
A Mathematician's Apology (1940) [pdf] - jw2013
https://www.math.ualberta.ca/mss/misc/A%20Mathematician%27s%20Apology.pdf
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earcaraxe
He's incredibly ageist and cynical about man's abilities to do great things.
Definitely a curmudgeon, but mixed in with some good quotes and advice.

I particularly thought this was cute:

"It is one of the first duties of a professor, for example, in any subject, to
exaggerate a little both the importance of his subject and his own importance
in it. A man who is always asking ‘Is what I do worth while?’ and ‘Am I the
right person to do it?’ will always be ineffective himself and a
discouragement to others. He must shut his eyes a little and think a little
more of his subject and himself than they deserve."

~~~
nextos
I like Hardy, but I dislike his ageism here too.

Erdős is a good counterexample to his argument. Even Euler. Many famous
mathematicians have produced good work late in their lives.

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getbucknaked
Erdos isn't a counter-example to anything. I mean I agree with you. Old people
can do math. Look at Yitang Zheng. But Erdos is the exception to every rule
ever.

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ttflee
Yitang Zhang, not Zheng.

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getbucknaked
Oh darn it. I originally spelled it Yiteng Zheng..I caught one typo. thanks

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modernerd
This was Aaron Swartz's inspiration for, “A Non-Programmer's Apology”, where
he battles with and ultimately justifies his own decision to favour teaching
and campaigning over programming, despite being a talented programmer:
[http://www.aaronsw.com/weblog/nonapology](http://www.aaronsw.com/weblog/nonapology)

“I am saved, I think, because it appears that Hardy’s logic to some extent
parallels mine. Why is it important for the man who “can bat unusually well”
to become “a professional cricketer”? It is, presumably, because those who can
bat unusually well are in short supply and so the few who are gifted with that
talent should do us all the favor of making use of it. If those whose
“judgment of the markets is quick and sound” become cricketers, while the good
batters become stockbrokers, we will end up with mediocre cricketers and
mediocre stockbrokers. Better for all of us if the reverse is the case.

But this, of course, is awfully similar to the logic I myself employed. It is
important for me to spend my life explaining what I’d learned because people
who had learned it are in short supply — much shorter supply, in fact (or so
it appears), than people who can bat well.”

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rckrd
Despite saying,

 _" I have never done anything 'useful'. No discovery of mine has made, or is
likely to make, directly or indirectly, for good or ill, the least difference
to the amenity of the world."_

He contributed a lot of practical findings in math. The Hardy-Weinberg
principle[0] comes to mind...

[0][https://en.wikipedia.org/wiki/Hardy%E2%80%93Weinberg_princip...](https://en.wikipedia.org/wiki/Hardy%E2%80%93Weinberg_principle)

~~~
Fordrus
It's almost frightening to me that the Hardy of the Hardy-Weinberg equilibrium
could be writing this. It's part of a healthy understanding of genetics at
all!

~~~
gjm11
I very much doubt that Hardy regarded that as a "discovery". From a pure-
mathematical point of view it's completely trivial.

(I do not say that to diminish its importance, which is an entirely separate
matter. And something can be mathematically trivial but still an important
discovery -- the cleverness may e.g. reside in noticing that it's a thing that
might be true at all. Be all that as it may, I can't imagine Hardy, given his
general dismissive attitude to applications of mathematics, seeing it as a
discovery rather than a triviality that happened to be useful to biologists.)

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thebarknight
Yes, that is true. He really did not care about it. The paper he wrote is
Mendelian Proportions in a Mixed Population
([http://science.sciencemag.org/content/28/706/49.full.pdf+htm...](http://science.sciencemag.org/content/28/706/49.full.pdf+html)).
It is brief, barely a page in length, and he introduces the HW equation with
the preamble "A little mathematics of the multiplication table type is enough
to that in the next generation the numbers will be [equation]".

As an added bonus, he cites Karl Pearson

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hackaflocka
The greatness of Hardy is that some unknown person from across the world
(Ramanujan) wrote him barely legible letters, and he read them, believed in
the writer, and helped expose him to the world.

I was once in a position where lots of people wrote me letters seeking to tell
me about their talents. All the letters went unread to my dustbin. True and
sad.

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srcerer
Anyone who enjoyed reading that (especially the bit about mathematical
reality) absolutely must read Anathem by Neal Stephenson. The proof is rather
enumerative, which I will leave as an exercise ;)

As for discussion. Is not the quote "We live either by rule of thumb or on
other people’s professional knowledge." the most antithetical to hacker
culture you've ever heard?!?

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goldenkey
I did not care much for Hardys opinion about how innocent pure math was. Since
it was later proved wrong by nukes. But the novella was a real glimpse into
the austere life of a curmudgeon and some of the oxford culture. In addition
to the culture of the elite as well, which unsurprisingly respect science and
math much more than proles.

~~~
Koshkin
Well, it's not math that kills, it's people... I mean, I don't think it is
fair to blame scientists, engineers, workers, etc. - let alone the tools that
they use - for the way the product of their work is used.

Also, to be fair, the elementary analysis book which Hardy wrote under the
title A Course of Pure Mathematics by today's standards would hardly qualify
as a book on 'pure math' anyway.

~~~
wamsachel
>I mean, I don't think it is fair to blame scientists, engineers, workers,
etc. - let alone the tools that they use

I think it should be fair. It's no secret what these precision guided bombs
are being used for, so why should the nerds that continue to work on them be
free of culpability?

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Consultant32452
The invention of the nuclear bomb has led to the most peaceful period in human
history. So to whatever extent the scientists and engineers who had some part
in creating those bombs are culpable, they should be considered heroes.

~~~
jknoepfler
No, it didn't. Democide in the 20th century, the death toll of which far
outstripped the death toll from conventional warfare, reached its peak after
the use of nuclear weapons against civilians in Japan. The notion that the
post-nuclear era has been "peaceful" either absolutely or relatively is
completely, ridiculously false.

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clifanatic
Is the apology for posting something that should have been HTML as a PDF?

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paulddraper
Why Hypertext Markup Language rather than Portable Document Format? Because
you like ads?

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robobro
PDF is meant for paper. HTML is meant for screens.

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wahern
Learn LaTeX and then come back here. Or better yet, learn LaTeX, write some
documents, wait 10 years, then come back after revisiting those documents.

I think I first started learning LaTeX in 2007 or 2008. I began writing HTML
around 1995. IMO, anything resembling a "document" that you expect to be
useful longer than a year or two should be written in LaTeX, or at least
something based directly on TeX. Alternatively, just use plain text. Anything
else just doesn't have a comparable shelf-life.

Whether it was intended to render to screen or print is totally irrelevant. If
anything, stay away from screen-oriented formats because there hasn't been a
standard "screen" format like, ever, with the possible exception of TTY
geometries.

And output format isn't even the half of the relevant qualities to worry about
when it comes to shelf-life. TeX is basically written in Pascal. TeX is a
standard as well as its own future-proof implementation, permitting pixel-
perfect reproduction across decades. I expect direct ports of TeX to Web
Assembly not long after the standard sees adoption.

Of course, TeX is not the same thing as PDF; not even remotely. But TeX is
oriented toward the world of hard copies, and I hardly see that as a fault.
But even if so, it's de minimis in the grand scheme of things.

