- Title
- Hilbert 13: Are there are any genuine continuous multivariate real-valued functions?
- Creator
- Morris, Sidney
- Date
- 2021
- Type
- Text; Journal article
- Identifier
- http://researchonline.federation.edu.au/vital/access/HandleResolver/1959.17/175356
- Identifier
- vital:14960
- Identifier
-
https://doi.org/10.1090/bull/1698
- Identifier
- ISSN:02730979
- Abstract
- This article begins with a provocative question: Are there any genuine continuous multivariate real-valued functions? This may seem to be a silly question, but it is in essence what David Hilbert asked as one of the 23 problems he posed at the second International Congress of Mathematicians, held in Paris in 1900. These problems guided a large portion of the research in mathematics of the 20th century. Hilbert’s 13th problem conjectured that there exists a continuous function (Formula presented), where (Formula presented), which cannot be expressed in terms of composition and addition of continuous functions from ℝ2 → ℝ, that is, as composition and addition of continuous real-valued functions of two variables. It took over 50 years to prove that Hilbert’s conjecture is false. This article discusses the solution. © 2021. American Mathematical Society.
- Publisher
- American Mathematical Society
- Relation
- Bulletin of the American Mathematical Society Vol. 58, no. 1 (2021), p. 107-118
- Rights
- All metadata describing materials held in, or linked to, the repository is freely available under a CC0 licence
- Subject
- 0101 Pure Mathematics
- Reviewed
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