We have all worked with certain mathematical software, which could be as simple as a calculator and as complex as Cadabra. Math has always been an integral part of AI in ways more than one. However, how close are we to solving the “Unsolved” Math problems? Is there a possibility to have an AI, in other words, a supercomputer, to solve the unsolved?
Humans started off with simple counting on an abacus (telraam) and progressed to computers (as complex as they come). With every age and era, mankind came up with new inventions to solve the unsolved, starting from counting cattle to modeling the economy of a nation. One area which remains a bit behind is the proving of theorems and lemmas. All mathematics students have heard of or worked with Waterproof, a software developed by one of our professors dr. Jim Portegies along with Thijs Beurskens and David Tuin. Waterproof began in Q4 of the 2018-2019 academic year as a Software Engineering Project (SEP). The major objective was to make a proof helper that looks attractive and is enjoyable to work with. This software works very well with theorems and lemmas which are already proven. But is there a way to build an AI to run certain algorithms or procedures to solve problems like the Birch and Swinnerton-Dyer conjecture?
On one hand, developing software for solving the unsolved would be a big step for humanity, on the other hand, humans might end up considering AI as their new partner and might end up using it as a substitute for their brains. Problems lead to inventions and creations. Once there is an invention solving all the unsolved, will there be any other inventions? Will that be the saturation point of mankind? Or will it lead us to creations that keep us in check? We may not have an answer to this as well and hence we can add it to the list of the unsolved.