[mcguire]

Many years ago I heard a mathematician speaking about some open problem and he said, "Sure, it's possible that there is a simple solution to the problem using basic techniques that everyone has just missed so far. And if you find that solution, mathematics will pat you on the head and tell you to run off and play.

"Mathematics advances by solving problems using new techniques because those techniques open up new areas of mathematics."

[lupire]

That's the attitude of poor mathematicians who are insecure about their own faults.

[mb7733]

What the hell is that quote? No, a simple proof is the absolute mathematical ideal!

[senderista]

Really? I've always had the impression that "elementary" proofs of hard problems are highly valued.

[ants_everywhere]

A proof of a long-open conjecture that uses only elementary techniques is typically long and convoluted.

Think of the problem as requiring spending a certain amount of complexity to solve. If you don't spend it on developing a new way of thinking then you spend it on long and tedious calculations that nobody can keep in working memory.

It's similar to how you can write an AI model in Pytorch or you can write down the logic gates that execute on the GPU. The logic gate representation uses only elementary techniques. But nobody wants to read or check it by hand.

[psunavy03]

That seems like a justification that is right on the knife's edge of being a self-licking ice cream cone.