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From the sixteenth Hilbert problem to tropical geometry

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Japanese Journal of Mathematics Aims and scope

Abstract.

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.

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Authors and Affiliations

  1. Petersburg Department of the Steklov Mathematical Institute, Fontanka 27, 191023, St. Petersburg, Russia

    Oleg Viro

  2. Institute for Mathematical Sciences, Stony Brook University, Stony Brook, NY, 11794-3660, USA

    Oleg Viro

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  1. Oleg Viro
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Correspondence to Oleg Viro.

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Communicated by: Kaoru Ono

This article is based on the 4th Takagi Lectures that the author delivered at Kyoto University on June 21, 2008.

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Viro, O. From the sixteenth Hilbert problem to tropical geometry. Jpn. J. Math. 3, 185–214 (2008). https://doi.org/10.1007/s11537-008-0832-6

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  • DOI: https://doi.org/10.1007/s11537-008-0832-6

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