Existence and uniqueness results are fundamental in mathematics because we often define objects by their properties, and then start calling them "the object", which is fantastically convenient.

But calling something "the object" only makes sense if there exists exactly one, and only one, object that satisfies the properties.

One particular context where these come up very explicitly is in solutions to differential equations, e.g. existence and uniqueness of solutions of partial differential equations.

Ciro Santilli intends to move his beauty list here little by little: github.com/cirosantilli/mathematics/blob/master/beauty.md

The most beautiful things in mathematics are results that are:

Good lists of such problems Lists of mathematical problems.

Whenever Ciro Santilli learns a bit of mathematics, he always wonders to himself:Unfortunately, due to how man books are written, it is not really possible to reach insight without first doing a bit of memorization. The better the book, the more insight is spread out, and less you have to learn before reaching each insight.

Eaten during Dragon Boat Festival, but can be bought year round.

Buy frozen. Pick the ones with meat and eggs!!! Boil.

Cost about 4 dollars for 2.

You can't eat them every day because too heavy, but they are so amazingly tasty!!!

The surprising thing is that a bunch of results are simpler in complex analysis!

Essentially, defining an holomorphic function on any open subset, no matter how small, also uniquely defines it everywhere.

This is basically why it makes sense to talk about analytic continuation at all.

One way to think about this is because the Taylor series matches the exact value of an holomorphic function no matter how large the difference from the starting point.

Therefore a holomorphic function basically only contains as much information as a countable sequence of numbers.

The laplace operator for Minkowski space.

Can be nicely written with Einstein notation as shown at: Section "d'Alembert operator in Einstein notation".

Made up mostly of calcium carbonate.

This operator case is surprisingly not necessarily mathematically trivial to describe formally because you often end up getting into the Dirac delta functions/continuous spectrum: as mentioned at: mathematical formulation of quantum mechanics

Can be contrasted with baryons as mentioned at baryon vs meson vs lepton.

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