We can only see a short distance ahead,

but we can see plenty there that needs to be done.

Alan Turing, From his paper on the Turing test

The 175th day of the year; 175 is the smallest number

*n*greater than 1 such that

*n*^6 + 6 is prime.

*Prime Curios

1191 "In the month of June, the Vigil of the Nativity of St John the Baptist (June 23), the 9 th day before the Kalends of

July, on the 27 th day of the Moon, at the 9 th hour of the day, the Sun was eclipsed and it lasted for three hours; the Sun was so obscured

that the darkness arose over the Earth and stars appeared in the sky. And when the eclipse withdrew, the Sun returned to its

original beauty." This was an annular solar eclipse.

1585 Thomas Harriot arrived oﬀ the coast of Virginia (actually Cape Lookout, NC). He was the ﬁrst substantial mathematician to visit North America. [John W. Shirley in Thomas Harriot: A Biography, 1983, p. 129; Thanks to Kullman] *VFR Thomas Harriot's name was once synonymous with a common method of solving quadratics taught in nearly every high school. Once commonly called Harriot's Method, today it is simply referred to as factoring.

And how did he come to be in the exploration of Virginia?? Here is the story from Encyclopedia Virginia, 2010:

Thomas Hariot (often spelled Harriot) was an English mathematician, astronomer, linguist, and experimental scientist. During the 1580s, he served as Sir Walter Raleigh's primary assistant in planning and attempting to establish the English colonies on Roanoke Island off the coast of present-day North Carolina. He taught Raleigh's sea captains to sail the Atlantic Ocean using sophisticated navigational methods not well understood in England at the time. He also learned the Algonquian language from two Virginia Indians, Wanchese and Manteo. In 1585, Hariot joined the expedition to Roanoke, which failed and returned to England the next year. During his stay in America, Hariot helped to explore the present-day Outer Banks region and, farther north, the Chesapeake Bay. He also collaborated with the artist John White in producing several maps notable at the time for their accuracy. Although Hariot left extensive papers, the only work published during his lifetime was "A Briefe and True Report of the New Found Land of Virginia", which evaluated the economic potential of Virginia. The report appeared most impressively in Theodor de Bry's 1590 edition that included etchings based on the White-Hariot maps and White's watercolors of Indian life. After a brief imprisonment in connection to the Gunpowder Plot (1605), Hariot calculated the orbit of Halley's Comet, sketched and mapped the moon, and observed sunspots. He died in 1621.

1676 Newton, via Oldenburg, sent his famous Epistola prior to Leibniz. It contained the ﬁrst use of fractional exponents as well as the newly discovered binomial theorem.*VFR

**In 1775**, the first American-made book was advertised in Philadelphia, Penn. Titled Impenetrable Secret, the book was printed and sold by Story and Humphreys. Their advertisement in the Pennsylvania Mercury announced it was "printed with types, paper and ink manufactured in this Province."*TIS

**1835**Mobius receives a letter from Bellavitis with a method for adding and subtracting non-collinear vectors. (A history of vector analysis: the evolution of the idea of a vectorial system By Michael J. Crowe) A geometrical work by Bellavitis was published in 1832 which also contains vector type quantities. His basic objects are line segments AB and he considers AB and BA as two distinct objects. He defines two line segments as 'equipollent' if they are equal and parallel, so, in modern notation, two line segments are equipollent if they represent the same vector. Bellavitis then defines the 'equipollent sum of line segments' and obtains an 'equipollent calculus' which is essentially a vector space. *SAU

**1993**Over the course of three lectures delivered at Isaac Newton Institute for Mathematical Sciences on June 21, 22, and 23 of 1993, Wiles announced his proof of the Taniyama–Shimura conjecture, and hence of Fermat's Last Theorem. There was a relatively large amount of press coverage afterwards. After announcing his results, (Nick) Katz was a referee on his manuscript and he asked Wiles a series of questions that led Wiles to recognize that the proof contained a gap. There was an error in a critical portion of the proof which gave a bound for the order of a particular group: the Euler system used to extend Flach's method was incomplete. Wiles and his former student Richard Taylor spent almost a year resolving it. Wiles indicates that on the morning of September 19, 1994 he realized that the specific reason why the Flach approach would not work directly suggested a new approach with the Iwasawa theory which resolved all of the previous issues with the latter and resulted in a CNF that was valid for all of the required cases. On 6 October Wiles sent the new proof to three colleagues including Faltings. The new proof was published and, despite its size, widely accepted as likely correct in its major components. *Wik

2013 The Moon will make its closest approach to the Earth (at perigee) for the year on Sunday, 23 June, at 11:11 (UTC), and at this time the Moon will be 356,989 km from the Earth (that means 221,823 miles for us non-geeks). *Bob Mrotek

**1902 Dr. Howard T. Engstrom**(23 Jun 1902, 9 Mar 1962 at age 59)American computer designer who promoted the first commercially available digital computer, the Univac. As a Yale professor he had written a paper on the mathematical basis for cryptanalysis techniques. During WW II he was called to the Navy and placed in command of the OP-20-G automated machines "Research Section" for message decryption. After the war, he was a co-founder of Engineering Research Associates, a private company to work on electronic digital circuit technology for the Navy on a contract basis, with former Navy researchers. ERA delivered its first Atlas computer to the National Security Agency in Dec 1950. As vice president for research, Engstrom took the initiative to make a commercial version, renamed Univac.*TIS

**1912 Alan Mathison Turing**(23 June 1912 – 7 June 1954) born. This British mathematician was one of the founders of recursion theory, invented the Turing machine (an abstract model of a computer), did important work in cryptography, and invented the computer. *Alan Turing. The Enigma by Andrew Hodges, 1983.

**1891 Wilhelm Eduard Weber**(24 October 1804 – 23 June 1891) German physicist who investigated terrestrial magnetism. For six years, from 1831, Weber worked in close collaboration with Gauss. Weber developed sensitive magnetometers, an electromagnetic telegraph (1833) and other magnetic instruments during this time. His later work (1855) on the ratio between the electrodynamic and electrostatic units of charge proved extremely important and was crucial to Maxwell in his electromagnetic theory of light. (Weber found the ratio was 3.1074 x 108 m/sec but failed to take any notice of the fact that this was close to the speed of light.) Weber's later years were devoted to work in electrodynamics and the electrical structure of matter. The magnetic unit, weber, is named after him.*TIS

1891 Norman Robert Pogson (23 Mar 1829; 23 Jun 1891 at age 62) English astronomer who devised the magnitude scale of the brightness of stars (1850) now in use. He divided the classical scale in which a first magnitude star is one hundred times brighter than a sixth magnitude star using five integer steps. Each step represents a fifth-root of 100 (about 2.512) increase in brightness. The Sun's magnitude on this scale is -26.91, whereby negative numbers denote objects brighter than first magnitude. Sirius is magnitude -1.58, Aldebaran is 1 and the faintest star detected is 30. His interest in astronomy began in his youth; by age 18 he had calculated orbits for two comets. He discovered 8 asteroids, 21 new variable stars and compiled a massive star catalogue. In 1860 he moved to India for the remainder of his life's work.*TIS

**1892 Pierre Ossian Bonnet**(22 December 1819, Montpellier – 23 June 1892, Paris)died. He worked on minimal surfaces, geodesics, and integral geometry. *VFR Bonnet made major contributions introducing the notion of geodesic curvature. A formula for the line integral of the geodesic curvature along a closed curve is known as the Gauss-Bonnet theorem. Gauss published a special case.

Credits

*CHM=Computer History Museum

*FFF=Kane, Famous First Facts

*NSEC= NASA Solar Eclipse Calendar

*SAU=St Andrews Univ. Math History

*TIS= Today in Science History

*VFR = V Frederick Rickey, USMA

*Wik = Wikipedia

*WM = Women of Mathematics, Grinstein & Campbell