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A Mathematician’s Apology

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Re: A Mathematician’s Apology

#21

Post by generationP »

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…

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.)

Re: A Mathematician’s Apology

#22

Post by LeanderK »

generationP wrote: post #21
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…

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?

Re: A Mathematician’s Apology

#23

Post by FabHK »

spanxx wrote: post #2

Would you recommend that book to a software engineer with an interest in Maths?

No. It's been a while since I read it, but I found it an unapologetic, tedious, arrogant, self-serving screed lionising pure mathematics (and its practitioners, but only the very best), denigrating anything applied or even applicable, yet basically asking the hoi polloi doing that nether pedestrian work of actually working to put food on his table.

And, it's not even particularly good in instilling some appreciation of the beauty of mathematics.

Save your time.

Re: A Mathematician’s Apology

#24

Post by galangalalgol »

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?

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!

Re: A Mathematician’s Apology

#25

Post by enriquto »

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 experimental science, a part of natural science. Mathematics is the part of physics where experiments are cheap.

The Jacobi identity (which forces the heights of a triangle to cross at one point) is an experimental fact in the same way as that the Earth is round (that is, homeomorphic to a ball). But it can be discovered with less expense. "

--[1] On Teaching Mathematics

"All mathematics is divided into three parts: cryptography (paid for by CIA, KGB and the like), hydrodynamics (supported by manufacturers of atomic submarines) and celestial mechanics (financed by military and by other institutions dealing with missiles, such as NASA.).

Cryptography has generated number theory, algebraic geometry over finite fields, algebra, combinatorics and computers.

Hydrodynamics procreated complex analysis, partial derivative equations, Lie groups and algebra theory, cohomology theory and scientific computing.

Celestial mechanics is the origin of dynamical systems, linear algebra, topology, variational calculus and symplectic geometry.

The existence of mysterious relations between all these different domains is the most striking and delightful feature of mathematics (having no rational explanation)."

--[2] Polymathematics: Is mathematics a single science or a set of arts?

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

[2] http://math.ucr.edu/home/baez/Polymath.pdf

[3] Link to many Arnold's writings: http://www.pdmi.ras.ru/~arnsem/Arnold/arn-papers.html

Re: A Mathematician’s Apology

#26

Post by valgor »

While Hardy's book is still relevant, there is a more modern attempt at answering the same questions for those interested: Mathematics without Apologies: Portrait of a Problematic Vocation by Michael Harris.

Re: A Mathematician’s Apology

#27

Post by nik61 »

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.

Re: A Mathematician’s Apology

#28

Post by nautilus12 »

Reminds me of how when designing software systems for companies you always start with the user access patterns otherwise you end up building some elegant stream based system for something that only needs batch access. Pure math can be the same way in alot of ways, why invest the precious resource of human innovation getting lost in the woods? It's possible alot of pure math is just us convincing ourselves of it's value unchecked by any actual means of producing value from it. Context: used to be a pure mathematician, now an engineer.

Re: A Mathematician’s Apology

#29

Post by oefrha »

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 procreated complex analysis, partial derivative equations, Lie groups and algebra theory, cohomology theory and scientific computing.

> Celestial mechanics is the origin of dynamical systems, linear algebra, topology, variational calculus and symplectic geometry.

Now those are just backwards.

Re: A Mathematician’s Apology

#30

Post by enriquto »

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…

> Now those are just backwards.

Of course, it is a rhetorical device. If you read the rest of the linked article you'll see that the author has quite a sense of humor. The content is rather serious though (about unexpected links between seemingly unrelated parts of math).

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