Entry
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Found in the goldmine that is the printed set of Number Theory lecture notes.
Theorem 4.1. Every positive integer n can be written as the sum of four integer squares.
This is a statement that your non-mathematical parents would understand. If they ask you what you've learned in three or four years on a maths degree you can mention this, and they'll be very impressed and think that your education has been worthwhile. Most of your other modules give you statements that are pure gobbledygook to the uninitiated. Galois Theory gives a few statements that your parents might understand but they're all negative: you can't solve a quintic, or contruct a heptagon, or trisect an angle. Number Theory gives positive assertions that broaden your horizons, and expand the frontiers of your knowledge...
If you've survived reading the previous paragraph without vomiting then you have strong constitution and is ready for the proof of the Four Squares Theorem.
Proof:...
