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A Mathematician’s Apology

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Re: A Mathematician’s Apology

#41

Post by jonjacky »

spanxx wrote: post #2

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

It's not much about maths, it's a memoir by a particular mathematician written at an unhappy point in his life, reflecting back on what he has done. It belongs more to the literature about artists and creativity, than to books of mathematical content. For that, see instead Hardy's Course of Pure Mathematics [1]

If you do read the Apology, be sure to get an edition with C.P. Snow's forward, which gives the back story that puts Hardy's memoir in context. It also includes the wonderful story of Hardy and Ramanujan.

[1] https://en.wikipedia.org/wiki/A_Course_of_Pure_Mathematics

Re: A Mathematician’s Apology

#42

Post by oarabbus_ »

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…

>"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.).

This seems like an odd classification or backwards. The mathematics existed, long before humans existed. Humans simply _discovered_ it when studying some of the disciplines mentioned above.

The statement "all mathematics is divided into cryptography, hydrodynamics, and celestial mechanics" seems untrue. I'd personally disagree that for example, topology can be entirely attributed to celestial mechanics, scientific computing to hydrodynamics, algebra to cryptography, etc.

Also, it seems fair to call Arnold a greater mathematician than Hardy, rather than just "arguably" so based on their direct work. Hardy's greatest contribution to mathematics was discovering and nurturing Ramanujan, who was a top 10 mathematical talent of all time.

Re: A Mathematician’s Apology

#43

Post by jjtheblunt »

oarabbus_ wrote: post #42
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…

>"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.). This seems like an odd classification or backwards. The mathematics existed, long before humans existed. Humans simply _discovered_ it when studying…

I wonder if he was alluding to Caesar asserting "All Gaul is divided into three parts:..." (albeit in Latin).

Re: A Mathematician’s Apology

#44

Post by chongli »

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!

make people's lives better

But arguably also making people’s lives worse. Applied mathematicians and physicists have contributed to the development of weapons of war since the time of Archimedes. As a committed and outspoken pacifist, Hardy wanted no part in warfare. This informed a good part of his philosophy, along with aesthetics.

I would hardly call that navel gazing.

Re: A Mathematician’s Apology

#45

Post by cma »

oarabbus_ wrote: post #42
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…

>"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.). This seems like an odd classification or backwards. The mathematics existed, long before humans existed. Humans simply _discovered_ it when studying…

Pretty sure it was intentionally facetious.

Re: A Mathematician’s Apology

#48

Post by enriquto »

oarabbus_ wrote: post #42
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…

>"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.). This seems like an odd classification or backwards. The mathematics existed, long before humans existed. Humans simply _discovered_ it when studying…

> The statement "all mathematics is divided into cryptography, hydrodynamics, and celestial mechanics" seems untrue.

He's obviously using an over-the-top generalization to be provocative and funny. I guess we are not supposed to understand these words literally.

The adscription of topology to mechanics is not entirely casual in his case. He's essentially the father of topological methods in dynamics, and he proved (with Kolmogorov and Moser) the famous "KAM" theorem about the long term stability of the solar system with probability one.

Notice that Hardy also uses exaggeration to state some of his finest claims, and he's probably a better writer than Arnold because he manages to do so without the reader noticing.

Re: A Mathematician’s Apology

#49

Post by solar_perplexus »

spanxx wrote: post #2

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

I would suggest picking up a textbook in mathematics for a specific area relevant to your interest.

I found that studying specific topics (currently probability theory and statistics) helped me comprehend the field better and in ways that make it practical for my planned career.

Re: A Mathematician’s Apology

#50

Post by domnomnom »

oarabbus_ wrote: post #42
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…

>"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.). This seems like an odd classification or backwards. The mathematics existed, long before humans existed. Humans simply _discovered_ it when studying…

>This seems like an odd classification or backwards. The mathematics existed, long before humans existed. Humans simply _discovered_ it when studying some of the disciplines mentioned above.

Nope. When you get into real analysis you see that this is not true. It's hard to even get the Real Numbers down.

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