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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, ma

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 https://www.uni-muenster.de/Physik.TP/~munsteg/arnold.html [2] http://math.ucr.edu/home/baez/Polymath.pdf 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 http://www.pdmi.ras.ru/~arnsem/Arnold/arn-papers.html

oefrha 7y ago
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.
- enriquto 7y ago
  > 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).
- deleted 7y ago
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oarabbus_ 7y ago
>"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.
- jjtheblunt 7y ago
  I wonder if he was alluding to Caesar asserting "All Gaul is divided into three parts:..." (albeit in Latin).
- cma 7y ago
  Pretty sure it was intentionally facetious.
- enriquto 7y ago
  > 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.
- domnomnom 7y ago
  >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.

oefrha 7y ago

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.

enriquto 7y ago
> 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).
deleted 7y ago
[deleted]

oarabbus_ 7y ago

>"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.

jjtheblunt 7y ago
I wonder if he was alluding to Caesar asserting "All Gaul is divided into three parts:..." (albeit in Latin).
cma 7y ago
Pretty sure it was intentionally facetious.
enriquto 7y ago
> 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.
domnomnom 7y ago
>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.