I always found interesting that the English mathematical terminology has two different names for "stuff that locally looks like R^n" (manifold) and "stuff that is the zero locus of a polynomial" (variety). Other languages use the same word for both, adding maybe an adjective to specify which one is meant if not clear from the context. In Italian for example they're both "varietà"

In English, not all varieties are manifolds, see forex https://math.stackexchange.com/a/9017/120475

FTA

> The term “manifold” comes from Riemann’s Mannigfaltigkeit, which is German for “variety” or “multiplicity.”

This is not really something limited to mathematics.

Is there a clear application to a practical, real world data set where TDA is the state of the art? Don’t get me wrong, I love maths and topology in particular but I’m trying to understand what are the advantages that these techniques bring to the table

I’ve used algebraic topology for certain robotics tasks when statistical saftey wasn’t good enough and when trying to generalize techniques to learn on graphs.

The results are spectacular, but the application set is indeed very limited.

any references you can share? would love to read more about robotics applications of these approaches

This is a decent place to get started https://arxiv.org/pdf/math/0009118.pdf

You can extend some of the thinking in this paper to cover action spaces for deep RL models to really have some fun!

no, at least not for anything non-contrived.

Tried on NYT and does not work…

uBlock Origin + Anti-paywall filter works well.

https://filterlists.com/lists/anti-paywall-filters

Yeah sure, I just wanted to check if there were any alternatives to the "usual" websites. Thanks anyway.