
A Mathematician’s Apology (1940) [pdf] - vixen99
http://www.math.ualberta.ca/~mss/misc/A%20Mathematician%27s%20Apology.pdf
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teilo
In case the title is confusing, this is the older meaning of "Apology." Not,
"I'm sorry," but "defense." This is a defense and justification for the field
of mathematics.

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undershirt
so that's where Christian "Apologetics" comes from

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escherplex
Yeah, interesting that the meanings shifted over time. EG, look at Google
Translate (E>L) where apology (E) becomes excusatione (L) with a back
translation (L>E) of 'excuse'. Today an apology may or may not come with an
excuse but back then an apology must have been a rationalization for some
action.

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enriquto
> No one has yet discovered any warlike purpose to be served by the theory of
> numbers or relativity, and it seems unlikely that anyone will do so for many
> years.

Poor guy, if he had just heard about gps and about modern cryptography!

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whatshisface
> _or relativity_

Which was used for the atomic bomb.

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enriquto
How come? I never heard about that.

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whatshisface
Relativity is essential for nuclear physics, because of the high energy
densities.

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auntienomen
Special relativity, not general, just to be clear.

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scrumper
You'd need general if you wanted to divert asteroids and crash them with
pinpoint accuracy on your enemy's cities.

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d_e_solomon
This is a favorite of mine and got me through some tough days in undergrad.
I'm no longer a young man and I don't really pursue mathematics anymore, but
it was a good reminder of a good days.

Thanks for posting :)

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enriquto
I also loved reading this book (and the prologue by C.P. Snow on the two
cultures). Yet, it is amazing to see that this is not the only possible world
view among mathematicians. For example, Vladimir Arnold has essentially the
opposite view [1]: "Mathematics is the part of physics where experiments are
cheap".

[1] [https://www.uni-
muenster.de/Physik.TP/~munsteg/arnold.html](https://www.uni-
muenster.de/Physik.TP/~munsteg/arnold.html)

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jhbadger
There is a bit of irony that for all the "maths for maths' sake" argument of
this apology, one of Hardy's most lasting achievements was a basic principle
of genetics -- the Hardy-Weinberg equilibrium
[https://en.wikipedia.org/wiki/Hardy%E2%80%93Weinberg_princip...](https://en.wikipedia.org/wiki/Hardy%E2%80%93Weinberg_principle)

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Arcana_
Hardy's idea that math is a young man's game is wrong & discriminatory against
those that lack opportunities to education early in their life. Or for
whatever reason pursued math at a later age.

See people like:
[https://en.wikipedia.org/wiki/Yitang_Zhang](https://en.wikipedia.org/wiki/Yitang_Zhang)
that produced good math at a later stage.

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amvalo
It’s an observation, not a prescription. Is it “discriminatory” to suggest
that gymnastics is a young person’s game?

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HiroshiSan
Yes

edit:

just to clarify, it would be an observation to say "Most Mathematicians
produce their best work when they're young" or "Most gymnasts who make it to
the olympics are young"

But to say that X is a young mans game is inherently discriminatory.

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frankling_
Isn't that a bit strict? It seems that "x is a young man's game" can be read
either in an empirical ("historically, only young men do x") or normative
("only young men should do x") sense, the former of which might be slightly
inaccurate because there are exceptions, but otherwise seems fine.

A view held by some seems to be that since even the empirical observation may
"perpetuate" the situation, stating it is "problematic" in itself, but I don't
suppose this is what you mean here.

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payne92
The current version (in print) includes a sizeable forward by Snow, which is
at least as interesting.

And the irony of this entire writeup is that number theory is now beyond
"useful", as the underpinning for cryptography and security in our modern
systems.

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nopearlclutcher
I have heard of this "apology", but never got around to reading it. On p. 12
right now. The author makes certain statements about age of people in math
which are basically statistics arguments from a few famous examples and his
"limited experience".

Also, a lot is different since the days of Hardy.

At least, now I see where some mathematicians get their pretentiousness :)

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willpiers
idk why people are getting so hung up on this point. it is obviously true that
more great mathematics has been produced by young people. obviously there are
exceptions, but they add credence to the general case

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rademacher
I've heard similar arguments about age and physics. I've always theorized that
as time progresses the body of work one must be familiar with in order to make
new contributions grows as well. We should therefore expect that in modern
times, major contributions should come from more experienced individuals.

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redbluegreendot
> I've always theorized that as time progresses the body of work one must be
> familiar with in order to make new contributions grows as well.

As I see it, this is not too big a problem. Usually people get on a very
narrow path and specialize in a tiny part of a larger discipline. There's a
lot of new research being done in algebra, analysis, geometry, statistics,
whatever; but as a researcher you are expected to choose a very narrow sub-sub
-...-sub-discipline and ignore everything else. That's very much doable. An
analyst who can't read number theory papers is not a rarity. Likely a rule.

