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From: Alexis <flexibeast@gmail.com>
Newsgroups: comp.lang.c
Subject: Re: Suggested method for returning a string from a C program?
Date: Sat, 22 Mar 2025 15:05:43 +1100
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Muttley@DastardlyHQ.org writes:

> But 99.99% of the time doesn't.

Famously, mathematician G.H. Hardy was a fan of number theory _because_
it seemed to have no 'real world' applications (i.e. applications
outside of mathematics itself). Eventually, of course, it became the
theoretical basis of public-key cryptography.

This is actually a common historical pattern - mathematics that doesn't
immediately appear to have any 'real world' applications eventually finds
such uses:

* Intuitionism's rejection of the Law of the Excluded Middle (LEM) and,
  consequently, Double-Negation Elimination (DNE) 
  initially seemed to be hobbling the practice of mathematics for no good
  reason[a]. But it turns out constructive reasoning is important in the
  context of computation and 'side-effects' (in the compsci sense of
  that phrase)[b].

* Why abandon Euclid's fifth postulate, that parallel lines never meet,
  and study the resulting non-Euclidean geometries? Well, Riemannian
  Geometry, first presented by Riemann in 1854, ended up allowing
  Einstein to develop the General Theory of Relativity ....

Here's an old Math Overflow post on 'real world' applications of
mathematics, by arXiv subject area:

  https://mathoverflow.net/questions/2556/real-world-applications-of-mathematics-by-arxiv-subject-area

(Which is much a coarser-grained classification scheme than the
Mathematical Subject Classification,
https://mathscinet.ams.org/mathscinet/msc/msc2020.html).

In fact, i would suggest that it's increasingly difficult to find
non-recent mathematics that _hasn't_ found direct or non-direct
'real world' applications.

i say "direct or non-direct", because even though proving or disproving
certain conjectures might not have any immediate impact[b], problems that
have been particularly resistant to proofs often require the development
of new mathematical approaches / techniques / knowledge that either find/s
'real world' uses, or support/s the development of mathematics which has
such uses.

Basic research is important, even in mathematics. We don't know what
'mere intellectual curiosities' of today will end up having
world-changing applications in the future.

All this is, of course, very much OT, so let me link to this old
tongue-in-cheek post of John Regehr, "C Compilers Disprove Fermat’s Last
Theorem":

  https://blog.regehr.org/archives/140

:-)


Alexis.


[a] Andrej Bauer has a post about how not having DNE still allows for "proof of
negation", even if not "proof by contradiction" stricto sensu:

  https://math.andrej.com/2010/03/29/proof-of-negation-and-proof-by-contradiction/

[b] Although cf.:

  https://queuea9.wordpress.com/2013/08/12/whats-so-nonconstructive-about-classical-logic/

[c] E.g. even if someone somehow successfully proved that P = NP, that
wouldn't _necessarily_ result in real-world consequences:

> Even in the remote eventuality that P=NP, essentially nobody actually
> thinks the algorithms will be practical. I mean, a polynomial
> algorithm for an NP problem that runs in time proportional to n^100 is
> not going to be helpful.
-- https://www.reddit.com/r/math/comments/behxgy/comment/el685q4/