Generating conjectures on fundamental constants with the Ramanujan Machine
vice.com
vice.com
> nothing considered remotely new by an expert
Or is the proof mentioned at the end of the article the proof for Catalans number (sorry, I’m a non mathematician)
One much always be very careful when claiming some identity like this is new. Even excellent researchers can get burned – it has happened to Doron Zeilberger, one of the pioneers of algorithmic mathematics, at least one. (I'm looking for the details but unfortunately can't find them at the moment...)
edit: The issue in the latter case may have been a very simple analytic proof existing, not novelty per se. He had posted correspondence between him and another mathematician on his website but apparently deleted it.
Also, the blog post linked above has been updated: https://www.galoisrepresentations.com/2021/02/11/ramanujan-m...
I wonder how long honest players can survive in this climate. AI Winter, where are you?
https://arxiv.org/abs/1907.00205
"We present two algorithms that proved useful in finding conjectures: a Meet-In-The-Middle (MITM) algorithm and a Gradient Descent (GD) tailored to the recurrent structure of continued fractions. Both algorithms are based on matching numerical values and thus they conjecture formulas without providing proofs and without requiring prior knowledge on any underlying mathematical structure. This approach is especially attractive for constants for which no mathematical structure is known, as it reverses the conventional approach of sequential logic in formal proofs. Instead, our work supports a different approach for research: algorithms utilizing numerical data to unveil mathematical structures, thus trying to play the role of intuition of great mathematicians of the past, providing leads to new mathematical research."
For a live version on which you can comment and discuss with your peers and other readers, see this link on SciHive:
1. https://www.nature.com/articles/s41586-021-03229-4