Yuri Matiyasevich
Native spelling: Юрий Владимирович Матиясевич
fl. 1947, Leningrad, Soviet Union (now Saint Petersburg, Russia)
Russian mathematician and logician who in 1970, at age 22, completed the negative solution to Hilbert's tenth problem by proving what is now called Matiyasevich's theorem.
Yuri Matiyasevich was born in Leningrad. A gold medallist at the 1964 International Mathematical Olympiad, he studied at Leningrad State University, graduating in 1969, and completed his doctoral work at the Leningrad branch of the Steklov Institute of Mathematics (LOMI).
Hilbert's tenth problem, posed in 1900, asked for a general algorithm to decide whether a Diophantine equation has integer solutions. Building on two decades of work by Martin Davis, Hilary Putnam and Julia Robinson, who had reduced the problem to showing that every recursively enumerable set is Diophantine (the DPRM conjecture), Matiyasevich supplied the missing step in 1970: using the Fibonacci sequence's exponential growth, he showed such a construction exists. Combined with the earlier work, this proved that no such algorithm can exist — a negative answer now known as the MRDP (Matiyasevich–Robinson–Davis–Putnam) theorem.
Matiyasevich spent his career at the Steklov Institute in Saint Petersburg, heading its Laboratory of Mathematical Logic from 1980 and becoming a full professor in 1995; he later served as President of the St. Petersburg Mathematical Society. His 1993 monograph Hilbert's Tenth Problem remains the standard reference on the subject.
Workplaces: Steklov Institute of Mathematics, Saint Petersburg, Saint Petersburg State University
Russia