## Sunday 14 July 2024

### On This Day in Math - July 14

 Antoine Caron: Astronomers Studying an Eclipse *TIA

Nature is not embarrassed by difficulties of analysis.

~Augustin Fresnel

The 195th day of the year..195 is the sum of eleven consecutive primes: 3 + 5 + 7 + 11 + 13 + 17 + 19 + 23 + 29 + 31 + 37 Students might wonder which numbers can (and cannot) be expressed as the sum of one or more consecutive Primes.

also, 1*95 = 19*5 Derek Orr tells me there are only four non-trivial 3-digit numbers with this property *@Derektionary

a Heronian triangle is a triangle that has side lengths and area that are all integers. There is an almost-equilateral, scalene triangle with one side of 195. The other sides are 194, and 193. Students can find the area using Heron's formula.

Take the basic 3x3 magic square, multiply by 13, and get
52 117 26
39   65 91
104 13 78
A magic square with a constant of 195.  13*15=195  different multiple gives you constants of 15k for any k.

195 is a palindrome in base 2, 4, 8, and 14.

195 is a palindrome in binary (11000011)  and as you can see, it is a balanced number with exactly the same number of zeros and ones. It is also a palindrome in base 4.  Divided the digits into groups of two and convert their value to decimals, 11=3, 00=0, 00=0, and 11=3 so in base four, it is (3003), and in base 8 (303) by taking three digits at a time (right to left)  11,   000,   011

If you take the basic 3x3 magic square with digits from 1 to 25, and multiply each term by 3, you get a 5x5 magic square with a magic constant for each row and column of 195
51   72   3   24   45
69   15   21   42  48
12   18   39   60  66
30   36   57   63  9
33   54   75   6    27

if you keep 39 in the middle and replace all numbers in their order by incrementing by one, you get another magic square for 195.  (42 will be 40, 36 will be 38, etc.)

Add one to each term and you have a magic square for day 200!

1956 =54980371265625 is the smallest sixth power that begins with 10 distinct digits.

195 is in the sequence of integers 6n+9 for n = 31 and so 195 = 34^2 - 31^2
and because it is in 10n+25 for n=17, 195 = 22^2 - 17^2, and like every odd number, 195 = 98^2 -97^2, , the difference of the squares of two consecutive numbers that add up to 195.

195=5^2 + 7^2 + 11^2  It is only  the third integer that is the sum of the squares of three consecutive primes.*Prime Curios

There are lots more ways to find distinct squares that sum to 195, as it is the smallest number expressed as a sum of distinct squares in 16 different ways. *Wik

"Betrothed Pairs" are similar to amicable numbers, all the non trivial divisors (don't count 1 or n)  sum to the other member, 195 and 140 are such a pair. There is only one other betrothed pair which are year days.

(1²+2²+3²+...+337²)/337=195²

EVENTS

1686 On June 20th Halley Wrote to Newton that Hooke has protested his "discovery" of the inverse square law should be noted in Principia. Newton responded On July 14, 1686, with a peace offering; "And now having sincerely told you the case between Mr Hooke and me, I hope I shall be free for the future from the prejudice of his letters. I have considered how best to compose the present dispute, and I think it may be done by the inclosed scholium to the fourth proposition." This scholium was "The inverse law of gravity holds in all the celestial motions, as was discovered also independently by my countrymen Wren, Hooke and Halley."

In January 1684 Sir Christopher Wren Halley, and Hooke were led to discuss the law of gravity, and although probably they all agreed in the truth of the law of the inverse square, yet this truth was not looked upon as established. It appears that Hooke professed to have a solution of the problem of the path of a body moving round a centre of force attracting as the inverse square of the distance ; but Halley, finding, after a delay of some months, that Hooke "had not been so good as his word" in showing his solution to Wren, started in the month of August 1684 for Cambridge to consult Newton on the August 1684 for Cambridge to consult Newton on the subject. Without mentioning the speculations which had been made, he went straight to the point and asked Newton what would be the curve described by a planet round the sun on the assumption that the sun’s force diminished as the square of the distance. Newton replied promptly, "an ellipse," and on being questioned by Halley as to the reason for his answer he replied, "Why, I have calculated it." He could not, however, put his hand upon his calculation, but he promised to send it to Halley. After the latter left Cambridg, Newton set to work to reproduce the calculation. After making a mistake a producing a different result he corrected his work obtained his former result. *Encyclopedia com

1696  Construction of the Eddystone lighthouse began today by Henry Winstanley.  Winstanley ...investing some of the money he had made from his work and commercial enterprises in five ships. Two of them were wrecked on the Eddystone Rocks near Plymouth, and he demanded to know why nothing was done to protect vessels from this hazard. Told that the reef was too treacherous to mark, he declared that he would build a lighthouse there himself, and the Admiralty agreed to support him with ships and men.
In the 1690s he opened a Mathematical Water Theatre known as "Winstanley's Water-works" in London's Piccadilly. This was a commercial visitor attraction which combined fireworks, perpetual fountains, automata and ingenious mechanisms of all kinds, including "The Wonderful Barrel" of 1696 which served visitors with hot and cold drinks from the same piece of equipment. It was a successful and profitable venture and continued to operate for some years after its creator’s death.(*Today in History)

The Eddystone Lighthouse is a lighthouse that is located on the Eddystone Rocks, 9 statute miles south of Rame Head in Cornwall, England. The rocks are submerged below the surface of the sea and are composed of Precambrian gneiss. The current structure is the fourth to be built on the site. *Wikipedia

1760 the Royal Society agreed to send Nevil Maskelyne to the island of St Helena to observe a transit of Venus which would take place on 6 June 1761. Maskelyne had earlier proposed that the same expedition should try to measure the parallax of the star Sirius.

This Venus transit was important since accurate measurements would allow the distance from the Earth to the Sun to be accurately measured and the scale of the solar system determined. He set sail on the ship Prince Henry on 18 January 1761. During the voyage he experimented with the lunar position method of determining longitude using the lunar tables produced by Tobias Mayer. He arrived in St Helena on 6 April 1761 in plenty of time to find a good site for observing and to set up his instruments. Sadly, the 6 June was cloudy and he was unable to make measurements of the transit. He spent several months on St Helena trying to compute the parallax of Sirius but eventually decided that his instruments were faulty. Disappointed, Maskelyne set sail for England on the ship Warwick in February 1762. Reaching Plymouth on 15 May, he went back to Chipping Barnet, where he was a curate, and worked on publishing a book. He published the lunar distance method for determining longitude in The British Mariner's Guide (1763) where he also included Tobias Mayer's tables.

1776 The beginning of Cook's third and last voyage made with the Resolution and the Discovery, which cleared the channel on 14 July 1776. This voyage, in which Cook was killed, came to an end in 1780.*Wik

1791 A mob in Birmingham, England, rioted during festivities marking the anniversary of the fall of the Bastille on this date in 1789. The mob, which ran wild for three days, destroyed the house, laboratory and library of Joseph Priestley, discoverer of oxygen, because of his anti religious views and espousal of revolutionary causes.*VFR

Within a few years, on 7 Apr 1794, he forever left England and traveled to the United States. Priestley discovered oxygen nearly 20 years earlier, on 1 Aug 1774.*TIS

Image: "The image is meant to depict the Constitutional Society of Birmingham that held a 'French Revolution Dinner' at Birmingham's Hotel to commemorate the second anniversary of the storming of the Bastille on 14th July 1791. The event has been transformed into a satirical cartoon by James Gillray, representing the London viewpoint of the riots and containing a number of false embelishments, one being that Joseph Priestley (standing, second from left) did not attend the dinner at the Hotel, nor did many of the others shown"

 A BIRMINGHAM TOAST, published 23 July 1791 following the dinnerat the Hotel which fired the Birmingham riots beginning 14 July 1791.Published in London.

1831 Evariste Galois again arrested, as a precautionary measure. He received a six months sentence. *VFR

In 1867, Alfred Nobel demonstrated dynamite for the first time at a quarry in Redhill, Surrey. In 1866 Nobel produced what he believed was a safe and manageable form of nitroglycerin called dynamite. He established his own factory to produce it but in 1864 an explosion at the plant killed Nobel's younger brother and four other workers. Deeply shocked by this event, he now worked on a safer explosive and in 1875 came up with gelignite. Other inventions followed including ballistite, a form of smokeless power, artificial gutta-percha and a mild steel for armour-plating.*TIS

 *http://connecticuthistory.org

1868 Alvin J. Fellows of New Haven, Connecticut, received patent #79,965 for the ﬁrst tape measure. It was enclosed in a circular case with a spring lock to hold the tape at any desired point. *VFR (for my son Robin, who seems to collect them as icons of his trade) Earlier, a machine to print ribbon for the supple sewing tape measures had already been patented on 3 Sep 1847, after four years of research by the French fashion designer, Lavigne. Further, however, Sheffield, England claims to be not just the home of stainless steel, but also where the spring tape measure was invented. *TIS  (This was for the spring type tapes common today. Earlier tapes were produced with a brass fold-out clip to rewind them... One my grand-daughter just found for her dad at a boot-sale for 50 pence was an old Chesterman that was marked in links (.01 chains) and rods (1/4 of a chain) on one side. .... "James Chesterman moved to Sheffield from London in 1820. Nine years later he patented the spring tape measure. He also invented the self-winding window blind, produced the first long steel Measuring tape and the first Woven metallic tape. His business adopted the bow as its trademark, and he named his factory the bow works which moved to this site in 1864.  James Chesterman & Co became synonymous with high quality measuring instruments, especially tapes, callipers and squares. In 1963 amalgamation with John Rabone & Sons created Rabone Chesterman, who were subsequently bought by Stanley Tools and transferred to Stanley's Woodside Plant.  Bow Works was refurbished and extended for its new occupants, Norwich Union in 1993."

1887 The ﬁrst textbook about the international language, Esperanto, was published by its inventor, Dr. Ludwig Zamenhof, a Pole. Esperanto means “one who hopes.” The Italian mathemati¬cian, Giuseppi Peano, created an international language of his own, Latina sina ﬂexione (Latin without inﬂections), but it was even less successful than Esperanto. *VFR

1897 The Dorabella Cipher is an enciphered letter written by composer Edward Elgar to Dora Penny, which was included with a "thank you" note from his wife dated July 14, 1897. Penny never deciphered it and its meaning remains unknown.

Elgar also named Variation 10 of his 1899 Variations on an Original Theme (Enigma) Dorabella as a dedication to Dora Penny. *Wik

1943 George Washington Carver was honored by U.S. President Franklin Delano Roosevelt dedicating \$30,000 for a National Monument to his accomplishments. The area of Carver's childhood near Diamond Grove, in southwest Missouri has been preserved as a park, with a bust of the agricultural researcher, instructor, and chemical investigator. This park was the first designated national monument to an African American in the United States. In 1850-65, Diamond was a typical "crossroads village" near a diamond-shaped grove of trees not far from the Carver farm in Newton County. Also called Diamond Grove, it consisted of a general store, a combination blacksmith shop and post office, and a church that served as a schoolhouse during the week.*TIS

1954 At a Conference for California Teachers of Mathematics, a Los Angeles dentist named Leon Bankoff presented a talk proving that the 2000 year old proof of Archimedes that there were a pair of congruent "Archimedean Twin Circles" in the Arbelos was in fact false. He produced a third identical circle, now usually called the "Bankoff triplet circle".
Later (1979) Thomas Schoch discovered a dozen new Archimedean circles; and then in 1998, Peter Y. Woo of Biola University, generalized two of Schoch's circles, to discover an infinite family of Archimedean circles named the Woo circles in 1999 *Wik *Mathematics Magazine For more on the Archimedean Circles, see my blog on  The Shoemaker's Knife Cuts Beautiful Math Across the Centuries

1965 In the Evening of July 14, the Mariner space craft sent back 22 minutes of imaging from a close pass of Mars. These first images came in in strips of 200 numbers, each representing a shade of black to white for one of 200 rows of such pixels to make an image of the surface of the Red Planet. Knowing that at their stage of image creation, it would be many hours before the images were prepared by the computer printers, the telecommunications engineers at JPL began to attach the numbered strips on a bulletin board, and hand color the pixels in red, brown, and yellow pastels. Too impatient to await the computer drawn images, the first press released photos were images of the hand drawn, paint by number image. *NASA

1977 Minor planet (2509) Chukotka 1977 NG. Discovered by N. S. Chernykh at Nauchnyj. Named for a National Area of the R.S.F.S.R., situated in the northeastern part of the U.S.S.R. The discoverer participated in an expedition there to observe the 1972 total solar eclipse. *NSEC

1995  In 1924 Albert Einstein predicted a new state of matter, the Bose-Einstein Condensate on the basis of calculations by Satyendra Nath Bose . 70 years later Eric Cornell and Carl Wieman achieved this extreme state of matter. Their resulting paper was published July 14, 1995. @nobelprize

2004 A patent application by John St. Clair was filed for a training program to teach people to walk through walls:Publication number US20060014125 A1   (Ok, just think about it a minute.  Someone had to say,  "Yeah, we'll give them a patent for that.")

2015 The New Horizons probe, launched on Jan. 19, 2006, with Clyde Tombaugh's ashes on board,  arrived at Pluto on July 14, 2015. *The Las Cruces Sun-New
Also on board was a 1991 US postage stamp which was a motivator for people in the project.

BIRTHS

1610 Ferdinand II (9 July 1578 – 15 February 1637) Fifth grand duke (granduca) of Tuscany, a patron of sciences, whose rule was subservient to Rome. Ferdinand II de' Medici was Grand Duke from 1621. He encouraged scientific studies, and he protected Galileo and the Accademia del Cimento (1657 - 1667). He also devised a sealed thermometer which, unlike Galileo's open one, was not affected by changes in air pressure. It was to him that Galileo dedicated the lens with which he had discovered the satellites of Jupiter and he also made him a gift of the armed lodestone. J. W. Blaeu dedicated to him one of his globes of the fifth type. Ferdinand II was also a patron of Robert Dudley.*TIS

1671 Jacques Eugène d'Allonville, Chevalier de Louville par Fontenelle (July 14, 1671 – September, 1732) French astronomer and mathematician.
He was born in the Château de Louville, and studied mathematics before joining the navy. He achieved the rank of colonel before retiring from military service in 1713, following the peace of Utrecht. He thereafter took up the study of astronomy.
He is noted for determining a method for precisely calculating the occurrence of solar eclipses.
The crater Louville on the Moon is named in his honor. *TIA

1793 George Green baptized in Nottingham, England. The date of his birth is unknown. His most famous work, An Essay on the Application of Mathematical Analysis to the Theory of Electricity and Magnetism was published, by subscription, in March 1828. Most of the ﬁfty-two subscribers were friends and patrons. The work lay unnoticed until William Thomson rediscovered it and showed it to Liouville and Sturm in Paris in 1845. The Theory of Potential it developed led to the modern mathematical theory of electicity. *VFR
George Green was an English mathematician, born near Nottingham, who was first to attempt to formulate a mathematical theory of electricity and magnetism. He was a baker while, remarkably, he became a self-taught mathematician. In March 1828 he published An Essay on the Application of Mathematical Analysis to the Theories of Electricity and Magnetism. He became an undergraduate at Cambridge in October 1833 at the age of 40. Lord Kelvin (William Thomson) subsequently saw, was excited by the Essay. Through Thomson, Maxwell, and others, the general mathematical theory of potential developed by an obscure, self-taught miller's son heralded the beginning of modern mathematical theories of electricity.*TIS

1862 Florence Bascom (July 14, 1862 – June 18, 1945) was an American pioneer for women as a geologist and educator. Bascom became an anomaly in the 19th century when she earned two bachelor's degrees. Earning a Bachelor of Arts in 1882, and a Bachelor of Science in 1884 both at the University of Wisconsin. Shortly after, in 1887, Bascom earned her master's degree in geology at the University of Wisconsin. Bascom was the second woman to earn her PhD in geology in the United States, in 1893. Receiving her PhD from Johns Hopkins University, this made her the first woman to earn a degree at the institution. After earning her doctorate in geology, in 1896 Bascom became the first woman to work for the United States Geological Survey as well as being one of the first women to earn a master's degree in geology. Bascom was known for her innovative findings in this field, and led the next generation of female geologists. Geologists consider Bascom to be the "first woman geologist in America".

By 1924, Bascom became a councillor of the Geological Society of America and in 1930 she was appointed as vice-president of that society making her the only woman to have ever held those offices. Bascom's career consisted of her being an editor of the American Geologist, a member of the National Academy of Sciences, the National Research Council, as well as the Geophysical Union and many other scientific societies.

1905 Laurence Chisholm Young (14 July 1905 – 24 December 2000) was a mathematician known for his contributions to measure theory, the calculus of variations, optimal control theory, and potential theory. He is the son of William Henry Young and Grace Chisholm Young, both prominent mathematicians. His sister was Rosalind Cecilia Hildegard Tanner, mathematician and Historian.

The concept of Young measure is named after him. *Wik

Young (standing right) at the ICM 1932

1918 Jay W(right) Forrester (born July 14, 1918- ) is a U.S. electrical engineer and management expert. In 1944-51 he supervised the building of the Whirlwind computer at the Massachusetts Institute of Technology, for which he invented the random-access magnetic core memory, the information-storage device employed in most digital computers. He also studied the application of computers to management problems, developing methods for computer simulation.*TIS

1933 Samuel Carlos Gitler Hammer (July 14, 1933 – September 9, 2014) was a Mexican mathematician. He was an expert in Yang–Mills theory and is known for the Brown–Gitler spectrum.

Born to a Jewish family in Mexico City, Gitler studied civil engineering at the National Autonomous University of Mexico, graduating in 1956. He then did his graduate studies in mathematics at Princeton University with Norman Steenrod, earning a doctorate in 1960. He taught briefly at Brandeis University and then returned to Mexico, where he was one of the founders of the mathematics department of CINVESTAV.

Gitler was president of the Mexican Mathematical Society from 1967 to 1969, and chair at CINVESTAV from 1973 to 1981. In the late 1980s he moved to the University of Rochester, where he chaired the mathematics department. After retiring from Rochester in 2000, he returned to CINVESTAV.

Gitler won Mexico's National Prize for Science in 1976. In 1986 he became a member of the Colegio Nacional. In 2012 he became a fellow of the American Mathematical Society.

1955 Gregory Francis Lawler (born July 14, 1955) is an American mathematician working in probability theory and best known for his work since 2000 on the Schramm–Loewner evolution.

He received his PhD from Princeton University in 1979 under the supervision of Edward Nelson. He was on the faculty of Duke University from 1979 to 2001, of Cornell University from 2001 to 2006, and since 2006 is at the University of Chicago.

He received the 2006 SIAM George Pólya Prize with Oded Schramm and Wendelin Werner.

In 2019 he received the Wolf Prize in Mathematics.

Lawler is a member of the National Academy of Sciences (since 2013) and the American Academy of Arts and Sciences (since 2005). Since 2012, he has been a fellow of the American Mathematical Society.  He gave an invited lecture at the International Congress of Mathematicians in Beijing (2002) and a plenary lecture at the ICM in Rio de Janeiro (2018).

DEATHS

1800 Lorenzo Mascheroni (May 13, 1750 – July 14, 1800) was a geometer who proved in 1797 that all Euclidean constructions can be made with compasses alone, so a straight edge in not needed. In fact this had been (unknown to Mascheroni) proved in 1672 by a little known Danish mathematician Georg Mohr. *SAU In his Adnotationes ad calculum integrale Euleri (1790) he published a calculation of what is now known as the Euler–Mascheroni constant, usually denoted as γ (gamma).*Wik

1808  John Wilkinson, an English ironmaster and machine-tool maker, died July 14, 1808, at the age of 80. Wilkinson helped kick-start the industrial revolution in England when he established the Bersham Ironworks in 1762. Bersham is near Wrexham, which is on the English-Welsh border, about 30 miles northwest of Shrewsbury, Charles Darwin's home town. Wilkinson soon became one of the major iron providers in England, establishing production facilities in various industrial cities, including Birmingham. Wilkinson was one of the three men responsible for erecting in 1779 the first cast-iron bridge in the world, called appropriately Iron Bridge, spanning the River Severn just southeast of Shrewsbury . A single building remains from the original Bresham works, but it does still stand, if barely. Wilkinson was crazy about iron, and before his death, he had a cast iron memorial obelisk fashioned, which still survives in Cumbria. He also had an iron casket made, but it has disappeared, along with Wilkinson's mortal remains.

Wilkinson was also one of the pioneers of the machine-tool industry, that is, the making by machine of tools for making other things. When James Watt invented the steam engine, he was unable to obtain steam-cylinders that were precisely bored and in which a piston would move snugly but freely. His eventual partner, Matthew Boulton, steered Watt to Wilkinson, who invented on request a massive boring engine that was then used to produce cylinders for all of the Watt-Boulton steam engines of the 1770s and beyond.

Wilkinson's brother-in-law was Joseph Priestly, notable chemist, religious dissenter, and political activist. Wilkinson, who grew very rich, provided Priestley with considerable funding, and also set Priestley's sons up in business, although they never amounted to much. He also provided Priestley with moral support after a mob, displeased with Priestley's sympathies with the French Revolution, attacked and burned his house in Birmingham (on this *Linda Hall Org very day, July 14, 1791). Almost a hundred letters from Priestley to Wilkinson survive. Priestley's eldest son, ungratefully, destroyed all of Wilkinson's letters to Priestley after Priestley died. *Linda Hall Org

 *Linda Hall Org

1827 Augustin Jean Fresnel (10 May 1788, Broglie (Eure)- 14 July 1827 (aged 39)
Ville-d'Avray (Hauts-de-Seine)) French physicist who first investigated the effect of interference of light, with results known as Fresnel fringes. This decisively work, together with further experiments with polarized light supported Thomas Young's wave theory of light Fresnel advanced the wave theory by identifying light as transverse waves rather than the longitudinal waves previously assumed by Young and Huygens. His pioneering work in optics included showing that white light is composed of a spectrum of innumerable wavelengths ranging from red to shorter violet wavelengths. In 1819, he improved the optical system of lighthouses by replacing metal reflectors with revolutionary stepped lenses of his design.*TIS

1865 Benjamin Gompertz (March 5, 1779 – July 14, 1865), was a self educated mathematician, denied admission to university because he was Jewish. Nevertheless he was made Fellow of the Royal Society in 1819. Gompertz is today mostly known for his Gompertz law (of mortality), a demographic model published in 1825. The model can be written in this way:

N(t) = N(0) e^{-c (e^{at}-1)},

where N(t) represents the number of individuals at time t, and c and a are constants.

This model is a refinement of the demographic model of Malthus. It was used by insurance companies to calculate the cost of life insurance. The equation, known as a Gompertz curve, is now used in many areas to model a time series where growth is slowest at the start and end of a period. The model has been extended to the Gompertz–Makeham law of mortality.

1899 Sir Arthur Thomas Cotton (15 May 1803 – 24 July 1899) British engineer whose life-work was constructing irrigation, navigation canals and dams for water storage in Southern India, saving thousands from famine and promoting local economy. He joined the Madras engineers in 1819, fought in the first Burmese war (1824-26) and began his ambitious irrigation project (1826-62). He built dams on several rivers, transforming the drought-stricken Tanjore district into the richest part of the state of Madras. His ambitious masterplan was not completed in his lifetime, but his ideas anticipated projects that were subsequently taken up. In the present time, India's goal of a National Water Grid confronts the problem of increasingly scarce water. Cotton founded the Indian school of hydraulic engineering.*TIS

1953 Richard von Mises (19 April 1883, Lviv – 14 July 1953, Boston, Massachusetts) Austrian-American mathematician and aerodynamicist who notably advanced statistics and the theory of probability. Von Mises' contributions range widely, also including fluid mechanics, aerodynamics, and aeronautics. His early work centred on aerodynamics. He investigated turbulence, making fundamental advances in boundary-layer-flow theory and airfoil design. Much of his work involved numerical methods and this led him to develop new techniques in numerical analysis. He introduced a stress tensor which was used in the study of the strength of materials. Von Mises' primary work in statistics concerned the theory of measure and applied mathematics. His most famous, yet controversial, work was in probability theory. *TIS He is often credited with the creation of the "Birthday Problem", but in this blog I suggest otherwise.

1956 John Miller studied at Glasgow and Göttingen. He returned to Glasgow to the Royal College of Science and Technology (the precursor to Strathclyde University). He became President of the EMS in 1913. *SAU

1960 Maurice de Broglie (27 April 1875–14 July 1960)(6th duke) (Louis-César-Victor-) Maurice de Broglie was a French physicist who made many contributions to the study of X rays. While in the navy (1895-1908), he first distinguished himself by installing the first French shipboard wireless. From 1912, his chief interest was X-ray spectroscopy. His "method of the rotating crystal" was an application of Bragg's "focussing effect" to eliminate spurious spectral lines. De Broglie discovered the third L absorption edge (1916), which led to the exploration of "corpuscular spectra." During 1921-22, he worked with his brother Louis to refine Bohr's specification of the substructure of the various atomic shells. He also did pioneer work in nuclear physics and cosmic radiation. *TIS

2016 Maryam Mirzakhani (12 May 1977 – 14 July 2017) was an Iranian mathematician and a professor of mathematics at Stanford University. Her research topics included Teichmüller theory, hyperbolic geometry, ergodic theory, and symplectic geometry. In 2005, as a result of her research, she was honored in Popular Science's fourth annual "Brilliant 10" in which she was acknowledged as one of the top 10 young minds who have pushed their fields in innovative directions.

Both Maryam Mirzakhani and her friend Roya Beheshti made the Iranian Mathematical Olympiad team in 1994. The international competition was held that year in Hong Kong and Mirzakhani scored 41 out of 42 and was awarded a gold medal. Beheshti was awarded a silver medal. Again in 1995 Mirzakhani was a member of the Iranian Mathematical Olympiad team. This time the international competition was held in Toronto, Canada, and Mirzakhani scored 42 out of 42 and was again awarded a gold medal.

On 13 August 2014, Mirzakhani was honored with the Fields Medal, the most prestigious award in mathematics, becoming the first Iranian to be honored with the award and the first of only two women to date. The award committee cited her work in "the dynamics and geometry of Riemann surfaces and their moduli spaces".

On 14 July 2017, Mirzakhani died of breast cancer at the age of 40

*Wik, *MacTutor

 Maryam, (+ epsilon) with the other Field's Medalist

2019 Hoàng Tụy (7 December 1927 – 14 July 2019) was an prominent Vietnamese applied mathematician. He was considered one of two founders of the mathematical institutions of Vietnam; the other was Lê Văn Thiêm.

Hoàng Tụy's early career coincided with the French war (1946–1954), which interrupted his studies. In December 1946, after two months as a mathematics student at Hanoi University of Science VNU, he had to return to the south, because the French had invaded and seized Hanoi, and the University had closed. Hoàng Tụy taught secondary school in Quảng Ngãi province in the Fifth Liberated Zone from 1947 to 1951, during which time he wrote a geometry textbook that was published by the Việt Minh press—perhaps the first time a guerrilla movement published a math book.

After returning to Vietnam from the Soviet Union, Hoàng Tụy changed his area of research from real analysis, which was too theoretical to be of immediate use in Vietnam, to operations research, a field of applied mathematics. It was Hoàng Tụy who first brought that field of research to Vietnam, and who invented the Vietnamese translation vận trù of "operations research."

In December 2007, an international conference on Nonconvex Programming was held in Rouen, France, to pay tribute to him on the occasion of his 80th birthday, in recognition of his pioneering achievements that advanced the field of global optimization.

In September 2011, Professor Hoàng Tụy was named as the first-ever recipient of the Constantin Carathéodory Prize of the International Society of Global Optimization for his pioneering work and fundamental contributions to global optimization.

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