GaussBonnet

4 ms·

1.
by GaussBonnet 6y ago
Proofs are only an example of what grade school teachers don't know. They are obviously missing all of the modern applications as well. Whether you want to call those applications "math" or something more specific ("engi
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by GaussBonnet 6y ago
The problem isn't that grade school teachers are sitting on a secret stash of cool theorems, and instead diabolically choose to have students solve quadratic equations year after year. It's that no one in the grade school pipeline
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by GaussBonnet 6y ago
You aren't wrong. Until extremely recently, algebraic geometry was a field by and for the purest of the pure mathematicians. These days algebraic geometry has made its way into string theory. https://en.wikipedia.org/wi
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by GaussBonnet 6y ago
The phenomenon you are talking about is essentially that of a homomorphism, or homomorphic structures. That is, structures that appear superficially different but share an underlying common structure. The concept of a 'functor' wa
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by GaussBonnet 6y ago
The first 10 pages of the following link may be helpful; it shows probably the simplest concrete nontrivial 2-form: https://math.berkeley.edu/~wodzicki/H185.S11/podrecznik/2for... The first example there is:
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by GaussBonnet 6y ago
The point of differential forms is that they give a way to express geometric theorems in a coordinate free way. Coordinates are seen as obscuring the pure geometric content of theorems. They are sometimes necessary artifacts of doing concre
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by GaussBonnet 6y ago
Background in pure math here. Generally researchers learn about what problems are fashionable as they talk to others in the field. As a PhD student, your advisor should give you ideas for problems to work on. Solutions to old problems tend