/sci/ - Science & Math

You are not a philosopher if you can't read this.

You may have a complex taste for literature and even read Kant on the side but if you can't formalise your thoughts there is no possibility for you to be able to actually craft knowledge which can be identified as such.

From the standpoint of the advancement of knowing, a thinker that won't formalise may as well be a stoner looking up to the stars, or, even worse a Glass Bead Game Player.

Why do I find logical proofs like pic related super easy, but struggle so much with even basic math?

I was mediocre in math through grade school. I usually figured stuff out on-the-spot by using a primitive version of induction to check if it works.

When I landed in college I took a class on logical proof and greatly enjoyed it. I had a bit of a knack for doing proofs quickly in my head.

My prof took notice and made the suggestion, "oh you like proofs? You should get into Math. It's all about proofs." However, I struggle with any proofs greater than basic arithmetic replacements.

for example, I'm working through Riley and Hobson's Foundations, and a problem is: Given distinct primes p and q, where p and q != 1, show that there is no rational number a such that p^(1/2) = a*q^(1/2).

my approach so far is kinda like "well the roots of prime numbers are irrational (wait are they? all I really know is that they're not integers, they could be rational). So the property this is going to hinge on is something like one irrational number can only be the factor of another if the other factor is also irrational. But, again, Idk whether or not that's true or how to prove that it's true.