Abstract:
In this talk, we present recent developments in experimental mathematics within the Ramanujan Machine project, specializing in automated conjecture generation in number theory, in particular involving continued fractions. Specifically, we present recent conjectures found, including a generalization of a famous result by Ramanujan, and present the search algorithm employed in finding them. The search algorithm employs a new heuristic for the likelihood of a conjecture to be true, based on available numerical data, and this heuristic will be explored in the talk. We will also present the convergence model used when evaluating continued fractions, and the recent efforts in making these findings and algorithms open to the public.
Advisor: Prof. Ido Kaminer