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How important is being able to write good mathematical proofs for quant finance?

I'm planning to break into quant and prop trading from undergrad. I'm a freshman majoring in math with a minor in CS and I've never studied how to write proofs before until I took my first proof based course in abstract linear algebra. It was really hard at first learning how to write proofs and writing proofs does not seem fun at all. If I have to be able to construct proofs for the rest of my math classes, I am considering switching out of being a math major to something that's still math heavy but doesn't incorporate as much proofs for its classes like physics. Luckily, the only required proof based class for my degree is Analysis. I can just take that class and get over with it, then avoiding any pure math classes and just taking applied math classes. I hear a lot of people who study math professionally say that "real" math is all about doing proofs and the math you learn in American highschools and the intro math sequences in college like calc 1-3 linear algebra, and differential equation are not "real math." Maybe I'm not suitable for being a math major if I don't like writing proofs and that makes me feel kind of insecure, but the reason why I majored in math is because I would like using math to solve real world problems.

Daniel Duffy

C++ author, trainer
At university we learned the axioms of Natural Numbers -> Integers -> Rationals -> Dedekind cuts -> Real numbers step-by-step (e.,g. each natural number has a successor). It was like learning Theology. Before the IEEE 754 era.

Now I can use these numbers in my sleep.

Now, here is maths thing that is both a proof *and* an algorithm rolled into one; life is not always binary.

e.g. solve x^2 = 2 by writing as a fixed point. The Babylonians invented the method

So, when we say we use the Babylonian method in a calculator we know what it means rather than just pressing buttons.

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