Physics for Mathematicians – Introduction
1–10 of 63 posts
Re: Physics for Mathematicians – Introduction
#2I am neither a physicist nor a mathematician, but this looks like an awesome undertaking that will benefit both communities! :)
Re: Physics for Mathematicians – Introduction
#3This is really cool. Can also serve as a Rosetta Stone for physicists wanting to better understand the language of mathematicians.
Re: Physics for Mathematicians – Introduction
#4I've never gotten a satisfactory explanation of what sort of mathematical object a physical unit (meter, kilo, second etc) is. There are plenty of bones of contention between maths and physics, but this one bothers me the most.
Anyone interested in coming at physics from a mathematics perspective should read Arnold's mechanics book.
Re: Physics for Mathematicians – Introduction
#5euler is the last titan of pure raw 'classic' mathematics because gauss was a pretty strong 'theoretical' physicist.
how have the mathematical contributions of quantum physics affected mathematics? have they??
maybe the field that's really lagging in recognizing the implications of "recent" scientific revolution (QM) is philosophy?
finally, I wonder how will the schizm in mathematics that is the IUT (mochizuki's theory) will finally pan out. apparently euler also left stuff behind that took over 70 years to be understood so I ain't holding my breath.
Re: Physics for Mathematicians – Introduction
#6Spivak (of differential geometry fame) wrote a book with this precise title:
https://archive.org/details/physics-for-mathematicians-mecha...
It's a very interesting take on classical mechanics.
Re: Physics for Mathematicians – Introduction
#7I've never gotten a satisfactory explanation of what sort of mathematical object a physical unit (meter, kilo, second etc) is. There are plenty of bones of contention between maths and physics, but this one bothers me the most. Anyone interested in coming at physics from a mathematics perspective should read Arnold's mechanics book.
Why is the measure not a satisfactory answer?
Re: Physics for Mathematicians – Introduction
#8I've never gotten a satisfactory explanation of what sort of mathematical object a physical unit (meter, kilo, second etc) is. There are plenty of bones of contention between maths and physics, but this one bothers me the most. Anyone interested in coming at physics from a mathematics perspective should read Arnold's mechanics book.
Terence Tao wrote a nice blog post about this: https://terrytao.wordpress.com/2012/12/29/a-mathematical-for...
Re: Physics for Mathematicians – Introduction
#9I've never gotten a satisfactory explanation of what sort of mathematical object a physical unit (meter, kilo, second etc) is. There are plenty of bones of contention between maths and physics, but this one bothers me the most. Anyone interested in coming at physics from a mathematics perspective should read Arnold's mechanics book.
One concern is that measures, out of the box, have issues in 3+ dimensions. Concretely due to paradoxes such as Banach-Tarski, that arise from the Zermelo Fraenkel (ZF) + Axiom of Choice (AC) = ZFC axiomatic formulation for set theory.
Since things need to conserve in pyhsics, one has to account for this issue and doing so is harder than it may seem as AC is part of the "fabric" of most mathematics which, at large, chooses to ignore the problem.
Re: Physics for Mathematicians – Introduction
#10I've never gotten a satisfactory explanation of what sort of mathematical object a physical unit (meter, kilo, second etc) is. There are plenty of bones of contention between maths and physics, but this one bothers me the most. Anyone interested in coming at physics from a mathematics perspective should read Arnold's mechanics book.
Why is the measure not a satisfactory answer? https://en.m.wikipedia.org/wiki/Measure_(mathematics)
Unfortunately, even though it is said to be a "generalization" of these things, mathematical measure theory has nothing to do with physical units of measure or dimensional analysis.