“Ramanujan Machine” – Auto-generator for mathematical conjectures

Supervisor(s):Prof. Ido Kaminar

Abstract:

Math is roughly divided to “theory provers” and “theory conjecturing”. Some of the greatest mathematician are known for their theory conjecturing more than their proofs (e.g., Fermat’s last theorem, Hilbert’s problems). We’re developing computer algorithms to create a “Ramanujan Machine” – an auto-generator of mathematical conjectures, similar to the role great mathematicians took in the past. This is a unique research for those who wish to help in pioneering a new field.
We have focused so far on analytic formulas of mathematical constants. We aim to find new formulas for constants to which no such previous representation is known (e.g. the Feigenbaum constants), which will enable “reverse-engineering” the field in which they arise (e.g. chaos and bifurcation theory).
We have recently found new analytic representations for a few important mathematical constants (pi, e, and Apery’s constant, related to the Riemann Zeta function), and are looking forward for creative and motivated students to pursue new directions in this research.