**I began to understand that pure mathematics was more than a collection of random tools mainly fashioned for use in the Cambridge treatment of natural philosophy.**

The 170th day of the year; the start of a record-breaking run of consecutive integers (170-176) with an odd number of prime factors.

170 is the smallest number that can be written as the sum of the squares of 2 distinct primes, where each of these primes is the square of a prime added to another prime (170 = (2

^{2}+ 3)

^{2}+ (3

^{2}+ 2)

^{2}).

*Prime Curios

170 is the largest integer for which its factorial can be stored in double-precision floating-point format. This is probably why it is also the largest factorial that Google's built-in calculator will calculate, returning the answer as 170! = 7.25741562 × 10

^{306}. (For 171! it returns "infinity".)

170 is the smallest number n for which phi(n)(the number of integers relatively prime to 170=64=8

^{2}) and sigma(n) (the sum of the divisors of 170=324=18

^{2}) are both square.

**1558**Robert Recorde’s will was admitted to probate, after he died in prison. He introduced the equals sign in The Whetstone of Witte (1557) with the words: “And to avoide the tediouse repetition of these woordes: is equalle to: I will sette as I doe often in woorke use, a pair of paralleles, or Gemowe lines of one lenghte, thus: because noe .2. thynges, can be moare equalle.” “Gemowe” (

*think Gemini*)is an old French work meaning “twin.”. *VFR When they are asked what they would use if this was not available, it seems difficult for students to imagine a different symbol.

Image from Wikipedia.

**1584**Jacob Christmann appointed professor of Hebrew at Heidelberg. In 1595 he defended the view that the circle could only be approximately squared. *VFR

**1864**Lewis Carroll ﬁnally decided to write up Alice’s Adventures in Wonderland. [Stuart Dodgson Collingwook, The Life and Letters of Lewis Carroll (1898), p. 96]

**1908**Alan Archibald Campbell Swinton took the first x-ray images in Britain in January 1896 and by a year later the medical professions were bringing him surgical cases for analysis. But "on this day he predicted exactly how another magic box would work, in a letter to Nature. He called it ‘Distant Electric Vision’, but we know it now as television." *Keith Moore, http://blogs.royalsociety.org

**1928**, aviator Amelia Earhart became the first woman to fly across the Atlantic Ocean. She had accepted the invitation of the American pilots Wilmer Stultz (1900-29) and Louis Gordon to join them on the transatlantic flight. The crossing from Newfoundland to Wales took about 21 hours. Amelia Earhart went on to establish herself as a respected role model, tirelessly demonstrating that young women were as capable as men in succeeding in their chosen vocations. In 1935 she crossed the Atlantic solo in record time: 13 hr 30 min. *TIS

**1983**Sally Ride, astrophysicist, becomes the ﬁrst American woman in space. The Soviets were ahead by twenty years and two days.*VFR

**1799 William Lassell**(18 June 1799 – 5 October 1880) was a wealthy amateur English astronomer. He set up an observatory at Starfield, near Liverpool. England, He built his own 24" diameter telescope, and devised steam-driven equipment for grinding an polishing the speculum metal mirror. This telescope was the first of its size to be mounted "equitorially" to allow easy tracking of the stars. He discovered Triton, a moon of Neptune, and Ariel and Umbriel, satellites of Uranus. Later, Lassell built a 48" diameter telescope with th same design and took it to Malta for observations with clearer skies.*TIS

**1818 Pietro Angelo Secchi**(18 Jun 1818, 26 Feb 1878 at age 59) Italian Jesuit priest and astrophysicist, who made the first survey of the spectra of over 4000 stars and suggested that stars be classified according to their spectral type. He studied the planets, especially Jupiter, which he discovered was composed of gasses. Secchi studied the dark lines which join the two hemispheres of Mars; he called them canals as if they where the works of living beings. (These studies were later continued by Schiaparelli.) Beyond astronomy, his interests ranged from archaeology to geodesy, from geophysics to meteorology. He also invented a meteorograph, an automated device for recording barometric pressure, temperature, wind direction and velocity, and rainfall.*TIS

**1858 Andrew Russell Forsyth**(18 June 1858, Glasgow – 2 June 1942, South Kensington) studied at Liverpool College and was tutored by Richard Pendlebury before entering Trinity College, Cambridge, graduating senior wrangler in 1881. 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. *Wik

In 1893 he published

*Theory of functions of a complex variable*which had such an impact at Cambridge that function theory dominated there for many years. Whittaker writes... that this text:-... had a greater influence on British mathematics than any work since Newton's Principia.

However the reputation of the book outside Britain was not high. In fact this is not surprising since the whole thrust of the book was to bring the great advances of Continental mathematics to Cambridge which Forsyth rightly saw as living in the past. He was well equipped to undertake this task for he traveled widely and, being a good linguist, was able to appreciate the advances made by authors writing in French and German.

On Cayley's death Forsyth was appointed to his chair in 1895 becoming the Sadleirian professor of Pure Mathematics. However his preference for technical mastery rather than rigorous analysis meant that he failed to inspire future pure mathematicians. In fact one would have to say that Forsyth was unlucky, for although he saw the importance of Continental mathematics, at the same time his greatest strengths lay in his ability to handle complex formulae. He therefore excelled at precisely the style of mathematics which he himself campaigned successfully to replace at Cambridge.

**1884**

**Charles Weatherburn (**18 June, 1884 in Australia - 1974 in Australia) worked on vector analysis and differential geometry.*SAU

**1884 Frieda Nugel**(18 June 1884 in Cottbus, Brandenburg, Germany- 6 Nov 1966 in Bad Godesberg, Bonn, Germany) was a German mathematician who was one of the first women to receive a doctorate in Germany *SAU

**1913**

**Oswald Teichmüller'**s (June 18, 1913 – September 11, 1943) main contribution is in the area of geometric function theory.*SAU

**1926 Allan Rex Sandage**(June 18, 1926 – November 13, 2010) U.S. astronomer who (with Thomas A. Matthews) discovered, in 1960, the first optical identification of a quasi-stellar radio source (quasar), a starlike object that is a strong emitter of radio waves. Although a strange source of radio emission, in visible light, it looked like a faint star. Yet this object was emitting more intense radio waves and ultraviolet radiation than a typical star. He is best known for determining the first reasonably accurate value for the Hubble constant and the age of the universe.*TIS & Wik

**DEATHS**

**1818 George Baron**(?? , June 18, 1818) was a mathematician who emigrated from Northumberland, England to Hallowell, Maine in the United States, thereafter moving to New York. He was the first superintendent and mathematics professor at what would become the United States Military Academy in 1801 and the founder and editor-in-chief of the Mathematical Correspondent, which was the first American "specialized scientific journal" and the first American mathematics journal, first published May 1, 1804.

Baron was first offered the position at the fledgling academy at West Point, New York by the newly elected United States President Thomas Jefferson's Secretary of War Henry Dearborn, a friend of Baron's who had lived near him in Maine. After agreeing upon salary and perks, instruction began on September 21, 1801 employing the use of Charles Hutton's A Course in Mathematics and a blackboard, the first recorded use of the latter in America. In October, there was a disagreement between Baron and one of the cadets, Joseph Gardner Swift. Swift was called upon to apologize and was reprimanded for the language he employed against Baron, but went on to become the Military Academy's first graduate, and later a Brigadier General. For a variety of reasons, Baron was court-martialled in December, and Major Jonathan Williams became the supervisor and Captain William Amherst Barron became the instructor of mathematics.

Baron became a teacher of mathematics in New York City, there joining the Theistical Society of New York, a deist group led by Elihu Palmer that came to public attention in the course of a pamphlet war between supporters of United States Vice President Aaron Burr and supporters of then United States Senator from New York DeWitt Clinton. *Wik

Baron may have been one of the earliest users of a blackboard in the US as, "use of the blackboard was a favorite method of Baron." *Edward S Holden, The Centenial of the US Military Academy at West Point, New York

**1922 Jacobus Cornelius Kapteyn**, (January 19, 1851, Barneveld, Gelderland – June 18, 1922) Dutch astronomer who used photography and statistical methods in determining the motions and spatial distribution of stars. Such work was the first major step after the works of William and John Herschel. He tried to solve the questions of space density of stars as a function of distance from the sun, and the distribution of starts according to brightness per unit volume. Some of his results had lasting value, but some were superceded because he had failed to account for the interstellar absorption. In studies using proper motion to determine stellar distances, he discovered stellar motions are not random, as previously thought, but that stars move in two "star streams" (1904). He introduced absolute magnitude and colour index as standard concepts.*TIS

**1935 Alexander von Brill**(20 September 1842 – 18 June 1935) died. He worked on algebraic geometry and the theory of algebraic functions. Born in Darmstadt, Hesse, he attended University of Giessen where he earned his doctorate under supervision of Alfred Clebsch. He held a chair at the University of Tübingen, where Max Planck was among his students.*Wik

**1980 Kazimierz Kuratowski**(February 2, 1896 – June 18, 1980) He worked in the area of topology and set theory. He is best known for his theorem giving a necessary and sufficient condition for a graph to be planar.*SAU

**Kuratowski's theorem**: "A finite graph is planar if and only if it does not contain a subgraph that is a subdivision of

*K*

_{5}(the complete graph on five vertices) or

*K*

_{3,3}(complete bipartite graph on six vertices, three of which connect to each of the other three)." (in simpler, but less exact terms, it can be drawn in such a way that no edges cross each other." The well-known recreational problem of connecting three houses to three utilities is not possible to draw because it is

*K*

_{3,3}(below). The utility problem posits three houses and three utility companies--say, gas, electric, and water--and asks if each utility can be connected to each house without having any of the gas/water/electric lines/pipes pass over any other. (1913 Dudeney: first publication of Gas, Water and Electricity Problem. according to David Singmaster, Gardner says 1917) (see June 21)

_{}

Kuratowski proved his theorem in 1930. Forty years later the dedication of Frank Harary’s classic Graph Theory was:

To KASIMIR KURATOWSKI,(In fact three other almost simultaneous discoveries of the theorem are recorded: Orrin Frink and Paul Althaus Smith; Lev Semenovich Pontrjagin; and Karl Menger!) With thanks to *

Who gave K_{5}and K_{3,3}

To those who thought planarity

Was nothing but topology.

**theoremoftheday**

**theoremoftheday**

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