[bawolff]

The articles don't contradict each other when it comes to cited facts - you can believe both!

I suppose its all in the implications though, which are contradicting as the nature article implies it is a big deal. The nature article doesn't give any examples of interesting conjectures, or examples of interesting consequences if any of the conjectures should be true. They talk a lot about alternate formulae to calculate things we already know how to calculate. Why would we care? Do they have a smaller big-oh? Nature references the theory of links between other areas of math, if true that's great, but if its true surely they would have mentioned an example of such a link? Anyways I lean towards this not being that interesting, even if you base that just on what the nature article said.

[sanxiyn]

Re why would we care: this is a search algorithm for numerical coincidences. Most numerical coincidences are trivial, for example can be derived from hypergeometric function relation which was known to Gauss. In fact it would be interesting to automatically filter formulae which can be derived from hypergeometric function relation... On the other hand, numerical coincidences can lead to deep theory, monstrous moonshine is a prime example. Hope is that by searching for numerical coincidences, we can discover one leading to deep theory without already knowing that deep theory. This seems reasonable.

[yharris]

That's a very good point - and it really motivates these kinds of computer searches.

The Nature paper has quite a lot of detail in its supplementary

https://static-content.springer.com/esm/art%3A10.1038%2Fs415...

Table 3 inside also shows new conjectures for constants such as Catalan's and zeta(3). These results do not seem to trivially arise from known knowledge.