Sergei Adian facts for kids

Sergei Ivanovich Adian (born January 1, 1931 – died May 5, 2020) was an important mathematician from the Soviet Union and Armenia. He taught as a professor at Moscow State University. Adian was famous for his work in a field called group theory, especially for helping to solve the difficult Burnside problem.

Biography

Sergei Adian was born near a city called Elizavetpol. He grew up there in an Armenian family. He studied at schools in Yerevan and Moscow. His main teacher was a mathematician named Pyotr Novikov. Adian started working at Moscow State University (MSU) in 1965. One of his well-known students was Alexander Razborov.

Mathematical Discoveries

In his first work as a student in 1950, Adian showed that the graph of a special type of mathematical function could be very spread out. This was an interesting early discovery.

By 1955, Adian made a big breakthrough. He proved that it's impossible to create a computer program (an algorithm) that can always tell if certain things are true about mathematical groups. For example, you can't always tell if two groups are exactly alike. This important result is now known as the Adian–Rabin theorem. It was a very complete and powerful finding in the study of groups. Even after many years, no one has added anything major to his original proof.

The Burnside Problem

The Burnside problem is a very famous and challenging question in group theory. It's a bit like Fermat's Last Theorem in number theory. It has a simple question but is incredibly hard to answer. This makes it very interesting to mathematicians.

Before Adian and Novikov worked on it, people only knew the answer to the Burnside problem for a few specific cases. Many mathematicians believed the answer would always be "yes." But they didn't have the right ways to prove it. It turned out that the problem was much more complicated than anyone thought.

In 1959, P. S. Novikov first suggested a way to solve the problem with a "no" answer. However, putting his ideas into practice was very difficult. In 1960, Adian joined Novikov to work on the Burnside problem. They worked together very hard for eight years.

In 1968, they published their famous paper. It showed that the answer to the Burnside problem was "no" for many cases. Specifically, it was "no" for all odd numbers greater than 4381. This was a huge discovery in mathematics.

Solving the Burnside problem was one of the most important and deep mathematical results of the last century. The proof was extremely complex. It showed how persistent Adian was in his work. Novikov even said that Adian was one of the most "penetrating" mathematicians he had ever met.

Unlike the Adian–Rabin theorem, their work on the Burnside problem didn't completely "close" the topic. Adian continued to improve and simplify their method for more than ten years. He also used it to solve other important problems in group theory. By the 1980s, their method became a powerful tool for creating and studying new types of mathematical groups.