What do Average Mathmaticians Do?

For the discussion of math. Duh.

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What do Average Mathmaticians Do?

Postby jewish_scientist » Wed Apr 03, 2019 10:45 pm UTC

Let’s say that John Doe University requires that all of their professors publish research. A biology professor is sitting in his office trying to think of some cool experiment he could do, but is coming up with nothing. In the end he decided to just expose a bunch of mice to some random chemical and count how many get cancer. This professor is not going to win any awards for his work, but he is contributing to the field.

A chemist in the same predicament could expose some random chemical to reactive chemicals and record what happens. An engineer could take some material and record all of its physical properties and a sociologists can do a survey about two random things people do.

For pretty much any academic field I can think of something productive for an uninspired professor to do, except for math. Do you have any ideas?
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Re: What do Average Mathmaticians Do?

Postby ConMan » Thu Apr 04, 2019 12:01 am UTC

You have an extremely twisted idea of how academia works.

But, if such a scenario were to happen, then depending on their field of expertise the mathematician could try to tackle an outstanding open problem (e.g. the abc conjecture), or investigate some mathematical construct and see what they can derive from it, or take some real-world problem and try to model it.
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Re: What do Average Mathmaticians Do?

Postby Soupspoon » Thu Apr 04, 2019 12:24 am UTC

When you say "Average Mathematician"(s), do you mean mean, mode, median…? ;)

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Re: What do Average Mathmaticians Do?

Postby Xanthir » Fri Apr 05, 2019 6:56 pm UTC

You get into academia in the *first* place because there are cool problems you enjoy working on. Math has a ton of these, just as biology and chemistry and all the others do. Nobody just says "well, I guess I'll mix some chemicals together, see what happens"; you need to write a grant proposal that explains why this is useful and worthwhile, pass ethics review for live testing, etc.

Watch some of the SixtySymbols videos, for example, to see mathematicians discussing problems they're currently working on. StandupMaths also has a number of mathematician interviews about something interesting they're working on or recently were.
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Re: What do Average Mathmaticians Do?

Postby Sungura » Sun Apr 07, 2019 12:04 am UTC

You get into a professorship because you have research ideas you want to pursue. So your question is highly unlikelunscenario (and no, a biologist or chemist cant just toss shit at animals and see what happens, no ethics board is ever going to allow that nor should they; and its kinda creepy to suggest that...)

But lets say you hit mid career crisis and dont know what the heck to do next because you just solved Your Big Question youve been working on.

You then go on to Next Big Question, because with math as wirh science, an answer just leads to a dozen more questions. Its the nature of the beast. Someone who is so uninspired as to not go down the rabbit hole is not going to last in acedemia. It just doesnt happen. They wash out. Its far too competative, mostly underpaid, and tons of beurocratic crap to deal with so you have to really love your research and the connections and collegues acedemia provides to stay in it.

Its not bad to quit acedemia. Many have for many reasons. But i know of litteraly no one who did for lack of inspiration or ideas to work on.
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Re: What do Average Mathmaticians Do?

Postby Pfhorrest » Sun Apr 07, 2019 12:29 am UTC

I’m not in academia, but one of the reasons for that is that I’ve gotten the impression that going into academia with big dreams of answering questions you care about is setting yourself up for disappointment, because the actual job will usually end up doing the grunt work for the project that was the big dream of one of the lucky few who got to be the head of a research project, and you, random passionate intellectual looking to spend your life pursuing the mysteries that have intrigued you since undergrad, probably won’t get to be one of those lucky few

Just like kids who go into game development because they have a game they want to make, but end up just doing some tiny part of making games someone else with a lot more money and/or connections wants to make.

and probably every other profession too
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Re: What do Average Mathmaticians Do?

Postby Sungura » Sun Apr 07, 2019 3:01 am UTC

Pfhorrest wrote:I’m not in academia, but one of the reasons for that is that I’ve gotten the impression that going into academia with big dreams of answering questions you care about is setting yourself up for disappointment, because the actual job will usually end up doing the grunt work

I started in biotech, moved to acedemia, then back.
Why?
Without a PhD and your own lab (which most PhDs eventually get) - yup you do gruntwork. I actually enjoy the benchtime.
With a PhD and your own lab - you barely step foot in the lab because youre going to meetings and writing papers and reports, you coalate the data and get the results figured out but the chunk the work typically isnt yours. (For me? Nothanks).

I did actually do maths to for a while. Same story different department. Lab is computer rather than wet bench.
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Re: What do Average Mathmaticians Do?

Postby MartianInvader » Sun Apr 07, 2019 4:09 am UTC

Pfhorrest wrote:I’m not in academia, but one of the reasons for that is that I’ve gotten the impression that going into academia with big dreams of answering questions you care about is setting yourself up for disappointment, because the actual job will usually end up doing the grunt work for the project that was the big dream of one of the lucky few who got to be the head of a research project, and you, random passionate intellectual looking to spend your life pursuing the mysteries that have intrigued you since undergrad, probably won’t get to be one of those lucky few

I think math is pretty different from a lot of the sciences in this respect. Since there's no cost of lab equipment, etc, the main thing the universities are spending money on is the people. This results in a lot more personal freedom for each researcher, since they don't need to be part of a lab. It's very rare to see a "primary author" of a math paper, while it's the norm in many lab sciences.

Personally, after finishing my PhD, I decided I didn't love my research enough to continue, and left academia to become a software engineer. Very happy with that job today :)
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Re: What do Average Mathmaticians Do?

Postby Eebster the Great » Sun Apr 07, 2019 8:16 am UTC

I was very surprised when I learned that most math papers list authors in alphabetical order by surname. It's a very different mentality from medicine.

I feel like this somehow privileges authors with surnames starting with A and Z.

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Re: What do Average Mathmaticians Do?

Postby Soupspoon » Sun Apr 07, 2019 1:47 pm UTC

[quote="Eebster the Great"][url=https://en.wikipedia.org/wiki/Alpher–Bethe–Gamow_paper]Or, occasionally, B.[/url]

;)

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Re: What do Average Mathmaticians Do?

Postby Soupspoon » Sun Apr 07, 2019 1:50 pm UTC

Eebster the Great wrote:I feel like this somehow privileges authors with surnames starting with A and Z.

Or, occasionally, B.

;)

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Re: What do Average Mathmaticians Do?

Postby jewish_scientist » Sun Apr 14, 2019 2:34 pm UTC

Xanthir wrote:You get into academia in the *first* place because there are cool problems you enjoy working on.

Not necessarily. My psychology professor told us that he used to work at a more prestigious university, but left because they expected him to publish. Teaching college level psychology was his goal, not just a means. That left me wondering if there was some way he could get around the requirement by doing serious and valuable studies that were not particularly taxing. The problem I found with math was that failing to find a solution to a problem is not a result in the same way that failing to reject a null hypothesis is.

Watch some of the SixtySymbols videos

I think you mean Numberphile. SixtySymbols is their physics channel.

Sungura wrote:[A] biologist or chemist cant just toss shit at animals and see what happens, no ethics board is ever going to allow that nor should they; and its kinda creepy to suggest that...

What I mean is any proposal of the form, 'Requesting funding to test if [insert chemical humans are exposed to daily] has an effect on [insert bodily function],' is a reasonable request.
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Re: What do Average Mathmaticians Do?

Postby Sungura » Sun Apr 14, 2019 4:00 pm UTC

jewish_scientist wrote:
Sungura wrote:[A] biologist or chemist cant just toss shit at animals and see what happens, no ethics board is ever going to allow that nor should they; and its kinda creepy to suggest that...

What I mean is any proposal of the form, 'Requesting funding to test if [insert chemical humans are exposed to daily] has an effect on [insert bodily function],' is a reasonable request.

I mean...only if they are reasonably sure that it does, have already tested this in non-animal studies, and have existing data and publications to show their hypothesis is likely true that it will have a certain effect as hypothesis states.

So...like no? Not that simple. As you stated it is not a reasonable request and would be denied.
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Re: What do Average Mathmaticians Do?

Postby jewish_scientist » Thu Apr 18, 2019 5:38 pm UTC

I simplified the complicated and multifaceted process of how to secure funding for research because my question is not about that. My point is that because scientific research is inherently different from mathematical research, I do not understand how mathematicians who are not like geniuses like Gauss can contribute to the field.
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Re: What do Average Mathmaticians Do?

Postby Eebster the Great » Thu Apr 18, 2019 9:29 pm UTC

jewish_scientist wrote:I simplified the complicated and multifaceted process of how to secure funding for research because my question is not about that. My point is that because scientific research is inherently different from mathematical research, I do not understand how mathematicians who are not like geniuses like Gauss can contribute to the field.

The frontier in mathematics is just as vast as it is in science. You don't have to work on the most advanced and difficult mathematical problems ever devised in order to contribute to the field. Typically, mathematicians will specialize somewhat (say, in algebraic topology), just like scientists. After you work on a problem for long enough, if you are a competent, educated mathematician, you can discover things nobody else has yet and prove them. It is not required that nobody before you be smart enough to prove those statements, just that they hadn't considered them.

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Re: What do Average Mathmaticians Do?

Postby elasto » Fri Apr 19, 2019 9:50 pm UTC

If you're genuinely interested there are some pretty approachable channels on youtube where people talk through math proofs in something approaching layman's terms, and you can get a reasonable insight into the day to day ways they approach tasks - Numberphile and Mathologer spring to mind.

As a random example, here's a Numberphile video where Matt Parker discusses his 'new favourite number' - because he discovered it...

(No, it's not profound or useful in any way, so I wish I could come up with a better example since I come across them not uncommonly, but it's a random instance of the vast frontier that Eebster speaks of...

In a way, it's the largest of all possible frontiers since, unlike the sciences, it's limited only by one's imagination...)

Edit: Here's a couple more random examples of novel proofs created specifically for youtube - the first being pretty user-friendly and the second being pretty technical:

Proof of irrationality of some square roots
Proof that (2 x 2 x 4 x 4 x 6 x 6 x ...) / (1 x 3 x 3 x 5 x 5 x 7 x ...) = pi / 2

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Re: What do Average Mathmaticians Do?

Postby ConMan » Mon Apr 22, 2019 11:32 pm UTC

And in fact sometimes it's enough to discover a new way to prove an old theorem, because it can open up a new means of proof, or show insight on how different fields are connected, or provide a more general version of the theorem.
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