[BeetleB]

> 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!"

[arrowsmith]

Knowledge for its own sake is great, but it's worth noting that many "useless" fields of mathematics turned out to be very practical in the long run.

Number theory was long thought to have no practical application, but now it's the backbone of cryptography. Boolean algebra was developed in the 19th century (George Boole died in 1864), decades before it was used to build computers.

Those "useless" theorems being proved today may turn out to unlock a world-changing technology centuries from now. When the breakthrough comes we'll be grateful for the people who laid the foundations.

[BeetleB]

No one is disputing that - not even most mathematicians. They just don't want it to be their job to know the useful applications.

[s3p]

Hear me out on this one:

For a lot of math departments, that is exactly why they teach this. Education is rooted in application. We have entire careers that depend on certain aspects of mathematics, so most companies gatekeep that career by a degree. The degree requires the class. The student taking the class may not even be old enough to drink alcohol yet, and they can't possibly be expected to know of all the applications. Knowing and not telling them is doing them a disservice.

[BeetleB]

> For a lot of math departments, that is exactly why they teach this.

Depends on the course. That's why some departments have separate calculus courses for math majors - because otherwise the whole class will be full of non-math majors (engineers, etc) and focusing on their needs does a disservice to the students in their own department.

> The degree requires the class. The student taking the class may not even be old enough to drink alcohol yet, and they can't possibly be expected to know of all the applications.

If I'm a CS major, and the degree is requiring a class outside of the CS department, you shouldn't expect the professor of the class to know why the CS department is requiring it. It's on the CS department and its faculty to explain it.

[samus]

The ultimate goal of university education is to raise researchers, who are the people that investigate the knowledge frontier of their field and then advancing it. To do that they have to understand a large part of the existing field so they can communicate with their peers, avoid investigating things that have already been throroughly explored, and draw useful connections to other fields.

Even in more applied fields it can take decades before advances become practically relevant. Restricting teaching to topics that have immediate practical relevance would therefore do students a huge disservice and prevent them from approaching the knowledge frontier of the field.

[andai]

> The ultimate goal of university education is to raise researchers

The head of my CS department was quoted as saying, "our job is to produce researchers!"

This was in the context of a conversation about why the program wasn't better suited for industry.

It turned out that in our department 7% of students ended up going into research.

So he was openly declaring his intention to disregard the needs of 93% of his students.

(I'm not arguing against research, or on going deep with the theory. I just thought that was kind of funny, and it seemed a bit wrong to me.)

[BeetleB]

CS is special in that it is about the science, and not the application. They'll teach you mostly theory. That's why some universities/countries have a separate degree called "SW Engineering".

Other engineering departments are not as fussy about the distinction.

[throwup238]

I think for many people (myself included) understanding mathematics is rooted in application because it helps bridge the divide between intuition and rote memorization. Without the application, IMO instructors are doing a disservice to their students and pedagogy of mathematics itself. They’re intentionally ignoring a significant fraction of the class, unless they’re teaching some esoteric grad level pure math.

[andai]

Yeah this was my position. I don't mean "Sally has six apples" necessarily, but my brain needs some concrete handles to grab onto so it can actually manipulate this stuff intuitively.

See also: Using spaced repetition to see through a piece of mathematics

https://news.ycombinator.com/item?id=18895613

Where the author describes his mind eventually turning the mathematical objects (symbols) into some kind of mental objects he was able to actually manipulate "directly". As a result of this facility, his mind spontaneously produced many new insights into the matter.

That level of fluency obviously requires a great deal of work, but in my experience it can be approximated and accelerated with analogies. (e.g. see Feynman's teaching.)