
Formal Abstracts – express mathematical publications in a computer-readable form - dgellow
https://formalabstracts.github.io/
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jevgeni
> precise definition of each term

I’m not a mathematician, but aren’t some fundamental terms in mathematics NOT
clearly defined? For example a set?

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dwohnitmok
Sets are clearly defined. The usual formalism for defining a set is ZFC set
theory. In fact to a first approximation all of modern mathematics is
sufficiently well-defined to be entirely formalized in a computer. This is an
approximation primarily because currently the burden to do so is immensely
high. With today's technology formalizing a proof can easily take several
orders of magnitude more time (if not more!) than writing the informal, but
commonly accepted as rigorous, proof.

There are philosophical questions around what it means to "define" something.
But if you want to go there, well then nothing is clearly defined.

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ganzuul
Isn't that definition just consistency, both in theory and in practice?

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manifestsilence
Wow, this could eventually enable some pretty amazing stuff. I'm just a
hobbyist, but this makes me think about how machine search through the space
of possible theorems butts up against the halting problem and/or Godel's
theorems (though one could argue that human searching of the space is subject
to the same limitations if our minds on some level represent formal systems as
Hofstadter thinks).

And I wonder about whether certain mathematical truths will be inherently
difficult to locate because they are far away from the space of other existing
problems, and thus subject to problems of a search algorithm getting stuck in
a local maximum.

In any case, an accelerated search through this space sounds really promising
and exciting!

