**"See if you can use this proof to show the square root of three is irrational. Then try the square root of four.**

**If it works, you did something wrong."**

The 153rd day of the year. 153 is the fixed point attracter of any multiple of three under the process of summing the cubes of the digits. For more detail and explanation see,"The Cubic Attractiveness of 153" ,

1^{3}+5^{3} + 3^{3} = 153. Numbers which are the sum of their own digits raised to the power of the number of digits are called Armstrong numbers. Except for the trivial one digit numbers, it is also the smallest. There are only three other numbers greater than one which are the sum of the cubes of their digits (Go fourth and seek them. hint: this is the only one which is a year date) This makes 153 a narcissistic or Armstrong number. There are 89 narcissistic numbers in base 10, but only 11 in base 4.

And to extend that, the amazing Cliff Pickover shared this:(although the digits are taken in sets)

ALSO, 153 = 1! + 2! + 3! +4! +5!, *Jim Wilder@wilderlab

I had never observed that 153 = 3 x 51, a product that uses all the digits of the number. HT to INDER J. TANEJA @IJTANEJA There are no numbers below 1000 that have the same digits as their prime factorization in a simple product (no powers) but there is one lingering just above that number, can you find it?

More Math facts here

**EVENTS**

1661 An eager Isaac Newton departs his farm home at Woolsthorpe for Trinity College, Cambridge, although the term would not begin until September. He would remain at Trinity for thirty-five years. He took almost nothing with him. *Thomas Levenson, Newton and The Counterfeiter

**1666 **John Wallis writes to Oldenburg at the Royal Society on the topic of tides. "Wallis adopts Galileo’s technique of explaining the tides through the motions of the earth, focusing on a third tidal cycle that Galileo’s theory did not adequately explain: the “menstrual” (i.e., monthly) cycle in which the tides change in accordance with the position of the moon. Wallis argues that the earth and moon revolve once a month around a common centre of gravity, and it is this point that revolves around the sun. The earth is therefore on a small epicycle with a period of one month, and this additional motion affects the timing and level of the tides. " (From PhD thesis of Adam D Richter, with my thanks). This was well before the universal reach of gravity was understood or accepted. Wallis gives a very mathematical response to inquiries about how he explains this "action at a distance." Wallis maintain that "his goal as a natural philosopher is to recognize phenomena and describe them mathematically, rather than to explain their underlying physical causes. " (A. Richter).

In addition, he points out that his approach is widely supported by Natural Philosophers acceptance of action at a distance in magnets.

**In 1686**, the publication of Newton's Principia was arranged in London at the Royal Society. The minutes of the meeting record that the astronomer Edmund Halley would "undertake the business of looking after it and printing it at his own charge." (As Newton was finalising his work the Royal Society was printing a book called The History of Fishes. "This book is quite lavishly illustrated and unfortunately the Society didn’t have enough budget to publish Principia,” Ms Sommerfeldt said.)

Image: Sir Isaac Newton's own first edition copy of his Philosophiae Naturalis Principia Mathematica with his handwritten corrections for the second edition. The first edition was published under the imprint of Samuel Pepys who was president of the Royal Society. By the time of the second edition, Newton himself had become president of the Royal Society, as noted in his corrections.

**1692** – Bridget Bishop is the first person to go to trial in the Salem witch trials in Salem, Massachusetts. Found guilty, she is hanged on June 10. Nineteen were hanged, and one, Giles Corey, was pressed to death. Altogether, about 200 people were tried.

Bridget was about sixty years old at her death.

**1858**, The Donati Comet was first seen and named after its discoverer, Giovanni Battista Donati, at Florence. It was the second-brightest comet of the nineteenth century It reached perihelion on 30 Sep 1858. When nearest the earth on 9 Oct 1858, it was about 0.5 AU away, and had developed a scimitar-shaped triple tail. At that time, its very prominent dust tail had with an apparent length of 50°, more than half the distance from the horizon to the zenith, a linear distance of over 72 million km (about 45 million mi). It was the first comet to be photographed. With an orbital period estimated at more than 2000 years, it will not return until about the year 4000. An astronomical unit, AU, equals 93 million miles, the Sun-Earth distance. On Sep 14th, the night before his third debate with Stephen Douglas, Abraham Lincoln sat on the porch of the Jonesboro, Illinois hotel and viewed the comet with a friend.

**1890**The ﬁrst census compiled by machine was started. The previous census took nearly a decade to compute. The 1890 census recorded the U.S. population at 62,979,766. See 8 January 1889. [Kane, p. 169] *VFR ... The 2010 census reported the population of the USA as 308,745,538.

*(*****NOTE...*

1890 Hollerith census card with fields coded |

**1913** Millikan announced the results of his experiment to measure the electron charge. *VFR

**1924 **– U.S. President Calvin Coolidge signs the Indian Citizenship Act into law, granting citizenship to all Native Americans born within the territorial limits of the United States.

**1925** – Because of a lineup revision by Miller Huggins, Wally Pipp is replaced by Lou Gehrig at first base for the New York Yankees, beginning a streak of 2,130 consecutive games played, topped only by Cal Ripken, Jr. in 1995. Exactly 16 years later to the day, in 1941, Gehrig dies from Amyotrophic lateral sclerosis (ALS).

Wally Pip *Wik |

1963 Between May 11 and June 2, Donald B. Gillies found three new primes. When the primes were confirmed the UIUC Math dept (which has a postal branch) used this cancellation stamp on all mail from roughly 1964 - 1976, when Appel and Haken proved the four color theorem ("Four Colors Suffice") and a new stamp was created. Trivia question : how far away from Gillies did Appel live in Urbana Illinois ??

Answer : He lived 3 houses away. *Wik

*Wik courtesy of Chris Caldwell |

**1966** Surveyor 1 Makes soft-landing on the moon. It was the first lunar soft-lander in the unmanned Surveyor program of the National Aeronautics and Space Administration (NASA, United States). It gathered data about the lunar surface that would be needed for the manned Apollo Moon landings that began in 1969. The successful soft landing of Surveyor 1 on the Ocean of Storms was the first by an American space probe onto any extraterrestrial body, and it occurred just four months after the first Moon landing by the Soviet Union's Luna 9 probe.

Surveyor 1 was launched May 30, 1966 and landed on the Moon on June 2, 1966. It transmitted 11,237 still photos of the lunar surface to the Earth by using a television camera and a sophisticated radio-telemetry system. *Wik

*Wik |

**BIRTHS**

**1817**

**George Corliss, an American mechanical engineer, was born June 2, 1817. In 1849, Corliss applied for a patent for a novel kind of valve gear for a stationary steam engine (second image). The steam engine was then almost 75 years old, and steam engines still used a sliding valve system that had changed little since the days of James Watt. Four of them were required to admit and exhaust steam for both the up and down strokes. The problem with sliding valves is that they are constantly exposed to a wide temperature range, as the steam cools and condenses, which means they expand and contract incessantly, and it is difficult to regulate the beginning and end of each cycle with precision.**

**Corliss invented a set of four rotary valves, each linked to a central rotating device called a wrist plate, as we can see in one of his patent illustrations (third image). Each valve stays at a constant temperature, and the intake cutoff points can be regulated with great precision. As a result, a Corliss engine is about 30% more efficient than a Watt engine. In manufacturing, increased efficiency is the blessing of all blessings. Corliss engines could also run at a constant speed under a variety of loads, due to a clever system of governors that were also included in the 1849 patent, which was a very useful feature for an engine being used to power a factory. So Corliss engines took over the place of honor in the factory workplace, in the first great steam engine revolution since Watt invented the thing in the first place.**

**At the 1876 Centennial Exhibition in Philadelphia, meant to showcase America's newfound industrial power, the central fixture was a mammoth operating Corliss steam engine, which powered everything else at the fair . It was built by Corliss at his factory in Rhode Island and donated to the Exhibition.**

**======================================================================**

**1884 ****Henry Thomas Herbert Piaggio**(2 June 1884–26 June 1967) graduated from Cambridge and then worked at the University of Nottingham. He is best known for his text-book on Differential Equations.

**1895 Tibor Radó** (June 2, 1895 – December 29, 1965) was a Hungarian mathematician who moved to the USA after World War I. He was born in Budapest and between 1913 and 1915 attended the Polytechnic Institute. In World War I, he became a First Lieutenant in the Hungarian Army and was captured on the Russian Front. He escaped from a Siberian prisoner camp and, traveling thousands of miles across Arctic wasteland, managed to return to Hungary.

He received a doctorate from the University of Szeged in 1923. He taught briefly at the university and then became a research fellow in Germany for the Rockefeller Foundation. In 1929, he moved to the United States and lectured at Harvard University and the Rice Institute before obtaining a faculty position in the Department of Mathematics at Ohio State University in 1930. In 1935 he was granted American citizenship.

In the 1920s, he proved that surfaces have an essentially unique triangulation.

In 1933, Radó published "On the Problem of Plateau" in which he gave a solution to Plateau's problem, and in 1935, "Subharmonic Functions".

In World War II he was science consultant to the United States government, interrupting his academic career.

He became Chairman of the Department of Mathematics at Ohio State University in 1948.

His work focused on computer science in the last decade of his life and in May 1962 he published one of his most famous results in the Bell System Technical Journal: the Busy Beaver function and its non-computability ("On Non-Computable Functions").

In computability theory, a busy beaver (from the colloquial expression for an "industrious person") is a Turing machine that attains the maximum "operational busyness" (such as measured by the number of steps performed, or the number of nonblank symbols finally on the tape) among all the Turing machines in a certain class. The Turing machines in this class must meet certain design specifications and are required to eventually halt after being started with a blank tape. *Wik

Courtesy of The Ohio State University Archives

**1916 Abraham Seidenbergwas** (June 2, 1916 – May 3, 1988) known for his research to commutative algebra, algebraic geometry, differential algebra, and the history of mathematics. He published Prime ideals and integral dependence written jointly with I S Cohen which greatly simplified the existing proofs of the going-up and going-down theorems of ideal theory. He also made important contributions to algebraic geometry. In 1950, he published a paper called The hyperplane sections of normal varieties which has proved fundamental in later advances. In 1968, he wrote Elements of the theory of algebraic curves, a book on algebraic geometry. He published several important papers.*Wik

**DEATHS**

**1785 Jean Paul de Gua de Malves**, (1713, Carcassonne – June 2, 1785, Paris) In 1740 he published a work on analytic geometry which, without the differential calculus, he found tangents, asymptotes, and various singular points of an algebraic function. He gave the proof of Descartes rule of signs which is found in modern texts. It is not known if Descartes ever proved it, and Newton seemed to think it was "obvious". (A short account of the history of mathematics By Walter William Rouse Ball)

**1917 William Henry Besant** FRS (1 November 1828, Portsea, Portsmouth – 2 June 1917, Cambridge) was a British mathematician, brother of novelist Walter Besant.

In a competition, William won a scholarship to Corpus Christi College, Cambridge in 1844. He took part in Cambridge Mathematical Tripos in 1850, gaining the title of Senior Wrangler. He was also winner of Smith's Prize.

In 1853 William became a Fellow of Saint John's College, Cambridge where he was a lecturer in mathematics until 1889. His pupils included William Burnside, A. W. Flux and G. B. Mathews. Besant served as an examiner for Tripos in 1856, 1857, and 1885. He was also an examiner for University of London from 1859 to 1864. Besant was also a coach for students taking the Tripos; twenty-one of his students placed in the ranks of top ten wranglers. According to Mathews, "he had the great advantage (for a coach) of being equally good in geometry, analysis, and dynamics."

In 1859 Besant vacated his Fellowship with Saint John's college to marry Margaret Elizabeth Willis, daughter of Rev. Robert Willis, a professor of natural philosophy at Cambridge. They had two sons and a daughter. In 1863 Besant published Elementary Hydrostatics, a textbook on fluid statics containing mathematical exercises such as students might face in examination. The book was reprinted several times, and revised in 1892. He also wrote Treatise on Hydromechanics (1867) covering fluid mechanics. His book Elementary Conics came out in 1901.

Besant was a Fellow of the Royal Astronomical Society from 10 February 1854. He became a Fellow of the Royal Society in 1871. In 1883 Cambridge University bestowed upon him, and Edward Routh, the degree Sc.D.. He died on 2 June 1917 and is buried at the Parish of the Ascension Burial Ground in Cambridge.

He created the term Glissettes for his studies on the objects for Notes on Roulettes and Glissettes(1871). He writes in the preface:

*Wik

**1929 Otto Schreier** (3 March 1901 in Vienna, Austria - 2 June 1929 in Hamburg, Germany) He will be best remembered for his work on subgroups of free groups which he studied in his habilitation thesis. He published the results in 1927 in the paper Die Untergruppen der freien Gruppe which is described as "... one of the most important papers ever published on combinatorial group theory. It took a long time for all its aspects to become effective, and it contains much more than the title indicates. "

In January 1926 Schreier attended a lecture given by Reidemeister in Hamburg on finding presentations for normal subgroups of finitely presented groups. Reidemeister published his method later in 1926. Schreier, who took a more algebraic approach compared to Reidemeister's geometrical approach, was able to extend Reidemeister's method to arbitrary subgroups and, by cleverly choosing generators for the subgroup, was able to greatly simplify the presentation obtained. Schreier published his method in his 1927 paper Die Untergruppen der freien Gruppe.

Other work of Schreier is described as follows:

... Schreier made important contributions to other parts of group theory. The classical Lie groups ... can be considered as topological spaces. Schreier (1927) showed that the fundamental group of such a space is always abelian. Schreier (1928) found an important refinement of the fundamental Jordan-Hölder theorem, 39 years after the publication of Hölder's paper. It is rare that such a widely used and basic theorem can be deepened after such a long time. (In this case, something even more unusual happened. Zassenhaus (1934) discovered a second improvement of the theorem.)

*SAU

**1942 Andrew Russell Forsyth** (18 June 1858, Glasgow – 2 June 1942, South Kensington) was a Scottish mathematician. He worked in diﬀerential equations, and function theory.

He studied at Liverpool College and was tutored by Richard Pendlebury before entering Trinity College, Cambridge, graduating senior wrangler in 1881.[1] He was elected a fellow of Trinity and then appointed to the chair of mathematics at the University of Liverpool at the age of 24. He returned to Cambridge as a lecturer in 1884 and became Sadleirian Professor of Pure Mathematics in 1895. He resigned his chair in 1910 after an affair with Marion Amelia Boys, the wife of C. V. Boys, who divorced her husband to marry him: this was unacceptable in Edwardian Cambridge. He became professor at the Imperial College of Science in 1913 and retired in 1923, remaining mathematically active into his seventies. He was elected a Fellow of the Royal Society in 1886 and won its Royal Medal in 1897.

He is now remembered much more as an author of treatises, than as an original researcher. His books have, however, often been criticized (for example by J. E. Littlewood, in his Mathematician's Miscellany). E. T. Whittaker was his only official student, according to the Mathematical Genealogy site. *Wik

**1946 William Peddie FRSE LLD** (31 May 1861 – 2 June 1946) was a Scottish physicist and applied mathematician, known for his research on colour vision and molecular magnetism.

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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