Japanese Journal of Mathematics

, Volume 3, Issue 2, pp 185-214

First online:

From the sixteenth Hilbert problem to tropical geometry

  • Oleg ViroAffiliated withPetersburg Department of the Steklov Mathematical InstituteInstitute for Mathematical Sciences, Stony Brook University Email author 

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Hilbert’s problem on the topology of algebraic curves and surfaces (the sixteenth problem from the famous list presented at the second International Congress of Mathematicians in 1900) was difficult to formulate. The way it was formulated made it difficult to anticipate that it has been solved. In the first part of the paper the history of the sixteenth Hilbert problem and its solution is presented. The second part of the paper traces one of the ways in which tropical geometry emerged.

Keywords and phrases:

sixteenth Hilbert problem real algebraic curve Gudkov’s conjecture patchworking tropical geometry idempotent mathematics

Mathematics Subject Classification(2000):

14P25 (primary) 14N10 (secondary)