The unreasonable effectiveness of computer algebra in the mathematical sciences

Despite the current renaissance of AI, the main theme of the talk is on more traditional lines: namely, to stress the huge potential of algorithmic mathematics, and of respective computer algebra software, for applications in pure mathematics and related fields.

For example, the Ramanujan Machine (Nature 590, 2021) creates mathematical conjectures using AI and computer automation. On the other hand, Cristian-Silviu Radu (RISC) developed a computer algebra algorithm which can be used to discover (and prove!) identities, which even Ramanujan would have appreciated to see.

In the talk we discuss a variety of such examples from different areas: optimization of antenna radiation, special functions and Gauss' contiguous relations, linear Diophantine inequalitites and partitions of numbers, symbolic summation in quantum field theory, a.s.o.