Being a research mathematician
78What this hub is about.
I am a research mathematician. In my case that means I am employed by the math department of a major university. (All right, sort of a major university.) But being a research mathematician just means that you discover new mathematics. In principle, you don't have to be employed anywhere to do that. Being an "amateur mathematician" used to be a popular calling. The trouble is that the ranks of amateurs tend to be filled with "Cranks." Cranks are people whose logic is impaired. Usually they are characterized by believing they have produced some profound mathematical result without this having any basis in fact.I am writing this set of hubs to encourage people to do mathematics. Some of them may be aimed at undergraduate or graduate students but the general public can be involved too provided it reasons correctly.
Cranks
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Why would anyone want to do research in mathematics?
No good reason. Only if they want to know the precise truth about things others consider unimportant. This is different from the reasons for being a professional mathematician, which can be summarized by saying that there is an entirely unreasonable amount of money supporting pure mathematics these days. By and large this money gets to the right places, but this is a fragile state of affairs depending on the traditions and values of the pure mathematicians.
More on why to do math. (Utter uselessness a plus)
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What equipment do you need?
The traditional answer is that all one needs to do mathematics is pencil and paper. These days, a mathematician probably needs a computer. But not very much of one. Recently, I bought a $320 netbook which I'm using as my main computer. You need a mathematical word processing system, and are best off with an implementation of TeX. This you can get for free. It might help, but is not essential, to have a symbolic algebra program. (This is in case you want to run computer experiments.) The companies that make these try to charge you an arm and a leg if you are not affiliated with a university but you can get relatively cheap fully-functional student versions of MAPLE on Ebay. If you are running under Linux, you can use Sage, an open source symbolic algebra. But you really mainly need to be able to browse the web to see what new preprints have been posted and what other mathematicians are writing on their blogs.
The perfect mathematician's computer.
 | Amazon Price: $259.99 |
A useful TeX implementation
- MiKTeX Project Page
This is the MiKTeX project page. MiKTeX is a typesetting system for the Windows operating system. The distribution includes TeX, pdfTeX and XeTeX.
Cheap symbolic algebra software
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Maple Student Edition Release 13 NEW by Maple
Current Bid: $29.61
|
Free symbolic algebra software
Check for preprints
A great mathematician
So what now?
You've gotten together all the equipment and now you'd like to do research mathematics. How do you start? How are my hubpages going to help you? I'll publish various kinds of hubpages. Some will discuss open problems. If you solve them, I'll get pretty excited. A few might discuss career paths if you want to become (shudder) a professional. Hint: A very important part of the career path of a research mathematician might be to solve some of the open problems. Other pages might be expository discussing some basic and useful ideas. Others might be aimed more at students, discussing how to pass certain exams. Stay tuned: Same bat time; same bat channel.
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David,
You're right of course. But as the internet improves this becomes less and less essential. Relatively recent work can usually be found on the Arxiv. For older ideas, you can find thin accounts on wikipedia and you can find expository notes all over the web. The art of writing math books is much in decline.
If the crank/amatuer desparately needs a library, in a pinch, even his local public library might suffice. If he really needs a certain book, interlibrary loan is always a possibility.
Nets
NHKatz, welcome to hubpages! I look forward to reading more of your hubs about mathematics. In the meanwhile, could you post a link to Arxiv?
Aya,
I did post a link to ArXiv above. It is under the heading Check For Preprints.
Nets
Nets, thanks. Sorry I missed that.
Hello nets, thanks for stopping by my Hub. "Cranks," I,ve never heard such a clear and precise definition for what we see in this world today. I believe I know many "Cranks," and I believe that I may have posted a "Crankish" comment on a Hub or two. Have a nice day Nets
B2BF
Born,
I agree completely. There are "scientific" disciplines that are becoming quite unscientific. You know this is true when controversies are solved by pedigree rather than logic.
Mathematics is still not there but might be healthier with more input from the cranks. I am planning some modest attempts to make that easier.
Best,
Nets
Good Hub, nhkatz.
I was never the best at the pure mathematics, but I have a great respect for those who come up with elegant solutions to mathematical problems.
With you on the 'unscientific' part - The politicians, funding system and media are partly to blame, but there is a woeful neglect of the philosophy underpinning science. Scientists are taught 'how' to do things, but rarely 'why.'
Sufi,
Thanks for your comment.
I'm not sure about the reasons. Failures of our educational system may be part of it, but I tend to blame the political system more. With so much of science being government funded, scientists have begun to see themselves as part of a lobby. This often distorts their thinking.
Nets
Certainly a large part - the recent insanity surrounding Global Warming is a case in point, and it is a near impossible task to find good, unbiased science, even when you know what to look for.
Good hub, and I look forward to keeping up with the world of mathematics!
Sufi,
I look forwards to hearing from you.
Nets
Welcome to HubPages - I'm staying tuned :)
Shalini, Thanks!
Yay! A mathematician with a sense of humor as well as smarts! Will be checking out these links for some meaty reading for a change from the usual internet pablum... don't get too excited, got moved around too much as a kid so never developed a higher math foundation... but as a conceptual learner and critical thinker I sure do love to read about math and physics! It really gets the creativity going and I always take away something profoundly useful.
Thanks for coming to HubPages! Guess it begs the question: but do you have the will and the patience to write for the public that have no background in math? The TV show Numbers does a good job of trying to attract the public to math is a way that applies to many concrete everyday sitations. It would really be nice to see an army of math folks out there writing to elevate the average person's math ability. Just a thought in my little corner of the world...
Denny,
Thanks for your encouragement. These pages will be written at different levels for different intended audiences.
Nets
Nets, I have a new insight concerning why bees do not distinguish between their own interests and those of the hive. I think I understand a little better what Kameda must have meant about all bees being kin.
If an animal reproduces asexually and all individuals are clones, then there will be no selective advantage for those individuals who are able to think of their own interests. On the other hand, with the advent of sexual reproduction, this creates a huge advantage for individuals and their progeny if they think of themselves first.
Bees do reproduce sexually, but they have only one mother, and only a few different fathers, who all had the same mother. There's very little genetic variation, so there is less selective advantage for selfishness.
Aya,
You're right. Kameda had some version of this insight: Immediately after showing a slide saying Bees are all kin, he had another saying something like Bees are all clones.
In any case, it doesn't belong on this hub. I have mixed feelings about whether it belongs on the Kameda hub, because that isn't really what the Kameda hub is about.
Sorry. You're right.
Now I can't tell if this is the right place to come or not. I was looking for info on the path to becoming a mathematician and career info for my son. It's hard to ever have a conversation with him because he's too busy calculating in his head - all the time - everywhere - about everything.
My dad's a physicist so it's in the genes I suppose. He's considered physics, engineering, wanted to be both but finally realized one can actually be a mathematician! Math on its own. Seeing a problem and jump into it for days or weeks until you solve it.
Sounds like some of your hubs are going to be good for him, from what I've said, do you agree? (He's only 15).
The foremost reason of doing reaserch in Math is that whatever you discover will never be contradicted, and it results into everlasting immortality of the discoverer. Also, mathematics is equally respected by all generations, and all people of the world, unlike other deciplines.
David Fisher 3 years ago
There is one more resource that is used by almost all professionals
and which you don't mention: books. Usually in the form of a
well-stocked math library. Some problems can be approached without much
background and so don't require much study from books. But a lot of
mathematics these days requires looking at and trying to read books.
Even just to understand what the problems are actually about.
Some of these books are available online various ways, a lot are not.
Some of the material from books is reproduced online in eprints, some not.
I'll be interested to see how you deal with this issue as you go along.