“Ramanujan Machine” – An Auto-generator of Mathematical Conjectures

Our group is developing computer algorithms to create a “Ramanujan Machine” – an auto-generator of mathematical conjectures, similar to the role great mathematicians took in the past (Hilberts problems, Fermat’s last theorem etc). Some progress has been done in the last decade about automatic theorem proving (ATP), but to the best of our knowledge, we’re the first to attack the problem of automatic conjecturing with artificial intelligence. This is a unique and aspiring research, for those who wish to take part in pioneering a new field.

We found new analytic representations for important mathematical constants (pi, e and Apery’s constant, related to the Riemann Zeta function), and are looking forward for more “exotic” ones such as the two Feigenbaum constants. As an example, the Feigenbaum constants are universal constants that appear in different bifurcation/chaotic systems in a wide range of fields. They have no known analytic representation despite their universal nature. A discovery of any new analytic representation could provide deep fundamental insights into fundamental open problems in chaos theory. Similarly, any auto-generated conjecture is expected to open new directions of research in the field from which the constant arises.

The useful skills-set for this project are fondness of mathematical riddles and a solid mathematical background (high grades in the basic math classes). Advantage for candidates with high grades in Algorithms and Machine Learning courses.


Supervisor : Prof. Ido Kaminer

Programming skills: python.  Additional helpful programming skills: scalable programming, distributed computing (over CPU cores & GPUs), fast DBs.