3 ms·

Is "any hamiltonian dynamics on any phase space of a physical system" not a major enough class of problems for you? This is one way mathematicians study physics

Is "any hamiltonian dynamics on any phase space of a physical system" not a major enough class of problems for you? This is one way mathematicians study physics. Are you asking for applications of symplectic geometry? If so, here, I've been reading a cluster of papers in this area for a few weeks now: https://www.math.colostate.edu/~clayton/research/papers/frames.pdf https://www.math.colostate.edu/~clayton/research/papers/fram...

ajkjk 7y ago
No, I'm plenty aware of the applications. My complaint is that this article hardly mentioned them! What's the point of an article explaining a theory without motivating why it exist?
- mikhailfranco 7y ago
  Yes, too many mathematicians write about areas of mathematics that could be useful to others, without giving any motivation, or any hand-waving explanations, or the critical distinctions that make it a useful approach. There is a barrier of communication that (most) mathematicians don't want to take any time to overcome. Often, the opening is enticing, then it's straight into lemmas, formal language, and citing of famous results by name. Their slight inclination to explain it to others dissipates in the first paragraph, then it's off to the races to impress their peers. This is easy to see on Wikipedia - most mathematics articles are utterly useless to any non-mathematician who wants to get a general appreciation of an approach to see if it could shed some light on their problem. In almost all cases, it is better to read domain generalists coming the other way into the higher mathematics. Of course, one shining exception is John Baez: http://math.ucr.edu/home/baez/twf.html http://math.ucr.edu/home/baez/twf.html http://math.ucr.edu/home/baez/symplectic.html http://math.ucr.edu/home/baez/symplectic.html
- danharaj 7y ago
  The blunt reason is that this article was written for mathematics grad students who already know that symplectic manifolds are a hot topic via diffusion.

ajkjk 7y ago

No, I'm plenty aware of the applications. My complaint is that this article hardly mentioned them! What's the point of an article explaining a theory without motivating why it exist?

mikhailfranco 7y ago
Yes, too many mathematicians write about areas of mathematics that could be useful to others, without giving any motivation, or any hand-waving explanations, or the critical distinctions that make it a useful approach. There is a barrier of communication that (most) mathematicians don't want to take any time to overcome. Often, the opening is enticing, then it's straight into lemmas, formal language, and citing of famous results by name. Their slight inclination to explain it to others dissipates in the first paragraph, then it's off to the races to impress their peers. This is easy to see on Wikipedia - most mathematics articles are utterly useless to any non-mathematician who wants to get a general appreciation of an approach to see if it could shed some light on their problem. In almost all cases, it is better to read domain generalists coming the other way into the higher mathematics. Of course, one shining exception is John Baez: http://math.ucr.edu/home/baez/twf.html http://math.ucr.edu/home/baez/twf.html http://math.ucr.edu/home/baez/symplectic.html http://math.ucr.edu/home/baez/symplectic.html
danharaj 7y ago
The blunt reason is that this article was written for mathematics grad students who already know that symplectic manifolds are a hot topic via diffusion.