Mathematics

Biography of the Mathematician Christian Goldbach



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Christian Goldbach is a mathematician famous for a conjecture in number theory named after him (Goldbach Conjecture).  It claims that any even integer greater than two can be expressed as the sum of two prime numbers.  There was a million dollar prize a few years ago for its proof, but no one claimed it.  Examples are 2+2=4, 7+3=10, 7+19=16, and 23+29=52.  He also studied law.        


He was born in Konigsberg, Prussia on March 18, 1690.  His father was a Protestant minister in Konigsberg.  He attended the Royal Albertus University.  He became a mathematics professor and historian at St. Petersburg Academy of Sciences in 1725 after writing to President of the proposed university  L L Blumentrost in Riga.  He tutored Czar Peter II in 1728.  From 1710 to 1724 he toured Europe and met some of the greatest minds of mathematics, including Gottfried Leibniz, Leonhard Euler, and Nicholas Bernoulli.  He visited England, Holland, Italy, and France.  He entered the Russian Ministry of Foreign Affairs in 1742. 


Goldbach met Leibniz in 1711 in Leipzig, Germany.  From 1711 to 1713, they wrote letters to each other in Latin.  He met Nicholas Bernoulli in 1712 in England.  In 1724 Goldbach returned to Konigsberg, where he met Jakob Hermann (Swiss mathematician 1678-1733).                   


He would correspond with several of these mathematicians.  One of these letters to the Swiss mathematician Leonhard Euler in 1742 introduced the aforementioned Goldbach Conjecture .   He also made a similar conjecture, the Ternary Conjecture, which claims that every odd number is the sum of three prime numbers.  A prime number is any integer that cannot be evenly divided by any other integer except one and itself.


In their letters, Euler and Goldbach discussed Fermat numbers (2^n+1), Mersenne numbers (2^n-1), perfect numbers, polynomials representing prime numbers, and Fermat’s Last Theorem.  Fermat’s Last Theorem claims that there are no solutions to the equation x^n+y^n=z^n unless n=2, which is the Pythagorean Theorem (proven by Pythagoras of ancient Greece).  Andrew Wiles recently proved the theorem.     


He made sucessful advances in the theory of curves and the integration of differential equations.  He proved a few conjectures on perfect powers, one of which was the Goldbach-Euler Theorem.  This theorem states that the sum of 1/(p-1) over the set of perfect powers p converges to 1.  Euler attributed the proof to Goldbach in a paper he wrote in 1737 titled “Variae Observationes Circa Series Infinitas”.  He also made important contributions to infinite series.     


There was a breakthrough in the progress toward Goldbach’s conjecture in 1930.  The Soviet mathematician Lev Genrikhovich Shnirelman proved that every positive integer can be expressed as the sum of at most 20 prime numbers.  In 1937, a soviet mathematician named Ivan Matveyevich Vinogradov proved that every “sufficiently large” odd positive integer can be expressed as the sum of no more than three prime numbers.  However, he did not say how large the “sufficiently large” odd Integer should be.

Goldbach died on November 20, 1764 in Moscow, Russia. 




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