Talk:Mathematics

Future of mathematics

Should Future of mathematics appear in "See also" section? Boris Tsirelson (talk) 08:32, 31 January 2016 (UTC)

No. — Preceding unsigned comment added by 212.159.119.123 (talk) 13:37, 23 March 2016 (UTC)

External links modified

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Invention or Discovery

One of the longest debates is whether mathematics was "invented" or "discovered". Interestingly, the article makes use of both words in various contexts (use Ctrl+F to search), but discover seems to be used more often. What's the stance that should be taken on this topic?

Jsmith7342 (talk) 07:29, 15 May 2016 (UTC)

This issue is specifically discussed in the final paragraph of the section "Mathematics as science". And both stances are found throughout the literature. I'm not sure that it would even be desirable to try to make the terminology consistent throughout the article. But it's possible that the inconsistency is confusing to some readers? Mgnbar (talk) 12:10, 15 May 2016 (UTC)

Fortran

This is like a certain type of circular method used in discovery. Type of math actually, like calculus or algebra. It has not anything other than a supposed language named after it for computers. — Preceding unsigned comment added by 23.117.16.22 (talk) 01:43, 24 October 2016 (UTC)

Godel's Incompleteness Theorem

In the part of the article fields of mathematics logic is mentioned. There Godel's incompleteness theorem is mentioned and it is said that it shows that for any valid axiomatic system there exists "a true mathematical fact" that can't be proved. This is incorrect and misleading since if a theorem is unprovable it is not in any way a "true mathematical fact. Godel's incompleteness theorem simply shows the for any axiomatic system that the peano arithmetic axioms are derived from it there exists a property that is unprovable to be true nor false.

Remomer (talk) 21:14, 18 November 2016 (UTC)

Yes, in some reasonable (but rather formal) sense you are right. On the other hand, in another, even more reasonable (and somewhat informal) sense, the statement "Peano arithmetics is consistent" IS true but not provable in the Peano arithmetics. And of course, it IS provable in the Zermelo-Frenkel set theory. Boris Tsirelson (talk) 21:32, 18 November 2016 (UTC)