#helfgott

[efleury-blog]

Chapeau l'artiste !

Chapeau l’artiste !

David Helfgott n’arrête pas de parler…. et alors ?

Arte diffuse un documentaire sur ce pianiste génial. Le film Shine lui a été consacré et raconte son parcours.

C’est visible en cliquant sur ce lien : https://www.arte.tv/fr/videos/068387-000-A/hello-i-am-david/

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Rachmaninov Fish at The Shore Club #lifeisbeautiful #Helfgott #youcanfindbeautyeverywhere #justlook (at The Shore Club Miami Beach)

[normalmodes]

Yesterday, Harald Andrés Helfgott (who got his B.A. from Brandeis University) posted a 133-page proof of the weak Goldbach conjecture to the arXiv. This is part of a conjecture that mathematicians have been working to prove for 270 years since it was first suggested in the letter above. 

The origin of this problem is in this letter written by Christian Goldbach to Leonhard Euler on June 7th, 1742. The first part of his conjecture is in the main body of the letter (translated into English here from the original German):

Every integer which can be written as the sum of two primes, can also be written as the sum of as many primes as one wishes, until all terms are units.

The second part is written in the margin:

Every integer greater than 2 can be written as the sum of three primes.

This second part is referred to as the 'weak Goldbach conjecture' because it would be proved by proving the first part (the 'strong' conjecture).

Helfgott has solved the 'three-prime' problem for any odd number greater than 5, which is a great number of numbers!  You can read the posting yourself here, at the arXiv.

He posted a comment on the blog of another mathematician, Terry Tao, who has also been working on the Goldbach conjecture, commenting on some back-and forth between the analytic and numerical aspects of the proof:

The least one can say is that the problem is now mortally wounded, and that the way it is finished off is now in part a matter of expediency and in part a matter of taste.

Problems of primes are especially interesting for mathematicians because they're of great concern to encryption theory. One of the main ways of encrypting information is using the RSA algorithm, which (very) basically assigns the encrypted information large prime values, comes up with other large prime numbers, and stores information as the product of the two. Factoring large numbers is extremely difficult, and the safety of encrypted keys relies on that difficulty. However, given the prime numbers used to encrypt, recovering the original information is a non-issue.

[polynumerous]

The ternary Goldbach conjecture, or three-primes problem, asserts that every odd integer N greater than 5 is the sum of three primes. The present paper proves this conjecture.

Harald A. Helfgott (via arXiv.org) This is a pretty big deal in my line of work.

[monseuldesir]

David Helfgott Up Close (by breathingtube)

Rachmaninov Preludes, Op.32 Nos. 5 & 12

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