The utilization of advanced computing technology in mathematical research: new mathematical results discovered partly or entirely with the aid of computer-based tools.
Experimental Mathematics is an approach to Mathematics in which computation is used to investigate mathematical objects and identify properties and patterns.
Experimental Mathematics makes use of numerical methods to calculate approximate values for integrals and infinite series. Arbitrary precision arithmetic is often used to establish these values to a high degree of precision – typically $100$ significant figures or more. Integer relation algorithms are then used to search for relations between these values and mathematical constants. Working with high precision values reduces the possibility of mistaking a mathematical coincidence for a true relation. A formal proof of a conjectured relation will then be sought – it is often easier to find a formal proof once the form of a conjectured relation is known.
For example,
- Roger Frye used experimental Mathematics techniques to find the smallest counterexample to Euler's sum of powers conjecture.
- The ZetaGrid project was set up to search for a counterexample to the Riemann hypothesis.
