they decide to take no more mathematics courses.

They might be able to hear the sound of closing doors.

~Caballero, James

The 212th day of the year; Besides being the Fahrenheit boiling point of water at sea level, 212 produces a prime of the form k^{10}+k^{9}+...+k^{2}+k+1, when k=212. Edward Shore@edward_shore sent me a note:" That number would be 184,251,916,841,751,188,170,917.")

(*students might explore different values of k, and different maximum exponents to produce primes..ie when k is 2, then 2 ^{6} +2^{5}+...+2^{2}+2+1 is prime*)

The smallest even three-digit integer, abc, such that (abc)/(a*b*c) is also prime. [ie 212/(2*1*2)= 53 ]*Prime Curios

212 is a palindrome whose square is also a palindrome, 212

^{2}= 44944. It is the last year date for which this is true. It is also a palindrome in base 3(21212) with a copy of it's base 10 representation.

And I just learned from @fermatslibrary that 212 is in a palindromic approximation for π

666/212 = 3.141509... good for four decimal places.

**1669** Lucasian professor Isaac Barrow sent John Collins a manuscript of Newton’s De analysi and thereby Newton’s anonymity began to dissolve. It was a summary of Newton’s work on the calculus and was written after Newton saw Nicholas Mercator’s Logarithmotechnia (1668).

\( ln(1+x) = x -\frac{x^2}{2} + \frac{x^3}{3} -\frac{x^4}{4}+\cdots \)

Newton wrote his paper in order that he would not lose credit for his work on inﬁnite series. Collins immediately recognized Newton’s genius. Although not published until 1711, this paper led to Newton’s appointment as Lucasian professor on 29 October 1669.*VFR

**1730** Goldbach proves that Fermat numbers are pairwise coprime. (Fermat had said that the he thought the numbers of the form \( 2^{2^n} +1 \) were all prime, although he could not prove it. The first five are (n=0...4) but Euler would prove the n=5 case was not prime by factoring it. No more primes have been found after n=4, but there is no proof there can not be more. I think this story, and Goldbach's discovery, make an interesting approach to proving the primes are infinite.) He claims that 1 is the only square among the triangular numbers *Euler Goldbach Correspondence

**1744 **Euler to Goldbach , "All around here chess is played passionately." He then mentions a certain strong local player he had been taking lessons from, then adds, "I am winning most games with him." Master of us all in more ways than I knew. *S. Strogatz

**1790**The U.S. Patent Office issued its ﬁrst patent to Samuel Hopkins of Vermont for his “process for making pot and pearl ashes,” whatever they are. Since George Washington and Thomas Jefferson signed Hopkins’ patent, more than 4 million have been issued. *VFR In 1790, the first U.S. patent was granted to Samuel Hopkins of Vermont for a process for making potash and pearl ashes. Potash was important as an ingredient in soap and fertilizer. The patent was granted for a term of 14 years and signed by President George Washington, who had the previous month signed the first U.S. patent statute into law on 10 April 1790. Hopkins did not get Patent with a serial No.1 as thousands of patents were issued before the Patent Office began to number them. Congress had passed the Patent Act on 10 Apr 1790. Two other patents were granted that year - one for a new candle-making process and the other the flour-milling machinery of Oliver Evans. The next year, 1791, Samuel Hopkins also was granted the first Canadian patent.*TIS

*C. Pickover |

*Elements*(1847), in which he used primary colors to demonstrate some of the steps in the Euclidean proofs. The result was certainly one of the most attractive and appealing textbooks of geometry ever printed. We see above the title-page with its Pythagorean theorem vignette, and below a theorem that demonstrates, geometrically, that (a + b)2 = a2 +2ab + b2. *Linda Hall Org

**1943**Ireland issued—as its ﬁrst stamp with a mathematical theme—two stamps to celebrate the centenary of the discovery of Quaternions by Sir William Rowan Hamilton. [Scott #126-7]. *VFR

**1851**Gauss witnessed the opening ceremonies when the newly constructed railway from Cassel reached Gottingen. *VFR

**1990**The U.S. government panel approved the use of gene therapy to treat human disease. Gene therapy uses DNA to treat disease, usually by replacing a faulty gene with a healthy copy. Recent clinical studies suggest this technique holds promise for the future treatment of Parkinson’s disease. *.rsc.org

**2015**The second full moon this month (the other was on the 2nd). This only happens “Once in a blue moon”—and this is the origin of the phrase. Consequently, there were be thirteen full moons this year. The last "blue moon" was in 1985, and the next is predicted in 2018.

**1704 Gabriel Cramer**(31 July 1704 – 4 January 1752). He is best known for “Cramer’s Rule,” a method for solving systems of simultaneous linear equations using determinants. *VFR Gabriel Cramer (31 July 1704 – 4 January 1752) was a Swiss mathematician, born in Geneva. He showed promise in mathematics from an early age. At 18 he received his doctorate and at 20 he was co-chair of mathematics. In 1728 he proposed a solution to the St. Petersburg Paradox that came very close to the concept of expected utility theory given ten years later by Daniel Bernoulli. He published his best known work in his forties. This was his treatise on algebraic curves, "Introduction à l'analyse des lignes courbes algébriques", published in 1750. It contains the earliest demonstration that a curve of the n-th degree is determined by n(n + 3)/2 points on it, in general position. He edited the works of the two elder Bernoullis; and wrote on the physical cause of the spheroidal shape of the planets and the motion of their apsides (1730), and on Newton's treatment of cubic curves (1746). He was professor at Geneva, and died at Bagnols-sur-Cèze.*Wik

*Geeks For Geeks |

**1712 Samuel König**(July 31, 1712, Büdingen – August 21, 1757, Zuilenstein near Amerongen) was a German mathematician who is best remembered for his part in a dispute with Maupertuis over the Principle of Least Action.*SAU

**1718 John Canton**(31 July 1718 – 22 March 1772) British physicist and teacher, born Stroud, Gloucestershire. He made a number of minor discoveries in physics and chemistry. As a result of preparing artificial magnets in 1749 he was elected to the Royal Society. In 1762, he demonstrated that water was slightly compressible. He invented a number of devices in connection with electricity. His notable work, between 1756 and 1759, was to record that on days when the aurora borealis was particularly bright, a compass needle behaved with more irregularity than usual. Thus he was the first to record this as an electromagnetic phenomenon for what is now known to be a magnetic storm.*TIS

**1826 Daniel Friedrich Ernst Meisse**mathematical work covers number theory, work on Möbius inversion and the theory of partitions as well as work on Bessel functions, asymptotic analysis, refraction of light and the three body problem. *SAU

**1843 Friedrich Robert Helmert**(July 31, 1843 – June 15, 1917) German geodesist and an important writer on the theory of errors.

From 1887 Helmert was professor of advanced geodesy at the University of Berlin and director of the Geodetic Institute.

Helmert received many honours. He was president of the global geodetic association of "Internationale Erdmessung", member of the Prussian Academy of Sciences in Berlin, was elected a member of the Royal Swedish Academy of Sciences in 1905, and recipient of some 25 German and foreign decorations. *TIA

**1858 Richard Dixon Oldham**(31 July 1858 – 15 July 1936) Irish geologist and seismologist who discovered evidence for the existence of the Earth's liquid core (1906). In studying seismograms of great 1897 Indian Earthquake he identified P (primary) and S (secondary) waves. It is interesting that he did not get a clue to the presence of the core from the S waves, which are actually incapable of being transmitted through the liquid of the outer core. (The liquid core does not transmit the shear wave energy released during an earthquake.) Rather he noted the existence of a shadow zone in which P waves from an earthquake in the opposite hemisphere of the earth failed to appear*TIS

**1863 George Abram Miller**(31 July 1863 – 10 February 1951) was an early group theorist whose many papers and texts were considered important by his contemporaries, but are now mostly considered only of historical importance.

Miller was born in Lynnville, Lehigh County, Pennsylvania, and died in Urbana, Illinois.*Wik

**1923 Joseph B. Keller**(born July 31, 1923, Paterson, New Jersey) is an American mathematician who specializes in applied mathematics. He is best known for his work on the "Geometrical Theory of Diffraction" (GTD).

He worked on the application of mathematics to problems in science and engineering, such as wave propagation. He contributed to the Einstein-Brillouin-Keller method for computing eigenvalues in quantum mechanical systems.

In 1988 he was awarded the U.S. National Medal of Science, and in 1997 he was awarded the Wolf Prize by the Israel-based Wolf Foundation. In 1996, he was awarded the Nemmers Prize in Mathematics.*Wik

**1927 F. E. Browder**born. Worked in Nonlinear monotone operators and convex sets in Banach spaces. and more.

**1943**Ireland issued—as its first stamp with a mathematical theme—two stamps to celebrate the centenary of the discovery of Quaternions by Sir William Rowan Hamilton. [Scott #126-7].*VFR

**1945 John O'Connor**(31st July 1945 in Luton, Bedfordshire, England.- )

Lists his Research interests A lapsed topologist, I am interested in Computational Algebra.

I am interested in the History of Mathematics and at present am supervising two research students in this area. * His Personal web page

**1726 Nikolaus II Bernoulli**died (February 6, 1695, Basel, Switzerland – July 31, 1726, St. Petersburg, Russia). *VFR Nicolaus(II) Bernoulli was the favourite of three sons of Johann Bernoulli. He made important mathematical contributions to the problem of trajectories while working on the mathematical arguments behind the dispute between Newton and Leibniz.*SAU

**1784 Denis Diderot**died. (October 5, 1713 – July 31, 1784) was a French philosopher, art critic, and writer. He was a prominent persona during the Enlightenment and is best-known for serving as co-founder and chief editor of and contributor to the

*Encyclopédie*. *Wik

**1896 Ludwig Christian Wiener**(7 December 1826 Darmstadt – 31 July 1896 Karlsruhe) was a German mathematician, physicist and philosopher, known for his explanation of Brownian motion , which identified him as a skillful experimenter. He mainly dealt with geometry.*Wik

**1913 John Milne**(30 December 1850 – 31 July 1913) English seismologist who invented the horizontal pendulum seismograph (1894) and was one of the European scientists that helped organize the seismic survey of Japan in the last half of the 1800's. Milne conducted experiments on the propagation of elastic waves from artificial sources, and building construction. He spent 20 years in Japan, until 1895, when a fire destroyed his property, and he returned home to the Isle of Wight. He set up a new laboratory and persuaded the Royal Society to fund initially 20 earthquake observatories around the world, equipped with his seismographs. By 1900, Milne seismographs were established on all of the inhabited continents and he was recognized as the world's leading seismologist. He died of Bright's disease*TIS

Credits :

*CHM=Computer History Museum

*FFF=Kane, Famous First Facts

*NSEC= NASA Solar Eclipse Calendar

*RMAT= The Renaissance Mathematicus, Thony Christie

*SAU=St Andrews Univ. Math History

*TIA = Today in Astronomy

*TIS= Today in Science History

*VFR = V Frederick Rickey, USMA

*Wik = Wikipedia

*WM = Women of Mathematics, Grinstein & Campbell

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