nLab
experimental mathematics

Contents

Contents

Idea

What is called experimental mathematics is the exploration of mathematics and the possibe truth of theorems not by general proof, but by checking special cases using computer programs.

Examples

Riemann hypothesis

A general proof of Riemann hypothesis remains famously open, but computer experiment so far confirms it, see there.

Volume conjecture

A general proof of the volume conjectures remains open (though various special cases do have proof), but computer experiment (such as using SnapPy) so far confirms (and motivates) these conjectures.

Image of beta

The image of the canonical homomorphism β\beta from the Burnside ring of a finite group to the representation ring over some field is partly known only by computer experiment, see there.

References

  • David H. Bailey, Jonathan M. Borwein, Experimental Mathematics: Examples, Methods and Implications, Notices of the AMS, Volume 52, Number 5, 502-514. (pdf)

  • David H. Bailey, Jonathan M. Borwein, Neil J. Calkin, Roland Girgensohn, D. Russell Luke, Victor H. Moll, Experimental Mathematics in Action. (pdf)

  • Herbert S. Wilf, Mathematics: An Experimental Science. (pdf)

See also

Last revised on August 24, 2019 at 04:29:00. See the history of this page for a list of all contributions to it.