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Classic Conjectures Allow Young Mathematicians to Commence Research

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Competitions for Young Mathematicians

Part of the book series: ICME-13 Monographs ((ICME13Mo))

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Abstract

The four classic conjectures of mathematics presented here are still open. They appear together with trains of thought that lead to them and relevant partial results. This material shows how strongly problems of mathematical Olympiads in general, and the Colorado Mathematical Olympiad in particular, are interwoven with the forefront of mathematics, and influence each other. These conjectures are “classic” because they are easy to understand and hard to prove or disprove. They are accessible to young high school and college mathematicians and allow students to commence research and creative work in mathematics.

This essay was first read as the Closing Plenary Talk at the 7th Congress of the World Federation of National Mathematics Competitions, very successfully organized in Barranquilla, Colombia by Maria Falk de Losada in July 2014. Its early version appeared in the journal of the World Federation of National Mathematics Competitions Mathematics Competitions 27(1), 2014, 16–39.

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Notes

  1. 1.

    I.e., no three points lie on a line.

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Acknowledgements

I thank Col. Dr. Robert Ewell for converting my hand-drawn sketches into computer-aided illustrations.

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  1. University of Colorado, 1420 Austin Bluffs Parkway, Osborne Center for Science, Office A423, Colorado Springs, CO, 80918, USA

    Alexander Soifer

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  1. Alexander Soifer
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Correspondence to Alexander Soifer .

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  1. Osborne Center for Science & Engineering, University of Colorado, Colorado Springs, Colorado Springs, Colorado, USA

    Alexander Soifer

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Soifer, A. (2017). Classic Conjectures Allow Young Mathematicians to Commence Research. In: Soifer, A. (eds) Competitions for Young Mathematicians. ICME-13 Monographs. Springer, Cham. https://doi.org/10.1007/978-3-319-56585-9_14

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  • DOI: https://doi.org/10.1007/978-3-319-56585-9_14

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