Thursday, August 14, 2014

One weak link in the chain of reasoning

In summary, it is whether these equations Mathematics - meant to describe fluid flow - always have a continuous 3D solution that does not end up becoming pathological adopting physically unrealistic features. This is a problem of mathematical physics whose solution would affect several branches of natural science, weather forecasting in the design of aircraft, for example, and perhaps even with the theory of black holes . Of course, as always in mathematics, it could also have unintended consequences in areas seemingly far removed from the theory of partial differential equations.

The mathematician Mukhtarbay Otelbayev spent 30 years working on the problem of the existence and uniqueness of solutions to the Navier-Stokes equations based on initial conditions.  This mathematical problem has many implications in fluid mechanics.

One weak link in the chain of reasoning

Several mathematicians talents were attacked and not just because the one who finds the solution would be given one of the Millennium Prize of Clay Mathematics Institute and the million dollars that goes with it. In 2006, the mathematician Penny Smith of Lehigh University in Bethlehem, Pennsylvania, thought he had found before Mukhtarbay Otelbaev the solution. She had become disillusioned and withdraw from arxiv article that she posted due to an error in his demonstration. The great mathematician Terence Tao there is also attacked with an innovative approach as he explains on his blog , though without conclusive results yet.

Colleagues of Otelbaev course have undertaken to verify its calculations. The task is difficult in itself and is added to the disadvantage that the Kazakh section of the researcher was written in Russian. Recently, Stephen Montgomery-Smith , a mathematician at the University of Missouri at Columbia who also embarked on the race for the Millennium Prize, sent an email to Mukhtarbay Otelbaev pointing him a problem. The Russian-speaking mathematician had to face the facts by answering: " To my shame, on page 56, the inequality (6.34) is incorrect so the 6.3 proposal is unproven (54 p.). I'm sorry ".

His argument therefore collapses. But the researcher does not abandon. He thinks he should be able to get around the obstacle in the next few months. A similar mishap had reached the British mathematician Andrew Wiles , a professor at Princeton University, best known for demonstrating's last theorem Fermat in 1994, Wiles was on the verge of abandonment after a year of work to correct them as a error in his argument when the path was suddenly opened before him.

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