Mathematical addiction - looking for your next fix, non?

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OK, so the word "addiction" has obvious negative connotations, but am I alone - methinks not - in being far more than just "interested" in maths, and actually more of a border-line addict, always looking for that next discovery/fix...?

Bad mammal! lol (Heidy)(Heidy)(Heidy)
 
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Of course you're not alone...I keep a syringe full of algebra nearby in case my usual dealer runs out.
 
(whispers) I'll trade you 3 full vials of Quantum Electrodynamics for a bottle of non-linear PDEs. It's a great value.

-Dan
 
I'm a bit confused by the conditions on the existence of coordinate basis given by Frobenius's theorem. Namely, let's take a n-dimensional smooth manifold and a set of n smooth vector fields defined on it. Suppose they are pointwise linearly independent and do commute each other (i.e. zero commutator/Lie bracket). That means they span the entire tangent space at any point and since commute, they define a local coordinate basis. What does this mean? Well, starting from any point on the...

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