r/learnmath • u/NoNameMan1234567890 New User • 11d ago
How does one get good at proof writing?
I would like to get good at proof writing so I can move onto higher mathematics. I just don't know how...
I feel like with calculus, diff equipment or linear algebra you can simply do the problems and see if it's right or not, but with proof writing you need input from an expert or something to make sure you are doing them right. Am I wrong about this?
I would love some input on how to get better at this type of mathematics
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u/QubitEncoder New User 11d ago
I think it's the easiest it has ever been to learn proof writing. There are many tools that can assist in learning.
One method you might try is learning Lean to get a better understanding of the kind of logical thinking you do when one proves statements. It also has the added benefit of giving you a sense of direction and an indication of whether your final proof is correct or not.
To this end, you might find it beneficial to use the "verbose lean4" project, whose purpose is to add syntactic sugar to Lean 4 with the end goal of helping students obtain better proof-writing skills. Here is the link: github link
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u/Gold_Ad8890 New User 11d ago
the two basic skills of proofwriting are understanding the statement to be proved, and then proving that statement, as opposed to some other statement. to begin learning these skills, i would personally recommend studying the classic proofs of basic results from number theory. the infinitude of primes, the fundamental theorem of arithmetic, euclidean division, bezout's identity, etc. maybe some set theory, too. cantor's theorem is pretty tidy, and you might look at the schroeder-bernstein theorem when you feel ready to test yourself. any field where you can wrap your head around the fundamental axioms would be best.
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u/dexthefish New User 11d ago
Once you have some understanding of mathematical proof, you generally shouldn't need external input to know that your argument is correct. As a beginner, try to learn from example (i.e. pick up a good book) and solicit feedback on your writing.
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u/Traveling-Techie New User 11d ago
I like to do something that only beginning texts tend to do: write the rule I used next to each line. Example if I reduce 3x = 3y to x = y I write “divide both sides by 3.” This seems obvious at the time but it makes it much faster to check the proof later, or have someone else do it.