about

I have a really hard time ‘getting’ proofs in algebra that are more than a few lines long. I think a lot of proofs you find tend to be more mechanical (like “assume arbitrary $a,b,c\in S$, now let’s do a bunch of things with $a,b,c$ to prove a general fact”) and this really hurts intuition.

So I’ve been collecting proofs that just “make sense” and are really short. I haven’t been able to pin down what makes them so effective for me particularly. The big idea is that anyone can make a proof rigorous once they understand the intuition (the “essence” of the proof). So why don’t we just write down the intuition instead?

“All truths are easy to understand once they are discovered; the point is to discover them.”

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