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A Mathematician’s Apology

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Re: A Mathematician’s Apology

#31

Post by [deleted] »

oefrha wrote: post #29
enriquto wrote: post #25

This is a beautiful read. It should not be taken too much seriously, though. For a nice complement, see the writings of another, and arguably much greater, mathematician V.I. Arnold. His contrasting view on the nature of mathematics is that "mathematics is the part of physics were experiments are cheap". EDIT: I add quotes and links to some of Arnold's writing. " Mathematics is a part of physics. Physics is an experi…

As a physicist who studied mathematics as an undergrad and was admitted into some top math graduate programs (but didn’t go because I pursued theoretical physics instead) — no, only part of mathematics has something to do with physics at all, let alone being inspired by physics. > Cryptography has generated number theory, algebraic geometry over finite fields, algebra, combinatorics and computers. > Hydrodynamics pro…

[deleted]

Re: A Mathematician’s Apology

#32

Post by madcaptenor »

EthanHeilman wrote: post #20
jesuslop wrote: post #10

Earlier quoted context omitted.

What about elliptic curve cryptography?

Yep, or RSA and most modern cryptography.

But not the cryptography that was in use at the time - for example Enigma is more combinatorial than number-theoretic.

Re: A Mathematician’s Apology

#33

Post by whatshisface »

mikorym wrote: post #13
karlicoss wrote: post #7

Great read! The bit that I found the most curious is actually listed on Wikipedia (this was written in 1940): > "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."

>> "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." > The GPS project was started by the U.S. Department of Defense in 1973 [1] [1] https://en.wikipedia.org/wiki/Global_Positioning_System

>From 1942 to 1946, the [Manhattan] project was under the direction of Major General Leslie Groves of the U.S. Army Corps of Engineers.

https://en.wikipedia.org/wiki/Manhattan_Project

Re: A Mathematician’s Apology

#34

Post by Ohn0 »

hjorthjort wrote: post #16

It almost sounds like this book is the reason we so often hear and talk about the imposed hierarchy between "pure" and "applied", and that "mathematics is a young man's game". Did it have a huge impact? Or were these ideas commonplace before it was published?

Sounds like the beginning of excluding women from stem.

Re: A Mathematician’s Apology

#35

Post by LeanderK »

galangalalgol wrote: post #24
LeanderK wrote: post #22

Earlier quoted context omitted.

but does it contain a philosophical argument like Hardy?

Philosophical arguments are for pure math navel gazers. Applied folks are too busy actually doing things that make people's lives better. That rant does not actually represent my beliefs, it just seemed like what the ggp wanted so, tada!

Not sure what you're getting at. I think it's often fascinating to read texts about the instrinsic motivation of these different crafts, as an example "the beauty of programming" from linus torvalds: https://www.brynmawr.edu/cs/resources/beauty-of-programming

So I wonder, since this is more or less direct attack on the beauty of applied mathematics how they would respond. What makes applied math beautiful? I can certainly say what I find beautiful about CS and Machine Learning! It strikes me as obvious, but that's probably why I like it.

Re: A Mathematician’s Apology

#36

Post by Ohn0 »

nik61 wrote: post #27

Many people, mathematicians and aspirants, would find "Mathematics made Difficult" by Carl E Linderholm (pub. 1972) entertaining and possibly instructive. PDFs are available to those without scruples.

How about those of us with scruples?

Re: A Mathematician’s Apology

#37

Post by bonoboTP »

LeanderK wrote: post #14

> On the other hand, Hardy denigrates much of the applied mathematics as either being "trivial", "ugly", or "dull", and contrasts it with "real mathematics", which is how he ranks the higher, pure mathematics. Not sure if this surprising, since he was a vocal pure mathematician. But since I don't agree (and it sometimes looks like the pure mathematicians look down on the applied), I wonder whether there are some text…

Look at this interview with Cornelius Lanczos: https://youtu.be/avSHHi9QCjA?t=141

At the linked timestamp he talks about how he doesn't like the split of "pure" and "applied" math and how it's a very new concept of the 20th century.

Re: A Mathematician’s Apology

#38

Post by generationP »

Ohn0 wrote: post #34
hjorthjort wrote: post #16

It almost sounds like this book is the reason we so often hear and talk about the imposed hierarchy between "pure" and "applied", and that "mathematics is a young man's game". Did it have a huge impact? Or were these ideas commonplace before it was published?

Sounds like the beginning of excluding women from stem.

The beginning?

Re: A Mathematician’s Apology

#39

Post by generationP »

LeanderK wrote: post #22
generationP wrote: post #21

Earlier quoted context omitted.

Tom Körner's "The Pleasures of Counting" ( https://www.amazon.com/Pleasures-Counting-T-W-K%C3%B6rner/dp... ) is an amusingly written yet intellectually challenging introduction to applied maths for the general audience. (His website https://www.dpmms.cam.ac.uk/~twk/ will give you an idea of the writing style.)

but does it contain a philosophical argument like Hardy?

It's not a philosophic pamphlet; Chapters 18 and 19 have some amount of philosophizing, but the rest of the book is heavily "show, don't tell". Which is the logical way to write a book on applied(!) maths.

Re: A Mathematician’s Apology

#40

Post by Anon84 »

Ohn0 wrote: post #36
nik61 wrote: post #27

Many people, mathematicians and aspirants, would find "Mathematics made Difficult" by Carl E Linderholm (pub. 1972) entertaining and possibly instructive. PDFs are available to those without scruples.

How about those of us with scruples?

In that case, Amazon is your friend: https://www.amazon.com/Mathematics-made-difficult-Carl-Linde...
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