How good is AI in math? Currently, AI is advancing fast in deep learning: Entire human chess knowledge learned and surpassed by DeepMind's AlphaZero in four hours.
As a layman, I'm taking this as a quite powerful searching algorithm, using artificial neural networks to identify the patterns of each game.
However, how good is AI doing in math?
For example, the key to the theory of the game Nim is the binary digital sum of the heap sizes, that is, the sum (in binary) neglecting all carries from one digit to another. This operation is also known as &quot;exclusive or&quot; (xor) or &quot;vector addition over GF(2)&quot;.
Is AI good enough to discover/invite operations/logics such as &quot;exclusive or&quot;, or, more advanced, abstract algebra in finite field?
Nim was actually one of the first games ever played by an electronic machine. It was called the Nimatron and was displayed at the 1940 New York World's Fair.
It is also well known that neural networks can model the Xor-function, if they have enough layers. Despite that, Marvin Minsky is supposed to have killed neural networks in the sixties, by asserting that networks with a single hidden layer, cannot model XOR.
I think there were also some large scale projects to classify finite groups using computers.
Additionally, there have long been automated theorem-proving programs, that had some success in mathematical logic. I recently saw a paper that used deep learning to improve one of these theorem provers.
That being said, doing real mathematics is probably as difficult as real language understanding. There doesn't seem to have been a real breakthrough yet.