Iván Matvéievich Vinográdov.
Iván Matvéievich Vinogradov (Velikoluksky, 1891- Moscow 1983) was one of the promoters of a branch of mathematics called analytical number theory and also directed the prestigious Steklov Institute of Mathematics in Moscow for almost 50 years. This and other administrative tasks made him accumulate a lot of power, which helped to forge a tough image, perhaps reaffirmed by his strength and physical form, qualities that have been the subject of several anecdotes. Some documented , such as the occasion when he squeezed a colleague until he conceded that he was "the strongest mathematician in the world", and others surely legendary, such as having raised a piano to a fourth floor by himself.
The mathematical achievement for which he better known is the proof, in 1937, that every odd number greater than a certain constant can be written as the sum of three prime numbers. Later authors calculated admissible values of this constant, the smallest of them with 1,347 digits, until in 2013 the Peruvian mathematician Harald Helfgott refined the result by proving that it applies to all odd greater than 5. This is tantalizingly close to Goldbach's conjecture and In fact, he was also indirectly considered by Christian Goldbach in his correspondence with Leonhard Euler , and even by René Descartes .
The mathematical achievement for which he is best known is the proof, in 1937, that every odd number greater than a certain constant can be written as the sum of three prime numbers.
For the proof of his result, Vinogradov studied the cancellation in the interference of sinusoidal waves –which correspond to pure tones– of different frequencies, and simplified the ideas of the circle method , –whose precursor was a famous work by Hardy and Ramanujan -. Specifically, he considered the wave obtained by the superposition of pure tones with frequencies given by prime numbers smaller than an arbitrarily large number. This wave has peaks that reflect certain structures of the sequence of primes and are the arithmetic analog of the Bragg peaks that appear in X-ray crystallography . With very ingenious arguments, Vinogradov proved that outside the peaks there was some quantifiable cancellation.
If we multiply two pure tones, we obtain a wave that is superposition of two tones whose frequency is the sum and the subtraction of the original frequencies – this is related with which when superimposing two sounds of close frequencies a strange low frequency pulse is heard. With a little technical dribble, which involves complex numbers, subtractions can be neglected. Cube the wave obtained by superimposing pure tones with frequencies given by prime numbers is like considering a multiplication with three factors, so the result will contain pure tones of all frequencies expressible as the sum of three primes.
Fourier analysis allows us to decompose any wave into pure tones and, by means of a certain formula, determine how much it has of each frequency
Fourier analysis allows us to decompose any wave into pure tones and, by means of a certain formula, determine how much it has of each frequency –in the previous case, the number of representations as the sum of three primes–. Although this seems very abstract, it is at the base of many everyday devices because pure tones are easy to deal with both analog and digital methods. Vinogradov approximated the result of this formula – for which it was essential that there were pronounced peaks – and thereby proved that all the large odd frequencies were there. Small ones are too affected by possible random interference difficult to control, which Helfgott avoided with some smoothing of the amplitudes . There is also a general limit to cancellation that introduces a serious theoretical obstacle to solving the Goldbach conjecture in this way, squaring rather than cubing.
This result gave Vinogradov a deserved fame and, only with him – even without the rest of his important production – would he be guaranteed a place in posterity. However, in his capacity as manager, the figure of Vinogradov was very controversial, since he applied anti-Semitic policies with special zeal. He apparently claimed to be proud of having "cleaned" the Steklov Institute of Jews, – although one source claims that he warmly welcomed world chess champion and mathematician Emanuel Lasker , a reprisal Jew from Nazi Germany. For many, he was the man of the regime, which gave him all kinds of awards and recognitions, with names as unmistakable as the Order of the October Revolution or the title of Hero of Socialist Labor . Paradoxically, Vinogradov did not belong to the communist party.
His enormous mathematical legacy is beyond any doubt and will last forever.
Vinogradov did not have a wife or children and there are hardly any references to his human side : he had a very reserved character and the person closest to him, his sister, was even more sullen. The famous mathematician and political dissident Igor Shapharevich described him as a lonely and extremely strange person while the also famous medalist mathematician Fields Sergey Novikov called him a rare misanthropic villain.
Surely many Russian mathematicians, or those who were under the Soviet orbit, will consider that The very long period in which Vinogradov had so much power – from Stalinism to the Brezhnevian stagnation – are a stage to forget, however, his enormous mathematical legacy is beyond any doubt and will remain forever.
Fernando Chamizo is a professor at the Autonomous University of Madrid and member of the ICMAT
Café y Teoremas is a section dedicated to mathematics and the environment in which they are created, coordinated by the Institute of Mathematical Sciences (ICMAT), in which researchers and members of the center describe the latest advances in this discipline, share meeting points between mathematics and other social expressions and c ultural and remember those who marked its development and knew how to transform coffee into theorems. The name evokes the definition of the Hungarian mathematician Alfred Rényi: "A mathematician is a machine that transforms coffee into theorems."
Editing and coordination: Ágata A. Timón García-Longoria (ICMAT)
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