin corresponded with Mersenne, Gassendi and Constantijn Huygens.
The crater Vendelinus on the Moon is named after him.
Wendelin died in Ghent on 24 October 1667. *Wik

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1842 Henry Martyn Taylor (6 June 1842, Bristol – 16 October 1927, Cambridge) born in Bristol, England. He was a fellow at Trinity College, Cambridge, and is most remembered because he devised a Braille notation when he was overtaken by blindness in 1894, when engaged in the preparation of an edition of Euclid for the Cambridge University Press. By means of his ingenious and well thought out Braille notation he was enabled to transcribe many advanced scientific and mathematical works, and in 1917, with the assistance of Mr. Emblen, a blind member of the staff of the National Institute for the Blind, he perfected it. It was recognised as so comprehensive that it was soon adopted as the standard mathematical and chemical notation. It seems that in the US it is more common to use the Nemeth code for mathematics and science symbols, first developed around 1947. I am not sure about usage at the present time in the rest of the world.

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1850 Karl Ferdinand Braun (6 June 1850 – 20 April 1918) was a German inventor, physicist and Nobel laureate in physics. Braun contributed significantly to the development of the radio and television technology: he shared with Guglielmo Marconi the 1909 Nobel Prize in Physics.
Braun was born in Fulda, Germany, and educated at the University of Marburg and received a Ph.D. from the University of Berlin in 1872. In 1874 he discovered that a point-contact semiconductor rectifies alternating current. He became director of the Physical Institute and professor of physics at the University of Strassburg in 1895.
In 1897 he built the first cathode-ray tube (CRT) and cathode ray tube oscilloscope. CRT technology has been replaced by flat screen technologies (such as liquid crystal display (LCD), light emitting diode (LED) and plasma displays) on television sets and computer monitors. The CRT is still called the "Braun tube" in German-speaking countries (Braunsche Röhre) and in Japan (ブラウン管: Buraun-kan). *Wik

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1857 Aleksandr Mikhailovich Lyapunov (June 6 [O.S. May 25] 1857 – November 3, 1918) born in Yaroslavl, Russia. He was the creator of the modern theory of stability of differential equations especially as applied to mechanical systems. He also proved the Central Limit Theorem under weaker hypotheses than his predecessors. *VFR He was a student of Chebyshev. In 1901, Lyapunov gave the first prominent proof of the Central Limit Theorem, which made the CLT one of the foundations of probability theory today. (Unlike the classical CLT, Lyapunov’s condition only requires the random variables in question to be independent instead of both independent and identically distributed.)

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1882 Clement Vavasor Durell (6 June 1882 in Fulbourn, near Cambridge, England, -10 December 1968 in South Africa) Durell was educated at Felsted School and, while still at school, he published his first note in the Mathematical Gazette, the journal of the Mathematical Association. The note was A geometrical method of trisecting any angle with the aid of a rectangular hyperbola written jointly with W F Beard.
Durell joined the Mathematical Association in 1900, the year in which he entered Clare College, Cambridge, to study mathematics. He was a First Class student in the Mathematical Tripos examinations, graduating in 1904. He was appointed as a mathematics teacher at Gresham's School immediately after graduating, and in the following year of 1905 he moved to take up the post of mathematics master at Winchester College.
Soon after taking up this post Durell's first textbook Elementary Problem Papers (1906) was published. He was promoted to senior mathematics master at Winchester College in 1910 and began publishing a series of articles in the Mathematical Gazette. Before the outbreak of World War I, Durell published The arithmetic syllabus in secondary schools (1911) and Analysis and projective geometry (1911) in the Mathematical Gazette. During World War I, Durell served in the Royal Garrison Artillery as a lieutenant. After the end of the war he returned to Winchester College and began publishing a series of articles in the Mathematical Gazette and a remarkable series of textbooks which would make him the best known writer of English school mathematics texts.

As well as writing articles for the Mathematical Gazette such as The use of limits in elementary geometry (1925) and The teaching of loci in the elementary geometry course to school certificate stage (1936), he was also actively involved with the committee work of the Mathematical Association and its report production. He wrote reports The teaching of geometry in schools (1925), Memo from the Girls' Schools' Committee: Mathematics for girls (1926), and Questionnaire on the teaching of mathematics in evening continuation schools (1926). Among the books he wrote around this time were: Readable relativity (1926), A Concise Geometry (1928), Matriculation Algebra (1929), Arithmetic (1929), Advanced Trigonometry (1930), A shorter geometry (1931), The Teaching of Elementary Algebra (1931), Elementary Calculus (1934), A School Mechanics (1935), and General Arithmetic (1936). In a catalogue produced by the Mathematical Association's publishers G Bell & Sons in 1934, they listed 20 textbooks by Durell and write

There can indeed be few secondary schools in the English-speaking world in which some at least of Mr Durell's books are not now employed in the teaching of mathematics.

*SAU

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1906 Max Zorn (June 6, 1906 in Krefeld, Germany – March 9, 1993 in Bloomington, Indiana, United States) To his chagrin, he is most famous for discovering something yellow and equivalent to the Axiom of Choice. *VFR (with a smile, I'm sure) He was an algebraist, group theorist, and numerical analyst. He is best known for Zorn's lemma, a powerful tool in set theory that is applicable to a wide range of mathematical constructs such as vector spaces, ordered sets, etc. Zorn's lemma was first discovered by K. Kuratowski (see June 18) in 1922, and then independently by Zorn in 1935.*Wik  Interesting that he was born on 6/6/6. 

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1929 Oliver Penrose FRS FRSE (6 June 1929, ) is a British theoretical physicist and emeritus professor at Heriot-Watt University. His topics of interest include statistical mechanics, phase transitions in metals and the physical chemistry of surfactants. He is known for introducing the concept of off-diagonal long-range order, important to the present understanding of superfluids and superconductors. He is also known for the Penrose criterion in plasma physics.

He was associated with the Open University for seventeen years and was a Professor of Mathematics at Heriot-Watt University in Edinburgh from 1986 until his retirement in 1994.

Penrose has worked in fundamental topics, which include understanding the physical basis for the direction of time and interpretations of quantum mechanics.

He is the son of the scientist Lionel Penrose and brother of the mathematical physicist and Nobel laureate in Physics Roger Penrose, chess Grandmaster Jonathan Penrose, and geneticist Shirley Hodgson. *Wik

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1933  Heinrich Rohrer (6 June 1933 – 16 May 2013) was a Swiss physicist who shared half of the 1986 Nobel Prize in Physics with Gerd Binnig for the design of the scanning tunneling microscope (STM). The other half of the Prize was awarded to Ernst Ruska. Ruska's electron microscope of the 1930s was unable to show surface structure at the atomic level. Rohrer and Binnig began work in 1978 on a scanning tunneling microscope in which a fine probe passes within a few angstroms of the surface of the sample. A positive voltage on the probe enables electrons to move from the sample to the probe by the tunnel effect, and the detected current can used to keep the probe at a constant distance from the surface. As the probe moves in parallel lines, a 3D image of the surface can be constructed.

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1943 Richard Errett Smalley (June 6, 1943 – October 28, 2005) was an American chemist who was the Gene and Norman Hackerman Professor of Chemistry, Physics, and Astronomy at Rice University. In 1996, along with Robert Curl, also a professor of chemistry at Rice, and Harold Kroto, a professor at the University of Sussex, he was awarded the Nobel Prize in Chemistry for the discovery of a new form of carbon, buckminsterfullerene, also known as buckyballs. He was an advocate of nanotechnology and its applications.

DEATHS

1834 Erastus Lyman De Forest (27 June 1834 in Watertown, Connecticut, USA - 6 June 1888 in Watertown, Connecticut, USA) His parents were Lucy Starr Lyman and Dr John De Forest. He was named after his mother's father, Erastus Lyman, who was from Litchfield, Connecticut. Both sides of the family were well off and Erastus was born into a privileged place in society. John De Forest graduated from Yale College and wished his son to follow in his footsteps as indeed he did, entering Yale at the age of sixteen to study mathematics. He was awarded his B.A. in 1854 and his father celebrated the occasion by endowing the De Forest Mathematical Prize at Yale. Erastus's maternal grandfather celebrated the occasion by making him a large bequest.

De Forest remained at Yale to study engineering and at this time was a fellow student with J Willard Gibbs who entered Yale in the year that De Forest was awarded his B.A. In 1856 De Forest was awarded a Ph.B. by Yale and then in February of the following year he set off with his aunt for New York to begin a journey with her to Havana. However, before the ship was due to depart De Forest vanished leaving his luggage. When his family could find no trace of him they put an advertisement in the New York Times asking for information. They received a reply which told them his body was in East River but a search revealed nothing.

For two years De Forest's family continued to make desperate efforts to locate him but receiving not a shred of information they came to believe that he must have been murdered. It was more than two years after he vanished that John De Forest received a letter from his son, posted in Australia. De Forest, depressed with his privileged life, had travelled to California where he had got a job at a mine. After a while he was appointed as a teacher in a private school where he taught for about a year before going to Australia where again he taught, this time at Melbourne Church of England Grammar School in South Yarra. After more than four years away, he returned to the United States in 1861 visiting India and England on his way. He returned to Europe in 1863 for a lengthy trip which lasted until 1865.

From his return to Connecticut in 1865 he devoted himself to the study of mathematics. After publishing papers interpolation and its applications, he was asked by his uncle, who was President of the Knickerbocker Life Insurance Company of New York, to examine the liabilities that the company's life policies involved. De Forest became deeply involved in improving mortality tables, publishing over 20 papers on the topic between 1870 and 1885.

The remarkable contributions of De Forest to statistics had little or no influence on the subject since those who later developed similar ideas were totally unaware of his contributions. This was for a number of reasons. De Forest was not associated with any institution so lacked the visibility that such a position would have meant. He worked in the United States at a time when little of mathematical significance was happening in that country. Also he published his work in somewhat obscure American journals. His contributions were recognized, however, by Pearson whose attention was drawn to De Forest's papers. Pearson acknowledged De Forest's priority in deriving the chi square distribution. The book contains reprints of four of De Forest's papers as well as a biographical article written by J Anderson. His life and work are both discussed by Stigler . Stigler uses information on De Forest available to him from a well researched but unpublished work on De Forest by H H Wolfenden.

De Forest never married and cared for his father for many years until his death in 1885, from which time his own health began to deteriorate. Shortly before he died he founded the Erastus L De Forest Professorship of Mathematics at Yale. *SAU

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1898 Henry Perigal, Jr. FRAS MRI (1 April 1801 – 6 June 1898) was a British stockbroker and amateur mathematician, known for his dissection-based proof of the Pythagorean theorem and for his unorthodox belief that the moon does not rotate.
In his booklet Geometric Dissections and Transpositions (London: Bell & Sons, 1891) Perigal provided a proof of the Pythagorean theorem based on the idea of dissecting two smaller squares into a larger square. The five-piece dissection that he found may be generated by overlaying a regular square tiling whose prototile is the larger square with a Pythagorean tiling generated by the
two smaller squares. Perigal had the same dissection printed on his business cards, and it also appears on his tombstone.

As well as being interested in mathematics, Perigal was an accomplished lathe worker, and made models of mathematical curves for Augustus De Morgan. He believed (falsely) that the moon does not rotate with respect to the fixed stars, and used his knowledge of curvilinear motion in an attempt to demonstrate this belief to others. *Wik

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1928 Luigi Bianchi (January 18, 1856 – June 6, 1928) He did fundamental work on Lie groups. *VFR He was a leading member of the vigorous geometric school which flourished in Italy during the later years of the 19th century and the early years of the twentieth century.
In 1898, Bianchi worked out the Bianchi classification of nine possible isometry classes of three-dimensional Lie groups of isometries of a (sufficiently symmetric) Riemannian manifold. As Bianchi knew, this is essentially the same thing as classifying, up to isomorphism, the three-dimensional real Lie algebras. This complements the earlier work of Lie himself, who had earlier classified the complex Lie algebras.
Through the influence of Luther P. Eisenhart and Abraham Haskel Taub, Bianchi's classification later came to play an important role in the development of the theory of general relativity. Bianchi's list of nine isometry classes, which can be regarded as Lie algebras, Lie groups, or as three dimensional homogeneous (possibly nonisotropic) Riemannian manifolds, are now often called collectively the Bianchi groups.
In 1902, Bianchi rediscovered what are now called the Bianchi identities for the Riemann tensor, which play an even more important role in general relativity. (They are essential for understanding the Einstein field equation.) According to Tullio Levi-Civita, these identities had first been discovered by Ricci in about 1880, but Ricci apparently forgot all about the matter, which led to Bianchi's rediscovery! *Wik

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1943 Guido Fubini (19 January 1879 – 6 June 1943) He is best known for a theorem on the exchange of order of integration. his research focused primarily on topics in mathematical analysis, especially differential equations, functional analysis, and complex analysis; but he also studied the calculus of variations, group theory, non-Euclidean geometry, and projective geometry, among other topics. With the outbreak of World War I, he shifted his work towards more applied topics, studying the accuracy of artillery fire; after the war, he continued in an applied direction, applying results from this work to problems in electrical circuits and acoustics. *Wik

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1946 Jean-Louis Loday (12 January 1946 in Le Pouliguen, Pays de la Loire, France
- 6 June 2012 in Les Sables-d'Olonne, France) was a French mathematician who worked on cyclic homology and who introduced Leibniz algebras (sometimes called Loday algebras) and Zinbiel algebras. He occasionally used the pseudonym Guillaume William Zinbiel, formed by reversing the last name of Gottfried Wilhelm Leibniz.
Loday died in a tragic boating accident, falling from his boat off Les Sables-d'Olonne. *Wik *SAU

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1948 Louis Jean Lumière (5 October 1864 Besançon – 6 June 1948, Bandol) was a French engineer and industrialist who played a key role in the development of photography and cinema.

Louis invented the 25-lb “Cinématographe” twin-function projector and camera, which improved on Thomas Edison's Kinetoscope by adding a intermittent film motion mechanism (based on the sewing machine). On 13 Feb 1895, they jointly patented the device (as was their custom). It was first demonstrated to an invited audience on 22 Mar 1895, showing their first film to an invited audience who viewed La Sortie des ouvriers de l'usine Lumière showing workers leaving the Lumière factory. The hugely successful first public screening on 28 Dec 1895 of their films in Paris was the “birth” of the cinema.*TiS

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1972 Abraham Adrian Albert (9 November 1905 Chicago, Illinois, USA - 6 June 1972 Chicago, Illinois, USA) A Adrian Albert's parents were Russian. His father, Elias Albert, came to the United States from England and had set up a retail business. His mother, Fannie Fradkin, had come to the United States from Russia. Adrian was the second of Elias and Fannie's three children, but he also had both a half-brother and half-sister from his mother's side.

Albert completed his B.S. degree in 1926 and was awarded his Master's degree in the following year. He remained at the University of Chicago undertaking research under L E Dickson's supervision.
By the time that he received his doctorate Albert was a married man, having married Freda Davis on 18 December 1927.
In his doctoral thesis Albert had made considerable progress in classifying division algebras. It was an impressive piece of work and it led to him being awarded a National Research Council Fellowship to enable him to undertake postdoctoral study at Princeton. He spent nine months at Princeton in 1928-29 and this was an important period for Albert since during his time there Lefschetz suggested that he look at open problems in the theory of Riemann matrices. These matrices arise in the theory of complex manifolds and Albert went on to write an important series of papers on these questions over the following years.

Albert was then offered a post as an instructor at Columbia University and he worked there for two years from 1929 to 1931. His first paper A determination of all normal division algebras in sixteen units was published in 1929. It was based on the second half of his doctoral thesis but Albert had, by this time, pushed the ideas further classifying division algebras of dimension 16 over their centres. The case of dimension 9, the next smaller case, had been solved by Wedderburn.

Albert returned to the University of Chicago in 1931 where he was appointed as assistant professor. He remained on the staff there for the rest of his life being promoted to associate professor in 1937 and full professor in 1941. During the years 1958 to 1962 he was chairman of the Chicago Department.

Shortly after beginning his second three year term as Chairman of the Department Albert was asked to take on the post of Dean of Physical Sciences. He served Chicago for 9 year in the role until 1971.
His main work was on associative algebras, non-associative algebras, and Riemann matrices. He worked on classifying division algebras building on the work of Wedderburn but Brauer, Hasse and Emmy Noether got the main result first. Albert's major contribution is, however, detailed in a joint paper with Hasse. Albert's book Structure of Algebras, published in 1939, remains a classic. The content of this treatise was the basis of the Colloquium Lectures which he gave to the American Mathematical Society in 1939.
Albert's work on Riemann matrices was, as we mentioned above, a consequence of suggestions made by Lefschetz.
During the Second World War Albert contributed to the war effort as associate director of the Applied Mathematics Group at Northwestern University which tackled military problems. Another interest of Albert's, which appears to have been prompted by the War, was that of cryptography. He lectured to the American Mathematical Society on Some mathematical aspects of cryptography at the Society's meeting in November 1941.
Albert investigated just about every aspect of non-associative algebras.
Albert received many honours for his outstanding achievements. He was elected to the National Academy of Sciences in 1943, the Brazilian Academy of Sciences in 1952, and the Argentine Academy of Sciences in 1963. He served as chairman of the Mathematics Section of the National Research Council from 1958 to 1961, and President of the American Mathematical Society in 1965-66. *SAU

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1977 Stefan Bergman (5 May 1895 in Częstochowa, Russian Empire (now Poland)- 6 June 1977 in Palo Alto, California, USA) Stefan Bergman (5 May 1895 – 6 June 1977) was a Polish-born American mathematician whose primary work was in complex analysis. He is best known for the kernel function he discovered while at Berlin University in 1922. This function is known today as the Bergman kernel. Bergman taught for many years at Stanford University, and served as an advisor to several students.
Bergman received his Ph.D. at Berlin University in 1921 for a dissertation on Fourier analysis. His adviser, Richard von Mises, had a strong influence on him, lasting for the rest of his career. In 1933, Bergman was forced to leave his post at the Berlin University because he was a Jew. He fled first to Russia, where he stayed until 1939, and then to Paris. In 1939, he emigrated to the United States, where he would remain for the rest of life. He was elected a Fellow of the American Academy of Arts and Sciences in 1951. In 1962 he was an invited speaker at the International Congress of Mathematicians in Stockholm (On meromorphic functions of several complex variables). He died in Palo Alto, California, aged 82.
The Stefan Bergman Prize in mathematics was initiated by Bergman's wife in her will, in memory of her husband's work. The American Mathematical Society supports the prize and selects the committee of judges. The prize is awarded for, "the theory of the kernel function and its applications in real and complex analysis; or function-theoretic methods in the theory of partial differential equations of elliptic type with a special attention to Bergman's and related operator methods." *Wik

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1985 András P Huhn (Szeged, 26 January 1947 – Szeged, 6 June 1985) was a Hungarian mathematician. Huhn's theorem on the representation of distributive semilattices is named after him. 

Huhn was on the editorial board of Algebra Universalis and of Acta Scientiarum Mathematicum Szeged. He also edited two proceeding of lattice theory conferences in Szeged of which he was an organiser. The first was the Colloquium Lattice theory held in Szeged from 27 August to 30 August 1974. The second of the two editors of these proceedings was Tamás Schmidt.

At the height of his creative powers at the age of 38, Huhn was killed in a tragic accident. *Wik

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2012 Jean-Louis Loday (12 January 1946 – 6 June 2012) was a French mathematician who worked on cyclic homology and who introduced Leibniz algebras (sometimes called Loday algebras) and Zinbiel algebras. He occasionally used the pseudonym Guillaume William Zinbiel, formed by reversing the last name of Gottfried Wilhelm Leibniz.

Loday studied at Lycée Louis-le-Grand and at École Normale Supérieure in Paris. He completed his Ph.D. at the University of Strasbourg in 1975 under the supervision of Max Karoubi, with a dissertation titled K-Théorie algébrique et représentations de groupes. He went on to become a senior scientist at CNRS and a member of the Institute for Advanced Mathematical Research (IRMA) at the University of Strasbourg.

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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