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 $\beta$ 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)