Seems slightly less rich than Doug Lenat's Automated Mathematician (which in turn led to Eurisko which was one of the earliest genuinely interesting AI systems):<p><a href="https://en.wikipedia.org/wiki/Automated_Mathematician" rel="nofollow">https://en.wikipedia.org/wiki/Automated_Mathematician</a>
Well, the continuous fraction for e is pretty well known. Doubt they discovered anything new here that can't be obtained from the original formula.
On the other hand, the continuous fraction for pi is irregular, so it's interesting to see what they discovered... but I can't really find any pattern in the "conjectures" for pi. Take the first one:<p>pi/−4 = 1/(−1 + 1/(−4 + −2 /(−7 + −9/(−10 + −20/(−13+...))))<p>What exactly am supposed to prove here? The denominators are an arithmetic progression but numerators (1, 1, -2, -9, -20, ...) are just some bizarre sequence without an obvious pattern. The thing with continous fractions is that every number has one, so the fact that pi is presented as continous fraction is not impressive in itself.
It seems aptly named because Ramanujan also dealt with infinite series. One of his most famous equations is the ramanujan summation [1] where he derives that the sum of infinite series 1 + 2 + 3 + 4 + ... = - 1 / 12<p>[1] <a href="https://en.wikipedia.org/wiki/Ramanujan_summation" rel="nofollow">https://en.wikipedia.org/wiki/Ramanujan_summation</a>
I wonder if it somehow can be integrated with Coq[1] and Univalent Foundations[2]. Probably these can be used as a more substantial "base" for this machine.<p>[1] <a href="https://github.com/coq/coq" rel="nofollow">https://github.com/coq/coq</a><p>[2] <a href="https://github.com/UniMath" rel="nofollow">https://github.com/UniMath</a>
Related: Robert Munafo's RIES [1] tries to synthesize increasingly complex formula which solution is a given number.<p>[1] <a href="https://mrob.com/pub/ries/" rel="nofollow">https://mrob.com/pub/ries/</a>
I was pondering a few weeks back about the prospects of using ML/AI to find new ways to factor primes and if their is any sequence in primes and how to calculate them in a way that you input N and it will produce the Nth prime.<p>That would be something.
"New mathematics" is a bit of an overstatement. There is a lot more to maths than continued fractions.<p>It bugs me a bit that the authors write (I would love for anyone affiliated with the project to talk to me about this) "Any new conjecture, proof, or algorithm suggested will be named after you.". No offense, but there are very few mathematicians out there with that kind of a world view.<p>Seems a bit like a high school project without proper guidance from a mathematician.