How Does Logic Influence Math Research?

[romsofia]

How exactly does math research work?

Thanks for all the help!

EDIT: Since it may vary by field, I'm asking about the logic area.

 

[DuncanM]

I suppose it works the same way as any other field of research: you figure out what kind of research you want to do, find a professor doing work in that field, and then when you get your Bachelor's degree apply to work on your Master's degree or Ph.D. with that professor.

 

[chiro]

How exactly does math research work?

Thanks for all the help!

EDIT: Since it may vary by field, I'm asking about the logic area.

If you take enough classes and gain enough knowledge in a particular field, you start to get a feel not only for the limits of the field, but also the problems that people are having. Often these problems help solve other problems which help solve other problems and so on.

When you have gotten far enough to go by yourself (whether its by passing qualifying exams and otherwise), then you basically try and do something original.

If you are doing your research an institution of higher learning (aka a university), then you have to defend your work before a committee and if its successful you get a PhD (or some other postgraduate award).

 

[romsofia]

I suppose it works the same way as any other field of research: you figure out what kind of research you want to do, find a professor doing work in that field, and then when you get your Bachelor's degree apply to work on your Master's degree or Ph.D. with that professor.

I know that much (not to sound snotty :P). Thanks for the input though!

If you take enough classes and gain enough knowledge in a particular field, you start to get a feel not only for the limits of the field, but also the problems that people are having. Often these problems help solve other problems which help solve other problems and so on.

When you have gotten far enough to go by yourself (whether its by passing qualifying exams and otherwise), then you basically try and do something original.

If you are doing your research an institution of higher learning (aka a university), then you have to defend your work before a committee and if its successful you get a PhD (or some other postgraduate award).

Well, my question pertains to the actual research being done. Do you just work on a certain problem all day?

 

[AtomicJoe]

basically just make something up so complicated nobody can understand it, then get it peer reviewed and you laughing - lol.

 

[romsofia]

basically just make something up so complicated nobody can understand it, then get it peer reviewed and you laughing - lol.

Well, no math is too complicated for me!

Any real help is much appreciated!

 

[pmsrw3]

Well, my question pertains to the actual research being done. Do you just work on a certain problem all day?

Well, different people work different ways, but as for me, yes, that's pretty much what I do. When I get into a problem, I will work on it all day every day for days on end. It's hard to stop, even to eat or sleep, and when I get up in the morning the first thing I want to do is dive back into it. It's intense. Your brain gets tired and stupid after several hours. I have to force myself to take a break, spend an hour at the gym or something, and even then I will think about the problem while I work out.

EDIT: Yes, I know. Normal is overrated.

 

[chiro]

Well, different people work different ways, but as for me, yes, that's pretty much what I do. When I get into a problem, I will work on it all day every day for days on end. It's hard to stop, even to eat or sleep, and when I get up in the morning the first thing I want to do is dive back into it. It's intense. Your brain gets tired and stupid after several hours. I have to force myself to take a break, spend an hour at the gym or something, and even then I will think about the problem while I work out.

EDIT: Yes, I know. Normal is overrated.

Couldn't have said it better myself.

 

[SteveL27]

I read an article years ago about a housewife who became curious about some tiling problem. She worked on it in her spare time over a number of years. Eventually she ended up with a publishable discovery. When she was interviewed afterward she said she kept her work on pads of paper which she'd stick in the kitchen drawer when it was time for her to make dinner.

There's more than one way to do research!

(edit)

Aha the Google knows all! Her name is Marjorie Rice. Here's her Wiki entry:

In 1975, Rice came across a Scientific American article on tessellations. Despite having only a high-school education, she began devoting her free time to discovering new ways to tile the plane using pentagons. She developed her own system of notation to represent the constraints on and relationships between the sides and angles of the polygons and used it to discover four new types of tessellating pentagons and over sixty distinct tessellations. Rice's work was eventually examined by mathematics professor Doris Schattschneider, who deciphered the unusual notation and formally announced her discoveries to the mathematics community.

http://en.wikipedia.org/wiki/Marjorie_RiceThis is a more detailed article ...

http://answers.yahoo.com/question/index?qid=20101201123822AAAeWPnAh, Google came up with this comprehensive article about Rice and her work. Here's the part that stuck in my mind about working in her kitchen. Like so many of us, she was inspired by something she read in Martin Gardner's column in Scientific American.

In 1975, Martin Gardner wrote two of his “Mathematical Games” columns in Scientific
American on tiling of the plane, thus prompting scores of trained and amateur mathematicians
to try their hands at tessellation. Marjorie Rice was not the first to succeed, but she was by far
the most prolific. Rice furtively read her son's Scientific American upon its arrival every
month, and Gardner's December column, which reported on the progress of amateur
tessellators, stirred her to action. “This was the busy Christmas season which took much of
my time,” she later recalled, “but I got back to the problem whenever I could and began
drawing little diagrams on my kitchen counter when no one was there, covering them up
quickly if someone came by, for I didn't wish to have to explain what I was doing to anyone.”

The article is titled: "PICTURE PUZZLING: Mathematicians Are Rediscovering the Power of Pictorial Reasoning." It's a very nice essay about the power of pictures and diagrams in math.

http://www.ivanrival.com/docs/picturepuzzling_2.pdfMarjorie Rice still works on tesselations and has a website ...

http://home.comcast.net/~tessellations/

These are her beautiful tesselations: http://home.comcast.net/~tessellations/tessellations.htm

 

[romsofia]

Alright, thanks guys! I have an interview tomorrow for an internship with a math professor, and if working on math is what the research is all about, I hope I get it!