Pig Latin Magic Square

 My friend David Brooks sent me this breaking Math News from Old Hickory, Tn on a newly discovered (June 8, 2014) Alpha-Magic Square :

consider  the following magic square:

Now this is the Pig-Latin (or if you prefer, Igpay Atinlay, notation of these same numbers:

Now count the number of letters in each word and replace them with the counts:

 

And in the words of Brahma Gupta..... BEHOLD!

My thanks to David Brooks the input... and I wondered, "Do students today still speak Pig-Latin?"

I recently learned that the idea of alphamagic squares is very young.  They were first invented by English Engineer and recreational mathematician Lee Sallows in 1986 Sallows, L. C. F. "Alphamagic squares." Abacus 4 (No. 1): 28-45, 1986.) Sallows is also known for inventing golygons, a polygon containing only right angles, such that adjacent sides exhibit consecutive integer lengths. He also recently discovered a very clever relationship about the triangles formed by the medians of another triangle, for which I was able to add a small extension.

It turns out that there is a surprisingly large number of alphamagic squares, not only in English but also in many other languages. In French, there is just one alphamagic square involving numbers up to 200, but an additional 255 squares if the size of the entries is increased to 300. For entries less than 100, none occurs in Danish or in Latin, but 6 occur in Dutch, 13 in Finnish, and an incredible 221 in German.
(From David Darling.info)
I have not seen a alphamagic square larger than 3x3, but they seem to be possible.....Anyone, Anyone, ......Bueller?

I live in France part time now and was interested in the single :

John D. Cook independently searched all candidates by computer and reported:

"My script did not find a French alphamagic with entries no larger than 200, but it did find 254 squares with entries no larger than 300."  (Close enough for me John!)

Here is the original with French spellings of the numbers, I leave it to the reader to confirm the magic square with the word lengths....

    3      204    102

202      103        4

104         2     203  

and the French spelling (I am told) is 

trois	deux cent quatre	cent deux

deux cent deux       cent trois                       quatre

cent quatra                 duex                       deux cent trois

If anybody knows a bi-magic square larger than a three by three I would love to see it.  

On This Day in Math - July 19

 

[The infinitesimals] neither have nor can have theory; in practise it is a dangerous instrument in the hands of beginners ... anticipating, for my part, the judgement of posterity, I would predict that this method will be accused one day, and rightly, of having retarded the progress of the mathematical sciences.
~Francois Servois


The 200th day of the year; 200 is the smallest unprimeable number - it can not be turned into a prime number by changing just one of its digits to any other digit. (What would be the next one? {easier}What is the smallest odd unprimeable number? {harder})

Sum of first 200 primes divides product of first 200 primes. (How often is this property true of integers?) *Math Year-Round ‏@MathYearRound

The smallest discernible movement of a computer mouse—equal to 1/200th of an inch—is called a MICKEY. Haggard Hawks @HaggardHawks The actual measure depends on the equipment of course, so, like the meter, it will have to be adjusted from time to time.  Many operating systems and mouse configuration software allow users to customize mickey settings, altering the sensitivity to match their specific needs and preferences. This is particularly useful for tasks that demand precise control, such as graphic design or gaming.

And don't forget, When you pass GO, collect $200 (except the lucky Brits, who get 200 Lb.

200  is not a palindrome in any base 2-10, but it is in Roman numerals  CC.  
Which reminds us that 200 is the sum of two squares, 10^2 + 10^2, but also 14^2 + 2^2, 

And as the difference of two squares, 200 = 51^2 - 49^2; 27^2 - 23^2; 15^2 - 5^2

See Here for more Math Facts for every Year Date

---

EVENTS

418 First report of a comet discovered during a solar eclipse, seen by the historian Philostorgius in Asia Minor. Many chronicles do mention this observation (12 western, 3 Byzantine). Philostorgius mentions that the sun was eclipsed at the 8th hour of the day. In his sketch there is a comet. This Total Solar Eclipse was from the Caribbean, Bay of Bengal, north Spain, central Italy, little Asia and ends in the north of India. *NSEC

Photograph of the Eclipse Comet of 1948 taken on November 13, 1948, taken by V.P. Victor at Harvard Observatory’s southern station in Boyden, South Africa. Courtesy of Harvard University.

---

1595 “God in creating the universe and regulating the order of the cosmos had in view the five regular bodies of geometry as known since the days of Pythagoras and Plato.” So did Kepler record his discovery that the universe was based on the Platonic solids, a conjecture he published in 1596. *VFR "as I was showing in my class how the great conjunctions [of Saturn and Jupiter] occur successively eight zodiacal signs later, and how they gradually pass from one trine to another, that I inscribed within a circle many triangles, or quasi-triangles such that the end of one was the beginning of the next. In this manner a smaller circle was outlined by the points where the line of the triangles crossed each other.
The proportion between the circles struck Kepler’s eye as almost identical with that between Saturn and Jupiter, and he immediately initiated a vain search for similar geometrical relations.
And then again it struck me: why have plane figures among three-dimensional orbits? Behold, reader, the invention and whole substance of this little book! In memory of the event, I am writing down for you the sentence in the words from that moment of conception: The earth’s orbit is the measure of all things; circumscribe around it a dodecahedron, and the circle containing this will be Mars; circumscribe around Mars a tetrahedron, and the circle containing this will be Jupiter; circumscribe around Jupiter a cube, and the circle containing this will be Saturn. Now inscribe within the earth an icosahedron, and the circle contained in it will be Venus; inscribe within Venus an octahedron, and the circle contained in it will be Mercury. You now have the reason for the number of planets.
Kepler of course based his argument on the fact that there are five and only five regular polyhedrons. *encyclopedia.com

Kepler's Platonic solid model of the Solar System, from Mysterium Cosmographicum (1596)

---

1676 Flamsteed began living at the Observatory with his two servants on July 10. On 19 July, his long series of Greenwich observations began? *Rebekah Higgitt, Teleskopos

---

1799 The Rosetta stone was found by Napoleon’s troops in the Nile delta. It attracted the interest of the learned men with Napoleon, which included several mathematicians, and copies were circulated to scholars. The text is in Greek, hieroglyphics and demotic Egyptian scripts and was deciphered by Thomas Young and Fran¸cois Champollion. The cartouches on the stone, which contained royal names, were the key to decipherment. It is now a prized possession of the British Museum.*VFR

---

1819 Poisson submitted a paper on the solution of the wave equation. He used the method of power series, but the techniques advocated by Cauchy and Fourier using complex variables and “Fourier analysis” won out. [Ivor Grattan-Guiness, Convolutions in French Mathematics, 1800–1840, pp. 682, 687ff, 1393] *VFR

---

1895 On April 30, George Cantor, first uses Aleph-null in a letter to Felix Klein. Prior to this he had use aleph-one for the first infinite cardinal. The first part of his Bietrage was already in print, so his letter to Klein is added, almost verbatim, to explain the changes with the publication date still showing March of that year. *From the Calculus to Set Theory, 1630-1910: An Introductory History, By I. Grattan-Guinness

On page 492 of  Mathematische Annalen we find the paragraph Die kleinste transfinite Cardinalzahl Alef-null [The minimum transfinite cardinal number Aleph null], and the following:

...wir nennen die ihr zukommende Cardinalzahl, in Zeichen,  ... [We call the cardinal number related to that (set); in symbol, ]

 

---

;1983 The first three-dimensional reconstruction of a human head via computed tomography (CT) is published. Michael W. Vannier (Mallinckrodt Institute of Radiology, St. Louis) and his co-workers J. Marsh (Cleft Palate and Craniofacial Deformities Institute, St. Louis Children's Hospital) and J. Warren (McDonnell Aircraft Company) published the first three-dimensional reconstruction of single computed tomography (CT) slices of the human head. Computer-aided aircraft design techniques were adapted to make the cranial imaging possible. Since then, CT imaging has become a cornerstone of the medical profession.*CHM

---

BIRTHS

1767 Francois-Joseph Servois born (19 July 1768 in Mont-de-Laval (N of Morteau), Doubs, France - 17 April 1847 in Mont-de-Laval, Doubs, France). He worked in projective geometry, functional equations and complex numbers. He introduced the word pole in projective geometry. He also came close to discovering the quaternions before Hamilton.
Servois introduced the terms "commutative" and "distributive" in a paper describing properties of operators, and he also gave some examples of noncommutativity. Although he does not use the concept of a ring explicitly, he does verify that linear commutative operators satisfy the ring axioms. In doing so he showed why operators could be manipulated like algebraic magnitudes. This work initiates the algebraic theory of operators.
Servois was critical of Argand's geometric interpretation of the complex numbers. He wrote to Gergonne telling him so in November 1813 and Gergonne published the letter in the Annales de mathématiques in January 1814. Servois wrote:- I confess that I do not yet see in this notation anything but a geometric mask applied to analytic forms the direct use of which seems to me simple and more expeditious.
Considered as a leading expert by many mathematicians of his day, he was consulted on many occasions by Poncelet while he was writing his book on projective geometry Traité des propriétés projective. *SAU

---

1806 Alexander (Dallas) Bache (July 19, 1806 – February 17, 1867) was Ben Franklin's great grandson. A West Point trained physicist, Bache became the second Superintendent of the Coast Survey (1844-65). He made an ingenious estimate of ocean depth in 1856. He studied records of a tidal wave that had taken 12 hours to cross the Pacific. Knowing that wave speeds depend on depth, he calculated a 2 1/5-mile average depth for the Pacific (within 15% of the right value). Bache created the National Academy of Sciences, securing greater government involvement in science. Through the Franklin Institute he instituted boiler tests to promote safety for steamboats.*TIS

---

1817 Charles Auguste Briot (July 19, 1817 - September 20, 1882) undertook research on analysis, heat, light and electricity. His first major work on analysis was Recherches sur la théorie des fonctions which he published in the Journal of the École Polytechnique in 1859, and he also published this work as a treatise in the same year. His researches on heat, light and electricity was all based on his theories of the aether. He was strongly influenced in developing these theories by Louis Pasteur, the famous chemist. Of course Pasteur was a great scientist, but Briot had an additional reason to hold him in high esteem for, like himself and his friend Bouquet, Pasteur was brought up in the Doubs region of France.

In 1859 Briot and Bouquet published their important two volume treatise on doubly periodic functions. They published another joint effort in 1875 when their treatise on elliptic functions appeared. In this same year they published a second edition to their two volume work of 1859. In 1879 Briot, this time in a single author work, produced his treatise on abelian functions. The physical motivation for the mathematical theories which gave rise to this work in analysis was published by Briot in 1864 when he published his work on light, Essai sur la théorie mathématique de la lumière and five years later when he published his work on heat, Théorie mécanique de la chaleur.
We noted above that Briot was a dedicated teacher and as such he wrote a great number of textbooks for his students. This was certainly a tradition in France at this time and it was natural for a teacher of Briot's quality to write up his courses as textbooks. He wrote textbooks which covered most of the topics from a mathematics course: arithmetic, algebra, calculus, geometry, analytic geometry, and mechanics. For his outstanding contributions to mathematics the Académie des Sciences in Paris awarded Briot their Poncelet Prize in 1882 shortly before he died. *SAU

---

1846 Edward Charles Pickering, (July 19, 1846–February 3, 1919)was born Boston, Mass., U.S. physicist and astronomer. After graduating from Harvard, he taught physics for ten years at MIT where he built the first instructional physics laboratory in the United States. At age 30, he directed the Harvard College Observatory for 42 years. His observations were assisted by a staff of women, including Annie Jump Cannon. He introduced the use of the meridian photometer to measure the magnitude of stars, and established the Harvard Photometry (1884), the first great photometric catalog. By establishing a station in Peru (1891) to make the southern photographs, he published the first all-sky photographic map (1903).*TIS

---

1851 William Edward Wilson,(19 July 1851 – 6 March 1908)  an Irish astronomer, was born July 19, 1851.  Wilson inherited a mansion, Daramona House, in Westmeath in central Ireland, and in 1871, he built an observatory next to the home, equipping it with a 12-inch reflector made by Howard Grubb, a noted telescope maker in Dublin.  No telescope owner is ever happy with their first telescope – it is always too small – and by 1881, Wilson had traded in the 12-inch reflector for a 24-inch silver-on-glass reflector, and he bought a new mount as well, with an accurate clock drive. 

Although, as we shall see, the 24-inch Grubb could take phenomenal deep-sky photographs, Wilson was initially interested in astronomical measurement.  For example, he and several colleagues used special instruments to measure the temperature of the Sun, and of sunspots.  He also measured the light output of stars, using a selenium cell.  He was amazed at the power of Betelgeuse in Orion, which has no measurable parallax (meaning it is very far away), but still sends a prodigious amount of light our way. One of his collaborators was George Francis FitzGerald, a professor in Dublin, who would later contribute to the Lorenz-FitzGgerald contractions used to explain the null result of the Michelson-Morley experiment.   The results of Wilson's scientific investigations of the Sun and stars were published in a half-dozen papers in the Philosophical Transactions and the Proceedings of the Royal Society of London, and the Monthly Notices of the Royal Astronomical Society.

The Ring Nebula in Lyra, M57, collotype, photo taken Sep. 9, 1894, with the 24-inch Grubb reflector at Daramona, 20 min. exposure, in William E. Wilson, Astronomical and Physical Researches, 1900 (Linda Hall Library)

*Linda Hall Org

---

1894 Aleksandr Yakovlevich Khinchin (July 19, 1894 – November 18, 1959) was a Russian mathematician who contributed to many fields including number theory and probability. Khinchin's book Mathematical Foundations of Information Theory, translated into English from the original Russian in 1957, is important. It consists of English translations of two articles: The entropy concept in probability theory and On the basic theorems of information theory which were both published earlier in Russian. The second of these articles provides a refinement of Shannon's concepts of the capacity of a noisy channel and the entropy of a source. Khinchin generalised some of Shannon's results in this book which was written in an elementary style yet gave a comprehensive account with full details of all the results.*SAU

---

1913 Mary Cannell (19 July 1913 in Liverpool, England - 18 April 2000) It was the work which she undertook after she retired which earns her a place as a highly respected historian of mathematics. Her work stemmed from the fact that George Green had worked as a miller near Nottingham. Green was a mathematician who was well known to almost all students of mathematics around the world, yet little was known of his life. Flauvel writes:- ... widespread knowledge of Green himself dates only from the 1970s when Cannell and other Nottingham colleagues worked to restore his windmill and his memory...When I first visited Green's windmill in Nottingham the booklet which I purchased was George Green Miller and Mathematician written in 1988 by Mary Cannell. She produced a major biography of Green, George Green : Mathematician and Physicist 1793-1841 : The Background to His Life and Work in 1993. In addition she wrote research articles on Green's life and work bringing to the world of mathematics an understanding of Green's remarkable life.
Flauvel writes:- She charmed audiences on several continents, promoting interest in Green and early 19th-century mathematical physics, in the clear tones and pure vowels of pre-war English, somewhere between Miss Marple and Dame Peggy Ashcroft. ... Mary Cannell was working on projects of one sort or another - the Green website, the revised edition of the biography, research papers, the catalogue in the university of Nottingham library - right to the end, in days filled with her characteristic energy and enthusiasm. *SAU

---

1921 Rosalyn Sussman Yalow (July 19, 1921 – May 30, 2011) was an American biophysicist who shared (with Andrew V. Schally and Roger Guillemin) the 1977 Nobel Prize for Physiology or Medicine, making her the second woman to win the Nobel Prize in medicine, “for the development of radioimmuno assays (RIA) of peptide hormone.” RIA brought about a revolution in biological and medical research. With her coworkers, she applied RIA to study of the physiology of the peptide hormones insulin, ACTH, growth hormone, and also to throw light upon the pathogenesis of diseases caused by abnormal secretion of these hormones. This was pioneering work that opened diabetes research in new directions. She has been called the “Madame Curie of the Bronx..” *TiS

---

DEATHS

1878 Egor Ivanovich Zolotarev (March 31, 1847, Saint Petersburg – July 19, 1878, Saint Petersburg) produced fundamental work on analysis and number theory. *SAU

 In 1857 he began to study at the fifth St Petersburg gymnasium, a school which centered on mathematics and natural science. He finished it with the silver medal in 1863. In the same year he was allowed to be an auditor at the physico-mathematical faculty of St Petersburg university.

He had not been able to become a student before 1864 because he was too young. Among his academic teachers were Somov, Chebyshev and Aleksandr Korkin, with whom he would have a tight scientific friendship. In November 1867 he defended his Kandidat thesis “About the Integration of Gyroscope Equations”, after 10 months there followed his thesis pro venia legendi About one question on Minima. With this work he was given the right to teach as a private lecturer at St Petersburg university.

Zolotarev's steep career ended abruptly with his early death. He was on his way to his dacha when he was run over by a train in the Tsarskoe Selo station. On 19 July 1878 he died from blood poisoning.

Yegor Ivanovich is not to be confused with the probabilist Vladimir Mikhaelovich Zolotarev, Kolmogorov's disciple, who worked on stable distributions with well known results on their parametrization.

---

1947 John Clark(30 April 1861, 9 July 1947)  graduated from Edinburgh University and became a teacher at George Heriot's School in Edinburgh. He went on to become Rector of this school. He became Secretary of the EMS in 1891 and President in 1897. *SAU

---

1982 Hugh Everett III (November 11, 1930 – July 19, 1982) was an American physicist who first proposed the many-worlds interpretation (MWI) of quantum physics, which he termed his "relative state" formulation.
Discouraged by the scorn of other physicists for MWI, Everett ended his physics career after completing his Ph.D. Afterwards, he developed the use of generalized Lagrange multipliers for operations research and applied this commercially as a defense analyst and a consultant. He was married to Nancy Everett née Gore. They had two children: Elizabeth Everett and Mark Oliver Everett, who became frontman of the musical band Eels.

---

1992 Allen Newell (March 19, 1927 – July 19, 1992) was a researcher in computer science and cognitive psychology at the RAND Corporation and at Carnegie Mellon University’s School of Computer Science, Tepper School of Business, and Department of Psychology. He contributed to the Information Processing Language (1956) and two of the earliest AI programs, the Logic Theory Machine (1956) and the General Problem Solver (1957) (with Herbert A. Simon). He was awarded the ACM's A.M. Turing Award along with Herbert A. Simon in 1975 for their basic contributions to artificial intelligence and the psychology of human cognition *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

Chen, Goldbach, and the Search for an Unsolved Proof

 3-5,     5-7,     11-13,     17-19...                        29-31 

            7-9...........13-15........19-21..... 23-25, 

 A few days before I set out to write this, scrolling through my twitter feed I found, @AlgebraFact · " Chen’s theorem: There are infinitely many primes p such that p+2 is either prime or the product of two primes." This read a little differently than how I remembered it so I set about milking the net to refresh myself. I concluded that Chen's Theorem is a lot like the parallel postulate, it is written lots of different ways. 

The theorem was first stated by Chinese mathematician Chen Jingrun in 1966, with further details of the proof in 1973.  

The statue of Chen Jingrun at Xiamen University.

 Here's another, Theorem(Chen): For any even integer h∈2Z, there exist infinitely many primes p such that p+h is either a prime or a semiprime. Ok, make h=2 and it's the same thing. 

 But then Wikipedia has " Chen's theorem states that every sufficiently large even number can be written as the sum of either two primes, or a prime and a semiprime (the product of two primes)." Now these are really very different statements, at least to young students. It is a link that number theorists recognize in some of math's long unproven conjectures. 

 So let's go back a bit, to the early twentieth century, and a German Mathematician named Edmund Landau. "At the 1912 International Congress of Mathematicians, Edmund Landau listed four basic problems about prime numbers. These problems were characterized in his speech as "unattackable at the present state of mathematics" and are now known as Landau's problems. 

They are as follows: 

 Goldbach's conjecture: Can every even integer greater than 2 be written as the sum of two primes? 

Twin prime conjecture: Are there infinitely many primes p such that p + 2 is prime? 

 Legendre's conjecture: Does there always exist at least one prime between consecutive perfect squares? 

 Are there infinitely many primes p such that p − 1 is a perfect square? In other words: Are there infinitely many primes of the form n^2 + 1? 

 As of June 2022, all four problems are unresolved." *Wikipedia. 

 Wow, so number 2 says almost the same as the twitter post, with a slight opening for "nearly prime", one of the terms sometimes used for semi-primes, or composite numbers that are the product of two primes. (As a teacher I hope that the students reading this would know the the two primes need not be distinct, so 9 and 25 are still semi-primes.) 

 Number one sounds more like the Wikipedia definition of the term. Obviously these two conjectures are interrelated. A little before Chinese mathematician Chen Jingrun, first wrote about this idea in 1966 , and expanded on his proof in 1973, in 1947, Alfréd Rényi had showed there exists a finite K such that any even number can be written as the sum of a prime number and the product of at most K primes. So Chen had reduced the number of factors of the non-prime from some unspecified K, to 2, and showed that and included that there are an infinite number of "nearly prime pairs" with any even separation.  So there are infinitely many primes p such that p + 4 is prime, or a semi-prime; and  there are infinitely many primes p such that p + 6 is prime, or a semi-prime; and p+8, p+10,.....

Number Theory folks have names for some of these pairings, Cousin primes differ by four, (7 and 11 for example), and sexy primes differ by six, and if one of two sexy primes has a twin that falls between the sexy pair, they are called a prime triplet, 7, 11, 13 for example, or 17, 19, 23. Chen's theorem says that there must be infinite examples of cousin and sexy pairs with a prime followed by a prime or a semi-prime. 

 Then in 2015, Tomohiro Yamada took away the "every sufficiently large even number " of Chen's theorem and gave a definite limit. Every even number greater than \(e^{e^{36}}\) , which is big. But in time someone will find a way to knock that "sufficiently large number" down a little, maybe a lot. But  that is with "nearly twin primes", it seems like Goldbach's conjecture and the twin prime conjecture still rest heavily in the "unattackable at the present state of mathematics" stage. 

 But then, in my youth most folks said we could never prove Fermat's Last Theorem, and then we did... well, not me, but it was the same type of whittling away at it through the ages until Andrew Wiles, inspired by a book he found in the library at age ten, completed a thirty year search for the "impossible" proof. Maybe one of your students will learn about this pair of "impossibles", and surprise us all.

Why not expose them to Goldbach's conjecture; what even numbers are the sum of two primes? It seems like all of them, at least every one we try.  It has been tested up to 4*10^18 though, and so far, so good. But there are still great things to explore, how many ways can even n be written as the sum of two primes, and by what rules.  10 = 5+5 = 3+7 = 7+3  are the last two different?  What if we don't allow doubles like 5+5?  If we want each sums primes to be distinct, 24 is the smallest even number expressible as the sum of two primes in three ways... and no, I'm not telling you, find them. 

Just as I was writing this, one of the Fields Medalist winners in 2022 was presented to Oxford Professor James Maynard for his work on primes.  One of his recent works about distributions of primes was toward a proof that there are an infinite number of prime numbers that do not have a 7 among their digits. (In truth, he showed that there were an infinite number of them that did not contain any particular digit you choose.)   He also cited the twin prime conjecture as one of his favorites.  

Now what's the smallest number that is expressible sums of primes in in four ways, five...

On This Day in Math - July 18

 

Math is the only place where truth and beauty mean the same thing.

-Danica McKellar

(I can't believe I'm doing math quotes by "Winnie" from Wonder Years)

The 199th day of the year; 199 is prime (in fact, all three permutations of the number are prime) and is the sum of three consecutive primes: 61 + 67 + 71, and of five consecutive primes: 31 + 37 + 41 + 43 + 47. (Suddenly struck me I don't know what is the smallest prime that is the sum of consecutive primes in more than one way!)(So the answer was right in front of my face, one of the primes listed above)

199 is the smallest number with an additive persistence of 3. (iterate the sum of the digits. The number of additions required to obtain a single digit from a number n is called the additive persistence of n, and the digit obtained is called the digital root of n. ) 1+9+9 =19, 1+9=10, 1+0 = 1. so the additive persistence is 3 and the digital root is 1.

I like "almost constants". For the 199th day,\( ( \frac{\sqrt{5} +1}{2})^{11}= 199.0050249987406414902082… \)

199 is the last year day that is part of a prime quadruplet, (191, 193, 197, 199)

199 is the smallest number that has an additive persistence of 3, 1+9+9 = 19; 1+9 =10; 1+0=3 *Prime Curios

199 = 100^2-99^2

199 as a palindrome of its own digits, 99+1+99=199= 9*9+9*1+9+1+9+1*9+9*9

199 is a permutable prime, and 919 and 991 are both prime

199 is the first prime number in a sequence of 10 consecutive prime numbers with common difference 210 (tao and green 2008; see R.Taschner "Die Farben der Quadratzahlen" p. 147)the ten primes are 199, 409, 619, 829, 1039, 1249, 1459, 1669, 1879, and 2089.

The next prime after 199 is 211. If they are concatenated in either order, they form a prime, 199211 and 211199 are both prime. *Prime Curios

199 is the smallest emirp (991 is prime also) that is also an invertible prime, it's 180 degree rotation (Strobagram)  produces the prime 661. *Prime Curios

199, 211, and 223 are the smallest triple of primes of the form n, n+12 and n+24, and it is the only triple less than 1000. *Prime Curios

go here more Math Facts for every Year Date,

---

EVENTS

1765 The Board of Longitude appointed Richard Dunthorne to be the first "Comparer of the Ephemeris and Corrector of the Proofs" for the (then still future) Nautical Almanac and Astronomical Ephemeris. *Wik Later there would be a small team of these "computers" creating lunar tables as a potential solution for the "longitude problem", determining longitude at sea. At this time calculator was a term used occasionally for accountants, but more commonly for a book of mathematical tables.One example of such was "The Assistant Calculator, or Cotton Spinners Guide, being a complete set of tables, of the greatest use in the cotton spinning business."

 Dunthorne was born in humble circumstances in Ramsey, Cambridgeshire, where he attended the free grammar school. There he attracted the notice of Roger Long (later Master of Pembroke Hall, Cambridge), whose protégé Dunthorne became. Dunthorne moved to Cambridge where Long first appointed him as a "footboy", and where he received some further education (though this does not seem to have been regular university education). Dunthorne then "managed" a preparatory school in Coggeshall, Essex, and later returned to Cambridge where Long obtained for him an appointment as a "butler" at Pembroke Hall, an office that Dunthorne retained for the rest of his life. Here, Dunthorne's main activity seems to have been in assisting Long in astronomical and scientific work.

Dunthorne also held an appointment for some years, concurrently with his work with Long, as superintendent of works of the Bedford Level Corporation, responsible for water management in the Fens; he began this work several years" before 1761, continuing into the 1770s. In this role, Dunthorne was concerned in a survey of the Fens in Cambridgeshire, and he also supervised construction of locks near Chesterton on the River Cam. 

Dunthorne's association with Long remained lifelong, and in the end Dunthorne acted as executor of Long's will. *Wik

---

1860  First wet plate photographs of an eclipse; they require 1/30 of the exposure time of a daguerreotype. *NSEC

Photo :Stanford SOLAR Center - History of Solar

---

1872 Weierstrass, in a lecture to the Berlin Academy, gave his classical example of a continuous nowhere differentiable function. See Big Kline, p. 956.*VFR

Under these conditions, Weierstrass proved that the function is:

continuous everywhere, because the series converges uniformly; yet

differentiable nowhere, despite being given by an explicit trigonometric series.

This was a profound shock to nineteenth-century analysts. Until then, many mathematicians believed that every continuous function encountered "in nature" would fail to have a tangent only at exceptional points. Weierstrass demonstrated that continuity alone places essentially no restriction on differentiability.*ChatGPT

---

1879  On this day in 1879,  George Chrystal was appointed to the chair of mathematics in the University of Edinburg. He is primarily known for his books on algebra and his studies of seiches.  [a temporary disturbance or oscillation in the water level of a lake or partially enclosed body of water, especially one caused by changes in atmospheric pressure.]

 He was educated at Aberdeen Grammar School and the University of Aberdeen. In 1872, he moved to study under James Clerk Maxwell at Peterhouse, Cambridge. He graduated Second Wrangler in 1875, joint with William Burnside, and was elected a fellow of Corpus Christi. He was appointed to the Regius Chair of Mathematics at the University of St Andrews in 1877, and then in 1879 to the Chair in Mathematics at the University of Edinburgh. In 1911, he was awarded the Royal Medal of the Royal Society for his researches into  seiches (the surface oscillations of Scottish lochs).  

---

1898 Marie and Pierre Curie discover the previously unknown element Polonium which she named for her home country, Poland. *Brody & Brody, The Science Class You Wished You Had

---

1962 Hearings on Mercury 13 Women suspended. The first potential US women in space, often called the Mercury 13 in comparison to the original Mercury 7 astronauts, had a hearing in congress beginning July 17th. The house convened public hearings before a special Subcommittee on Science and Astronautics. Significantly, the hearings investigated the possibility of gender discrimination two full years before the Civil Rights Act of 1964 made that illegal, making these hearings a marker of how ideas about women's rights permeated political discourse even before they were enshrined in law. The hearings would abruptly be terminated at lunch on the 18th. In less than a year, Soviet cosmonaut Valentina Tereshkova became the first woman in space on June 16, 1963. In response, Clare Boothe Luce published an article in Life criticizing NASA and American decision makers. By including photographs of all thirteen Lovelace finalists, she made the names of all thirteen women public for the first time. (The Time issue is available at Google Books here. Astronaut Sally Ride became the first American woman in space in 1983 on STS-7. *Wik

---

1968  Intel Founded.  Robert Noyce, Andy Grove and Gordon Moore incorporated Intel, a company they built on production of the microprocessor. The component that has allowed computers to increase in speed and decrease in size, the microprocessor also built Intel, whose Pentium processors now power most IBM-compatible personal computers.

Moore is famous for Moore's Law, which dictates that every 18 months microprocessors double in speed and decrease in size by half.

---

1979 Great Britain issued a stamp honoring Alice’s Adventures in Wonderland. *VFR

---

2014 first "Sun-spotless day" on the Earthward side of sun since 2011, *David Dickinson ‏@Astroguyz

Spaceweather.com reports that today we surpassed the largest number of spotless days (270) of the previous 2008 Solar Minimum cycle. The current spotless streak stands at 33 days and is quite possibly on its way to surpass the previous longest streak of this minimum at 36 days.  And you have to go back to 1913 to find a year that had more spotless days (311)!

You might be wondering: when is the next Solar Maximum?  That’s forecast to be July 2025.  Both the minimum & maximum forecasts have a +/- 6-month error. *The Swinging Post 

The blank sun on Dec. 8, 2019. Credit: NASA/Solar Dynamics Observatory 

---

BIRTHS

1013 Hermann of Reichenau (July 18, 1013 – September 24, 1054), was a German mathematician who was important for the transmission of Arabic mathematics, astronomy and scientific instruments into central Europe.*SAU

Blessed Hermann of Reichenau or Herman the Cripple (18 July 1013 – 24 September 1054), also known by other names, was an 11th-century Benedictine monk and scholar. He composed works on history, music theory, mathematics, and astronomy, as well as many hymns. He has traditionally been credited with the composition of "Salve Regina", "Veni Sancte Spiritus", and "Alma Redemptoris Mater", although these attributions are sometimes questioned. His cultus and beatification were confirmed by the Roman Catholic Church in 1863. *Wik

*stignatiusmobile

---

1635 Robert Hooke ( 18 July[NS 28 July] 1635 – 3 March 1703) born.English natural philosopher, architect and polymath. His adult life comprised three distinct periods: as a scientific inquirer lacking money; achieving great wealth and standing through his reputation for hard work and scrupulous honesty following the great fire of 1666, but eventually becoming ill and party to jealous intellectual disputes. These issues may have contributed to his relative historical obscurity.
He was at one time simultaneously the curator of experiments of the Royal Society and a member of its council, Gresham Professor of Geometry and a Surveyor to the City of London after the Great Fire of London , in which capacity he appears to have performed more than half of all the surveys after the fire. He was also an important architect of his time, though few of his buildings now survive and some of those are generally misattributed, and was instrumental in devising a set of planning controls for London whose influence remains today. Allan Chapman has characterised him as "England's Leonardo" *wik
He was born in Freshwater, Isle of Wight, and discovered the law of elasticity, known as Hooke's law, and invented the balance spring for clocks. He was a virtuoso scientist whose scope of research ranged widely, including physics, astronomy, chemistry, biology, geology, architecture and naval technology. On 5 Nov 1662, Hooke was appointed the Curator of Experiments at the Royal Society, London. After the Great Fire of London (1666), he served as Chief Surveyor and helped rebuild the city. He also invented or improved meteorological instruments such as the barometer, anemometer, and hygrometer. Hooke authored the influential Micrographia (1665)*TIS

One of my favorites, a louse seems to be marching off to war

---

1768 Jean Robert Argand born (July 18, 1768 – August 13, 1822). His single original contribution to mathematics was the invention and elaboration of a geometric representation of complex numbers and operations on them. In this he was preceded by Wessel and followed by Gauss.*VFR Swiss mathematician who was one of the earliest to use complex numbers, which he applied to show that all algebraic equations have roots. He invented the Argand diagram - a geometrical representation of complex numbers as a point with the real portion of the number on the x axis and the imaginary part on the y axis.*Wik

More detail about the history of the diagram here.

---

1813 Pierre Laurent (July 18, 1813 – September 2, 1854) was a French mathematician best-known for his study of the so-called Laurent Series in Complex analysis. *SAU

The Laurent series is an expansion of a function into an infinite power series, generalizing the Taylor series expansion.*Wik

---

1853 Antoon Lorentz (18 July 1853 – 4 February 1928) was a Dutch physicist who shared the 1902 Nobel Prize in Physics with Pieter Zeeman for the discovery and theoretical explanation of the Zeeman effect. He also derived the transformation equations subsequently used by Albert Einstein to describe space and time. *Wik
Lorentz is best known for his work on electromagnetic radiation and the FitzGerald-Lorentz contraction. He developed the mathematical theory of the electron.*SAU

---

1856 Giacinto Morera (Novara, 18 July 1856 – Turin, 8 February 1909), was an Italian engineer and mathematician. He is remembered for Morera's theorem in the theory of functions of a complex variables and for his work in the theory of linear elasticity. 

Morera's theorem states that a continuous, complex-valued function f defined on an open set D in the complex plane that satisfies{\displaystyle \oint _{\gamma }f(z)\,dz=0}

for every closed piecewise C1 curve   𝛾{\displaystyle \gamma } in D must be holomorphic on D.

He was member of the Accademia Nazionale dei Lincei (first elected corresponding member on 18 July 1896, then elected national member on 26 August 1907)[20] and of the Accademia delle Scienze di Torino (elected on 9 February 1902).[21] Maggi (1910, p. 317) refers that also the Kharkov Mathematical Society elected him corresponding member during the meeting of the society held on 31 October 1909 (Old Calendar), being apparently not aware of his death.*Wik

---

1891 Emil Julius Gumbel (18 July 1891, in Munich – 10 September 1966, in New York City) was an American mathematician and statistician is known for his work in reliability theory and order statistics. His name remains on the Type 1 extreme value distribution, known as the Gumbel distribution. In his early life, during WW I, he militantly advocated for pacifism. Gumbel acted as a historian and statistician recording the political murders in the early Weimar Republic. His activities caused ostracization and political harassment. When he moved to France (1932), he could better concentrate on his mathematical work, most notably examining the statistical distributions most used by actuaries. He also applied his skills in the fields of hydrology (floods) and meteorology (drought). Eight years later, due to WW II, he moved to the U.S. (1940) and continue this work. *TiS

---

1899 Robert Schlapp (18 July 1899 in Edinburgh, Scotland - 31 May 1991 in Ashford, Kent, England)studied at Edinburgh and Cambridge universities. He spent his whole career at Edinburgh University teaching mathematics and Physics. He was also interested in the History of Mathematics. He became President of the EMS in 1942 and 1943. *SAU

He was born in Edinburgh on 18 July 1899, the youngest of three children of Anna Lotze and Otto Schlapp.[2] His father only appears in Post Office Directories around 1910, at which point he is listed as a university lecturer living at 54a George Square. His father lectured in German at the University of Edinburgh and later (1926) became the University's first Professor of German.

In the First World War, obviously a potential problem due to his German background, he enlisted under the Derby Scheme and joined the 31st battalion of the Middlesex Regiment in 1917 at the age of 18. This was a labouring unit rather than a fighting battalion, involved in tasks such as trench construction. After the war, Schlapp studied mathematics and physics at the University of Edinburgh graduating MA around 1923 then doing postgraduate studies at the University of Cambridge gaining a doctorate (PhD) in 1925.

Returning to the University of Edinburgh he began lecturing in Natural Philosophy (Physics) and Applied Mathematics in autumn 1925. He became Senior Lecturer in Mathematical Physics in 1927.[6] In this role he was assistant to Charles Galton Darwin (who had recently replaced Cargill Gilston Knott).

In 1927, he was elected a Fellow of the Royal Society of Edinburgh. His proposers were Sir Edmund Taylor Whittaker, Sir Charles Galton Darwin, David Gibb, and Edward Thomas Copson. He served as Curator of the Society's artefacts from 1959 to 1969 and as their Vice President from 1969 to 1972.

In 1983, he won the Society's bicentenary medal (presented to him by Queen Elizabeth II). He was President of the Edinburgh Mathematical Society.

In 1936 Professor Darwin retired and was replaced by Max Born whom Schlapp then assisted in turn. Schlapp retired in 1969, and died in Ashford in Kent on 31 May 1991.

Whilst (A beautiful British word) playing cello in his brother, Walter Schlapp's, string quartet, he met Mary Fleure (who played second violin). He married her in 1940. They had two daughters. Mary died in 1975.

---

1906 Edwin Ford Beckenbach (July 18, 1906 – September 5, 1982) was an American mathematician

In 1929 he earned a master's degree at Rice University, and in 1931 a PhD under the direction of Lester R. Ford. As a postdoc, he was a National Research Fellow at Princeton University, Ohio State University, and the University of Chicago. 

At UCLA, he led the development of the graduate program in mathematics. The first mathematics PhD was granted under his direction as thesis advisor.

Beckenbach was also a leader in the founding (in 1948) of the Institute of Numerical Analysis, which was then a branch of the National Bureau of Standards. His institute developed in 1948 and 1949 a vacuum-tube computer (SWAC), which began operation in July 1950 and was for a short time the fastest computer in the world. In 1974 he retired from UCLA as professor emeritus. From 1949 to 1963, he was a consultant for the Rand Corporation and in the academic year 1951/1952 he was a visiting professor at the Institute for Advanced Study.

In the academic year 1958/59 he was a Guggenheim Fellow at ETH Zürich. With František Wolf, Beckenbach founded in 1951 the Pacific Journal of Mathematics, of which he was the first editor. In 1983, he received the Distinguished Service Award from the Mathematical Association of America. The Beckenbach Book Prize, first awarded in January 1985, is named in his honor. *Wik

---

1922 Thomas S(amuel) Kuhn (July 18, 1922 – June 17, 1996) was an American historian of science, MIT professor, noted for The Structure of Scientific Revolutions (1962), one of the most influential works of history and philosophy written in the 20th century. His thesis was that science was not a steady, cumulative acquisition of knowledge, but it is "a series of peaceful interludes punctuated by intellectually violent revolutions." Then appears a Lavoisier or an Einstein, often a young scientist not indoctrinated in the accepted theories, to sweep the old paradigm away. Such revolutions, he said, came only after long periods of tradition-bound normal science. "Frameworks must be lived with and explored before they can be broken," *TIS This was the first modern use of the term "paradigm" in this way.

---

1939 Marjorie Lee Senechal (née Wikler,July 18,1939 - ) is an American mathematician and historian of science, the Louise Wolff Kahn Professor Emerita in Mathematics and History of Science and Technology at Smith College and editor-in-chief of The Mathematical Intelligencer. In mathematics, she is known for her work on tessellations and quasicrystals; she has also studied ancient Parthian electric batteries and published several books about silk.

Senechal won the Mathematical Association of America's Carl B. Allendoerfer Award for excellence in expository writing in Mathematics Magazine in 1982, for her article, "Which Tetrahedra Fill Space?" In 2008, her book American Silk 1830 – 1930 won the Millia Davenport Publication Award of the Costume Society of America. In 2012, she became a fellow of the American Mathematical Society.

Her Homepage at Smith is here

---

1940  John David Philip Meldrum (18 July 1940 in Rabat, Morocco; died 9 August 2018 in Edinburgh, Scotland) was a British mathematician. Meldrum was an algebraist and his research was mostly related to group theory.

In 1964 he was appointed as a supernumerary fellow and college lecturer in mathematics at Emmanuel College.Meldrum received his PhD from the University of Cambridge in 1967 on the topic of "Central Series in Wreath Products". His supervisor was Derek Roy Taunt.

In 1969 he became a lecturer for mathematics at the University of Edinburgh and in 1982 he was appointed there as a senior lecturer.

He died on 9 August 2018 in Edinburgh after a battle with the Parkinson's disease. *Wik

---

1948 Michel Hartmut (German pronunciation: [18 July, 1948 - ) is a German biochemist, who received the 1988 Nobel Prize,along with Johann Deisenhofer and Robert Huber, in Chemistry for determination of the first crystal structure of an integral membrane protein, a membrane-bound complex of proteins and co-factors that is essential to photosynthesis. 

They are the first to succeed in unraveling the full details of how a membrane-bound protein is built up, revealing the structure of the molecule atom by atom. The protein is taken from a bacterium which, like green plants and algae, uses light energy from the sun to build organic substances. All our nourishment has its origin in this process, which is called photosynthesis and which is a condition for all life on earth.*TiS

---

DEATHS

1650 Christoph Scheiner SJ (25 July 1573 (or 1575) – 18 July 1650) was a Jesuit priest, physicist and astronomer in Ingolstadt. In 1603, Scheiner invented the pantograph, an instrument which could duplicate plans and drawings to an adjustable scale. Later in life he would invent a sunspot viewing appartus. In 1611, Scheiner observed sunspots; in 1612 he published the "Apelles letters" in Augsburg. Marcus Welser had the first three Apelles letters printed in Augsburg on January 5, 1612. They provided one of many reasons for the subsequent unpleasant argument between Scheiner and Galileo Galilei. *Wik Thus, in 1614, Galileo found himself in an unresoved dispute over priority with a mean and determined Jesuit. The fight was to grow meaner in subsequent years. It would play a major role in Galileo's Inquisitional trial eighteen years later. *James Reston, Jr., Galileo: A Life

Sunspots observed and drawn in October, 1611, engraving by Alexander Mair, in Christoph Scheiner, Tres epistolae de maculis solaribus, in Galileo Galilei, Istoria e dimostrazioni intorno alle macchie solari, 1613 (Linda Hall Library) 

---

1742 Abraham Sharp (1653– 18 July 1742) was an English mathematician who worked with Flamsteed. He calculated π to 72 places (using an arcsine sequence, briefly holding the record until John Machin calculated 100 digits in 1706).*SAU

---

1807 Thomas Jones (23 June 1756 – 18 July 1807) was Head Tutor at Trinity College, Cambridge for twenty years and an outstanding teacher of mathematics. He is notable as a mentor of Adam Sedgwick.
He was born at Berriew, Montgomeryshire, in Wales. On completing his studies at Shrewsbury School, Jones was admitted to St John's College, Cambridge on 28 May 1774, as a 'pensioner' (i.e. a fee-paying student, as opposed to a scholar or sizar). He was believed to be an illegitimate son of Mr Owen Owen, of Tyncoed, and his housekeeper, who afterwards married a Mr Jones, of Traffin, County Kerry, Thomas then being brought up as his son.
On 27 June 1776, Jones migrated from St John's College to Trinity College. He became a scholar in 1777 and obtained his BA in 1779, winning the First Smith's Prize and becoming Senior Wrangler. In 1782, he obtained his MA and became a Fellow of Trinity College in 1781. He became a Junior Dean, 1787–1789 and a Tutor, 1787-1807. He was ordained a deacon at the Peterborough parish on 18 June 1780. Then he was ordained priest, at the Ely parish on 6 June 1784, canon of Fen Ditton, Cambridgeshire, in 1784, and then canon of Swaffham Prior, also 1784. On 11 December 1791, he preached before the University, at Great St Mary's, a sermon against duelling (from Exodus XX. 13), which was prompted by a duel that had lately taken place near Newmarket between Henry Applewhaite and Richard Ryecroft, undergraduates of Pembroke, in which the latter was fatally wounded. Jones died on 18 July 1807, in lodgings in Edgware Road, London. He is buried in the cemetery of Dulwich College. A bust and a memorial tablet are in the ante-chapel of Trinity College. *Wik

---

1930 Karl Emmanuel Robert Fricke (September 24, 1861 in Helmstedt, Germany ; July 18, 1930 in Bad Harzburg, Germany) was a German mathematician, known for his work in function theory, especially on elliptic, modular and automorphic functions. He was one of the main collaborators of Felix Klein, with whom he produced two classic two volume monographs on elliptic modular functions and automorphic functions.

In 1893 in Chicago, his paper Die Theorie der automorphen Functionen und die Arithmetik was read (but not by Fricke) at the International Mathematical Congress held in connection with the World's Columbian Exposition. From 1894 to 1930 Fricke was professor of Higher Mathematics at the Technische Hochschule Carolo-Wilhelmina in Braunschweig.*Wik

---

1977 Georgi Delchev Bradistilov (25 October 1904 [12 October 1904 O.S.] – 18 June 1977) was a Bulgarian mathematician.

He attended 3rd Sofia gymnasium and in 1922 entered Sofia University to study physics and mathematics. In 1927 he graduated with honors and the same year was appointed as assistant professor in mathematics. In the 1930s he studied at the University of Paris and the University of Munich. Bradistilov was one of the last students to take Arnold Sommerfeld's course in theoretical physics before his retirement. In 1938, he defended his doctorate, with Oskar Perron as advisor, at the University of Munich.

Georgi Bradistilov's contributions to applied mathematics are related to nonlinear differential equations and their applications to mechanics and electrotechnics, to electrostatic potential, to nonlinear oscillations.

He was notorious for his sense of humor and openness, for his love of arts and nature as well as for his refined taste, his wife being an artist educated in Florence.(QED?)

During his lifetime Georgi Bradistilov received many Bulgarian state decorations and awards. Recently a street in Sofia near the Technical University was named after him. *Wik

---

2018 Burton Richter (22 Mar 1931, ) American physicist who was jointly awarded the 1976 Nobel Prize for Physics with Samuel C.C. Ting for the discovery of a new subatomic particle, the J/psi particle. *TIS He led the Stanford Linear Accelerator Center (SLAC) team which co-discovered the J/ψ meson in 1974, alongside the Brookhaven National Laboratory (BNL) team led by Samuel Ting. This discovery was part of the so-called November Revolution of particle physics. He was the SLAC director from 1984 to 1999.*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