[sdenton4]

How many people drive cars without knowing how an engine works? Or make a phone call without knowing how voice compression for a cellular network does it's thing? Or eats food without knowing how it came together from the supply chain?

[robrain]

The mechanic who repairs the cars knows how the engine works.

The telco that manages loads and allocates networks knows how voice compression works.

The farmers and supermarkets know how the supply chain works.

None of your questions show why mathematics should include blobs of incomprehensible gloop, where no mathematician, no logician, no philosopher, no man on the street can make sense of said gloop, or use it in any way to further human knowledge.

When it's been decomposed down we can discuss this further, but now it's like saying red is red, just because.

[sdenton4]

Well, you said people can't use things they don't understand.

But I'll take your expanded statement, to include riding a horse, something even older than the engine. We don't understand fully how a horse works -- biology is still a matter of seeing fragments of the whole -- but people had no problem riding and breeding them before the invention of the car, and before the discovery of genetics.

Meanwhile, understanding the math of a thing -- like stock markets, or nuclear bombs -- does not prevent its use from going badly.

Math is useful and beautiful, and a helpful tool for expanding our understanding of the world, but it is not the whole of understanding, or the sole factor in successful application of science to the world .

Signed, a mathematician.

[robrain]

I said no such thing - the comment that you just replied to is the first thing I’ve said in this thread.

[VBprogrammer]

This feels like a stretch. It would be impossible for someone who didn't know how an engine worked to repair or improve the design of it.

[drdaeman]

Why not? One can surely use math even if they have no clue about how to prove theorems. I suck at math, but I use it every day, without knowing how to advance it.

I think it might be fair to say that a proof cannot be without value if it proves something meaningful to a human, that a human can use somehow? But such proof probably doesn’t belong in a library seemingly explicitly dedicated to human-graspable proofs. Just because it violates the intent.

It’s not like such proofs mustn’t exist at all.