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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"?

mavavilj
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  • You might be interested in this question: http://academia.stackexchange.com/questions/48208/how-possible-is-it-to-do-mathematical-research-outside-academia – coldnumber Aug 14 '15 at 00:42
  • The second paragraph has a really long sentence that's hard to parse. Could you clarify what you mean, especially about peer review? – Chris Culter Aug 14 '15 at 00:51
  • @ChrisCulter I have an impression that the academy holds the highest criteria for peer-review since it's in general thought to contain the brightest minds in the field as well. – mavavilj Aug 14 '15 at 01:01
  • But it sounds as if you're saying the opposite -- that academics' experience grants them the blessing to deviate from peer-reviewed channels. – Chris Culter Aug 14 '15 at 01:06
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    What is this "academy" you speak of? – Santiago Canez Aug 14 '15 at 01:43
  • It already exists...it is called viXra. This is what happens when anyone is allowed to publish anything they want. – Winther Aug 14 '15 at 02:12
  • @Winther So is there something wrong with viXra? – mavavilj Aug 14 '15 at 08:32
  • There is no quality control so terrible papers outnumber decent ones 100-1 so there is no reason to trust any paper you read there unless you can explicitly check it yourself. The academic equivalent is arXiv which is also free and in principle open for all, but there is some quality control in that new people need to have an endorsement to be able to post. – Winther Aug 14 '15 at 14:48

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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.

guest
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  • My personal problem with the academy is its societal status and how it divides those that get paid for doing science to those that don't, but may still produce it. Science should be public and not "elevated" into some magical ivory tower. That is, my interest in non-academic mathematics is mainly rebellious and somewhat anti-authoritarian as well (not in political sense, but in the sense of how information is passed and what are thought to be the top or dominant paradigms at any given time). That is, I'd like to use e.g. the internet for doing "better" research than what the academics do. – mavavilj Aug 14 '15 at 01:04
  • An interesting personality could be for example Grigori Perelman who's reported to work with the academy, but having a mixed relationship with "academic mathematics" and preferring to publish outside of the academia. – mavavilj Aug 14 '15 at 01:09
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    This is a good answer! @mavavilj You have no idea how little status there is attached to being an academic:) Also most academics could not care less who you are and if you get paid or not as long as you have performed some interesting work. However there is some scepticism towards ‘outsiders’ for the simple reason that 99.99% of the time we get e-mails from the ‘outside’ it’s from proper crazy people that have solved the Riemann hypothesis and demands a Noble prize. – Winther Aug 14 '15 at 01:59
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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.

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