Explore, abstract, compute, verify, can we do (all) mathematics by computer?

Computers have changed the face of research in mathematics says professor Automated math Assia Mahboubi in her lecture. We use them to observe and conjecture, but also to invent patterns, and to substantiate proof steps⁠. The boom of computer-aided mathematics, in the making, in proofs and in applications, owes much to the stunning progress in the art of computing and programming⁠. 

A wide corpus exist today of sophisticated methods for constructing and for estimating mathematical objects, developed in par with their implementation in actual software⁠. Computer-aided hunches but also actual computer-aided proofs, pervade all fields of mathematics, and this impacts us all⁠. For instance, the advent of digital communication channels has turned number theory, one of the most ancient branch of mathematics, into the pillar of modern coding theory and cryptography⁠. And spectacular applications in security and privacy followed⁠.  But how do we trust computers when they are doing mathematics? Are humans and computer talking the same language of mathematics? Mahboubi gives the answers in her lecture.