Non-academic mathematics development?

Question

How do you see non-academic mathematics?

I have an impression that the academy has still a quite significant prestige and is thought to be the safe-guard for "real science". That is, to verify that those that have the most experience in science, can produce science and have the "blessing" of the academy, in order to deviate from informal publications made outside of academia, whose content cannot be guaranteed and that do not necessarily go through peer-review.

However, esp. in mathematics, there's no real reason why mathematics cannot be produced anywhere. I.e. academy does not add much to the process of doing mathematics. Social connections to like-minded people perhaps.

Then there's the internet, which makes all information pretty accessible.

So do you think there's a place for "open source, non-academic mathematics"?

Answer 1

I think it is likely that mathematics, outside of areas where work is secret (cryptography, finance) or very deep/structured areas that need years of training and immersion to be successful (arithmetic algebraic geometry), will increasingly be done outside of academia to a point where the production from non-academia is comparable to what is done in universities. Part of that may be from a shrinking of academia.

Answer 2

A place? Sure! I think it's great. I am not in academics, but I really do like reading about and doing math now and again.

But doing research requires a lot of time to invest in reading literature, thinking about problems, trying your hand at different approaches, etc. It's a full time job. Productive mathematicians might put out a paper or two a year. That's a full time job. They also have access to colleagues right around the corner that they can go and talk to, just about mathematics in general, even if not their particular research problem. Research institutions frequently have visiting scholars, colloquium talks, seminars, topics courses, etc which all stimulate academic research and introducing people to ideas they might have never otherwise encountered.

As a non-academic mathematician, you're going to miss out on all of these things. Also, it's probably not going to be easy for you to travel to conferences (you'll probably need to take a vacation day from work). I think math is a great hobby. I love it, and I don't need anything in particular to fiddle with ideas all by my lonesome. But I don't really think I'll ever be on the cutting edge of research, nor do I much desire to be.