German mathematician (1845-1918) who created set theory, which has become a fundamental theory in mathematics. Cantor established the importance of one-to-one correspondence between the members of two sets, defined infinite and well-ordered sets, and proved that the real numbers are more numerous than the natural numbers. ALS in German, two pages on adjoining sheets, 4.5 x 3.5, April 25, 1895. Handwritten letter to important French mathematician Charles-Ange Laisant, in which Cantor explains his strategy to prove the long-standing (and, to this day, unsolved) Goldbach’s conjecture, a fascinating open problem in arithmetic which states that every even number greater than 2 is the sum of two prime numbers. This exceptional document sheds light on the efforts of the creator of set theory to tackle a fundamental question regarding the very nature of numbers, as well as on his prominent role in advocating the idea of an International Congress of Mathematicians.
In part: "My dear colleague, a few days ago I was sent a separate offprint of the Table for the Goldbach Theorem published in the ‘French Association.’ However, I have not yet received the 50 copies which I have ordered. I draw your attention to the very striking phenomenon that you may wish to highlight in your magazine." Cantor goes on describing technical details about relative maxima in the number of decompositions of integers as a sum of prime numbers, quoting his data to make his point. He then continues: "And so it goes on without exception until the end of the table. Is it not strange? It would be extremely interesting if the table continued until 2N=2000. How are going our plans regarding the International Congress of Mathematicians? The matter has probably been discussed at the occasion of the centenary celebrations of the École Normale. From the newspaper, I see that Messrs ‘Amandus,’ Schwarz and Fuchs have been there. Incidentally, ‘the great’ Felix Klein is said to be very interested in the idea of the congress." In fine condition.
The recipient of this letter, Charles-Ange Laisant (1841-1920), was a French mathematician and politician. In 1888, he served as President of the Société Mathématique de France. Cantor played a prominent role in establishing the International Congress of Mathematicians. He is credited along with Felix Klein (mentioned in this letter) with putting forward the idea of such a congress in the 1890s. Apart from its wonderful mathematical content, this letter sheds a very precious light on the early history of the ICM, three years before the Zurich congress in 1897. Schwarz and Fuchs were prominent mathematicians at the time. ‘Amandus’ may be a nickname by which Cantor refers to another mathematician.
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