>mathematics is basically the only scientific discipline that rejected any notion of utility

I think this might depend on the department, but I was at a pure math department last year, and struggling with my Linear Algebra textbook (written by the professor, incidentally, who was not a great communicator).

I consulted the machines, and learned, to my great delight, that linear algebra is used in like 20 different fields in the real world. It's "perhaps the most applied branch of mathematics in existence".

I complained in the group chat, that our didactic materials, specifically tasked with providing motivation and concrete examples, did not contain a single application, of this most richly applied field.

I was promptly pilloried, and shunned.

(Apparently that particular department was the wrong one, to ask a question like that!)

> I complained in the group chat, that our didactic materials, specifically tasked with providing motivation and concrete examples, did not contain a single application, of this most richly applied field.

> I was promptly pilloried, and shunned.

Heh. In my day I may have participated in the pillorying.

I do think that there is value/merit in professors mentioning real world applications, where they exist.

What they're sensitive about are the theorems where there aren't real world applications. They don't want to (and shouldn't) justify them.

So even when there are real world applications, the posture is "Who knows if someone is making good use of this in the world somewhere? I don't care. It's not why we learn or teach this!"

I love teaching kids and young adults calculus by socratic method. They get so mad when they figure out you were teaching them math, but they often admit it was pretty fun. Only had the chance to teach like that a few times but it's dynamite when it happens.

I thought linear algebra was pretty much the poster child of applied mathematics - the entire field was invented to represent computations in a regularized form to feed into computers. Well not really, but much like Boolean algebra or the Fourier Transform, it was pretty much a curiosity until computers came along.

despite being theoretical i would have greatly benefitted in learning linear algebra if i had seen even one or two not-obvious applications, like galois fields for reid solomon erasure coding.

>(Apparently that particular department was the wrong one, to ask a question like that!)

Yes, the math department.

In any case linear algebra, stochastics, calculus; plenty of engineering and science applications for all these.

As a friend of mine who also happens to be a math professor once said: mathematicians are like sculptors who marvel about the beauty of their creation, and are kind of disgusted when a physicist comes nearby and says “that's a cool hammer you got there, may I borrow it?”.

As my Linear Algebra prof used to say, basically everything is applied Linear Algebra.

I’m a physicist, so I’m biased, but my experience of pure maths was about the same. We had to do it, but at no point was any utility actually demonstrated - that was left to the physics professors. It was all just “look at this thing I can do with these symbols” without any actual tangible relationship to anything.

Then again, I remember how we were taught calculus at high school - we were taught how to mechanistically integrate and derive everything under the sun. At no point did anyone think to explain that we were measuring the areas under curves, or their rates of change - it was all just “memorise this operation”. Again it was left to the physics teachers to explain why this was useful, and what we were actually doing.

Poor teaching, if you ask me, and it more often than not left me retrospectively wondering if said mathematicians had actually understood any of what they did, or if they just had little blind symbol manipulation Turing machines in their heads.

Typical pure-math linear algebra course has to cover so much material that there's really no time for applications! That's why applied math is typically separate track.

If it was the students, then students can have things they think are cool or uncool.

If it was the professor, then that would be very embarassing on his or her part.