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Ask HN: is the number of interesting (mathematical) concepts infinite?

5 points by Tichy ↗ HN
I have often heard about the possible infinity of the mathematical universe, but what about the universe of abstract thoughts (or let's say, mathematics)?

Do you think there is an infinite number of mathematical ideas out there (in the platonic universe of ideas)? Clearly the amount of possible mathematical constructs is infinite, but how many are really interesting?

I suppose at the moment it can only be a matter of opinions, as it is hard to give a proper definition of "interesting". Would be interested in links to articles that deal with the problem of defining interesting.

3 comments

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gukjoon
Which infinity?
Tichy
Any infinity (countable is the "smallest" infinity, I think?). I was inspired to this question by reading "down and out in the magic kingdom", where people live forever , but occasionally get bored and commit suicide. So I wonder if in theory, there would be enough new stuff to discover to make it interesting to live forver.
stcredzero
In one of Larry Niven's novels, an AI who was a recording of a human mind discovered this trick on a long interstellar flight:

When things get really boring, arrange to have all references to the concept of "boredom" wiped from your memory. Then, when things get boring the next time, it's a novel experience!