29. August 2017

Two down, five to go A further Millennium Problem solved!?

A computer scientist from the University of Bonn believes to have solved one of the great mathematical mysteries.

Two down, five to go

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If Norbert Blum is right, he has solved one of the most challenging mathematical problems. Remarkable, as many researchers have tried, in vain, their hand at solving the P versus NP Problem. We met the computer scientist from the University of Bonn for lunch.

The meal fits the person: Fried fish and potatoes - grounded and without bells and whistles. This is how we experience Norbert Blum at lunch. The computer scientist from the University of Bonn does not want to say anything yet, he wants to wait to see how his fellow researchers react to his latest publication. A publication heavy with substance.

Entitled "A Solution of the P versus NP Problem", Norbert Blum thinks he has solved one of the great mathematical problems. The P versus NP Problem is one of the seven so-called Millennium Problems, identified by the Clay Mathematics Institute in Cambridge at the turn of the century. As an incentive, the institute placed prize money of over one million US dollars for anyone who could solve one of the problems. So far only one has been answered.

Norbert Blum could now have solved the P versus NP Problem. P problems can be solved efficiently by a computer program. The program creates a solution. The most difficult problems in NP can be efficiently verified by a program, which means a program can efficiently determine whether or not a proposal solves the problem or not. The difficulty is finding a suitable candidate. If P were to equal NP, then such a candidate could be found efficiently. If P does not equal NP implies that this is not possible. This has an impact on modern encryption techniques. If his work stands, then P is not equal to NP and thus modern encryption techniques are safe.

Now it is up to the research community to confirm or disprove Norbert Blum's argument. Discussion in relevant blogs and networks is already abundant. Anticipation is high for someone immersed in Norbert Blum's work to speak out. Until then the connoisseur remains silent: in the case of Norbert Blum, with a dessert of yogurt and fruit.

Update 01.09.2017

Prof. Blum has revoked his paper. On the publication platform Arxiv he writes: "The proof is wrong. I shall elaborate precisely what the mistake is. For doing this, I need some time. I shall put the explanation on my homepage."

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