Would the new discovery for catalans number be considered a counter to:
> 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)
> 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...