"[The universe] can not be read until we have learnt the language and become familiar with the characters which it is written. It is written in mathematical language, and the letters are triangles, circles and other geometrical figures, without which means it is humanly impossible to comprehend a single word."Galileo Galilei , physician, mathematician and teacher revolutionized the Tychonic system that stated that everything in the universe revolved around the sun. He became one of the first pioneers in astronomy that based his arguments on observation and mathematical analysis of planetary orbits. He taught medical students astronomy in order to make use of astrology in their diagnosis. Throughout his career as a mathematician and a workman, Galileo devised telescopes that enabled him to view Venus, Neptune and the moons of Jupiter. Galileo's unconventional forms of astronomy and natural philosophy, however, threatened Catholic scripture. As a result, Galileo was charged with heresy and placed under house arrest in 1632. Despite the efforts of the Catholic Church to silence Galileo, several of his books were smuggled out of Italy and published for the international market.
-Galileo Galilei, Opere Il Saggiatore p. 171.
Author: Henry D. Sheen
References:
http://www-history.mcs.st-and.ac.uk/~history/Mathematicians/Galileo.html
Marin Mersenne was a French mathematician born in 1588. Mersenne was a Franciscan friar who made it his business to become acquainted and correspond with other French mathematicians and foreign contemporaries. During this period, Mersenne held weekly meeting with geometricians like Pascal, Descartes, Roberval and Desargues. These informal meetings would later serve as the foundation for the French Academy.
In 1634 Mersenne published a translation of Galileo's mechanics; in 1644 he published his "Cogitata Physico-Mathematica" containing accounts of some experiement in physics. This is his best known work. He also wrote a synopsis of mathematics which was published posthumously in 1664. The average student of mathematics, though, is probably reminded of prime numbers when the name "Mersenne" enters the conversation.
In the preface to his "Cogitata," Mersenne stated the the numbers 2n-1 were prime for n = 2, 3, 5, 7, 13, 17, 19, 31, 67, 127 and 257, and were composite for all other integers less than 257. His incorrect conjecture was only slightly better than those of other mathematicians, but so much so to have his name attached to the numbers of this form.
"When 2n-1 is prime, it is said to be a Mersenne prime."
Although it was obvious that Mersenne could not have tested all of these cases (in fact, he admitted as much), neither could his peers. It was not until a century later that Euler verified the n = 31 case. Approximately another century later, Lucas verified the n = 127 case. By 1947, Mersenne's range from 2 to 258 had been completely checked out. The correct list is for when n = 2, 3, 5, 7, 13, 17, 19, 31, 61, 89, 107, amd 127. Two interesting theorems sprung forth from this work:
Theorem 1: k is an even perfect number iff it has the form2n-1*2n-1
where 2n-1 is prime.
Theorem 2: If 2n-1 is prime, then n is
prime.
So, in essence, the search for Mersenne primes is also a search for even perfect numbers. The last and largest Mersenne prime was found by 19-year old southern California college student Rolando Clarkson on January 27, 1998. What was it?
23,021,377-1. Calculate that!
Author: Clarence L. Terry
References:
http://www.utm.edu/research/primes/mersenne.shtml
http://www.mersenne.org/prime.html
http://www.maths.tcd.ie/pub/HistMath/People/RBallHist.html
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