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Harry Lime
09-01-2008, 05:18 PM
I registered for a History of Mathematics course this semester at my school because it was the only available math elective. Although the class seems interesting (the professor actually has a PhD in History of Mathematics), I would like to get more out of it with regards to my interests in economics.

There are only 7 or 8 people in the class and it is being taught seminar-style. The professor says we have two choices: we each may do 4 papers that will be assigned (4-5 pages each), or we can do one research paper (15-20 pages) of a topic of our choice related to the history of mathematics, he's pretty flexible. I am leaning toward the one research paper, but I don't have any idea for a topic. I want to do something related to economics, history of economic thought/anaylsis, etc.. Anyone have any suggestions?

I was also thinking that if I can't come up with a good historical economic analysis topic, I might do something unrelated to economics, but related to mathematics that I might use in future economic studies. Put more simply, I was considering doing some kind of paper that has a lot to do with proofs, so I can get more exposure to that kind of thinking. Maybe it can help me later on down the road. Any ideas with respect to that?


A little background: I am at a very early stage in the journey to becoming an economist, I am just starting my sophomore year, and have only taken principals of macro and micro. I have taken and am taking mostly math classes (I am technically in a mathematics program, but I am transferring in the spring). I'm mentioning this because the choice of economic topics that are feasible for me are rather limited as I don't know any advanced economic analysis at this point. So the history of the 16th proof of Appendix C of Hyper Game Theory for Quantum Economists, 16th edition, is pretty much off the table as a potential topic.

Lokayot
09-01-2008, 05:23 PM
Maybe how development of a particular field in mathematics affected theories of a related field in economics?

I apologize for not being specific, I am entering my third year and haven't done much of econ or math.

YoungEconomist
09-01-2008, 05:29 PM
I don't know a lot about the history of economics or mathematics, so some of what I say may not be accurate and you'll have to look into it deeper if my ideas interest you.

1. I think Alfred Marshall was trained as a mathematician, and I'm under the impression that he was one of the first economists to start using mathematics as a tool/language for economics. I think Gary Becker once stated that many of our modern tools in economics can be traced back to Marshall. He even has a famous textbook that was used for many years to teach students economics.

2. You could do a paper on game theory. Many people know about John Nash and how he was a mathematician who made huge contributions to economics for his work on game theory, so you could do a paper that focused on Nash. However, if I was going to do a paper I'd focus more on John Von Neumann. Your math teacher would probably like this better as well, because I think Von Neumann is more respected as a mathematician (and over all intellectual) than John Nash. I guess if you did a paper on game theory, you wouldn't have to focus on one particular person, and could just cover the math/econ history of the subject.

Anyway, these were just a couple topics that immediately came to mind. If I think of anymore, I will post them. You could also put some of your ideas in this thread and receive feedback and input from other TMers

jeeves0923
09-01-2008, 06:54 PM
You could write about how Chinggis Khan and Alexander the Great used mathematical and economic theory in their respective conquests :-)

Dannyb19
09-01-2008, 10:38 PM
The development of Game Theory has a fascinating history. In the foreword of the sixtieth-anniversary addition of Theory of Games and Economic Behavior, Harold Kuhn has a nice summary which would be a good start. I also think Von Neumann's response to Nash's PhD thesis is a neat story too - I think the book A Beautiful Mind has a nice description of Von Neumann's, say, lack of enthusiasm for Nash's work (I believe Von Neumann referred to Nash's paper as a trivial application of Kakutani's fixed point theorem).

Note: Game theory was at first developed at the math department at Princeton, not the econ department, and it seems the econ field was quite resistant to game theory (and the mathematizing of economics in general) for a number of years.

polkaparty
09-02-2008, 03:24 AM
You could broadly cover the history of mathematics in economics, but you might have a hard time contributing something original without simply summarizing.

Antichron wrote a paper (http://www.pareto-optimal.com/research/econ207paper.pdf) similar to this for one of his undergrad classes.

Here are some resources I suggest you investigate at your university library:

(1) How Economics Became a Mathematical Science by E. Roy Weintraub

(2) Mainstream mathematical economics in the 20th century by by Pier Carlo Nicola

(3) Economic theory in retrospect by Mark Blaug

These books should have plenty of other references for you to follow up on.

Consider writing about a specific point in the history of mathematical economics rather than a broad summary. For example, the marginal revolution, history of general equilibrium analysis, or Paul Samuelson's role in modern mathematical economics (I believe there are several books on this topic).

These topics might require a bit too much of a time investment given that you don't have an extremely extensive background in economics.

The book "The origins of Cauchy's rigorous calculus" by Judith V. Grabiner is excellent as a history of, well, rigorous calculus (i.e., analysis). I think you'd benefit from looking into this book just as well as you would writing a paper on math in economics. This book certainly helps one appreciate the precision of modern mathematics.

C152dude
09-02-2008, 04:21 AM
So much for retirement polka?

asianeconomist
09-02-2008, 06:26 AM
In our 'Mathematical Economics' course we had to write a paper on 'Usefulness of Mathematics in Economics'. We basically argued how mathematics has enriched/hindered the development of the economic thought.

I found this paper especially useful:

Gerard Debreu (1986); Theoretic Models: Mathematical Form and Economic Content, Econometrica, Vol. 54, No. 6, pp. 1259-1270.

Harry Lime
09-03-2008, 12:53 AM
Wow, thanks for all the replies, great stuff.


However, if I was going to do a paper I'd focus more on John Von Neumann. Your math teacher would probably like this better as well, because I think Von Neumann is more respected as a mathematician (and over all intellectual) than John Nash. I guess if you did a paper on game theory, you wouldn't have to focus on one particular person, and could just cover the math/econ history of the subject.
Well, I read up on Von Neumann (*cough* wikipedia) and he seems to be a great subject. I'd rather do more research on theory. But in case I get in over my head because I'm taking so many other class this semester, Von Neumann seems to have had a really interesting personality and career that I could fall back on if the theory is too much. Thanks so much for the suggestion.

"During a Senate committee hearing he described his political ideology as "violently anti-communist, and much more militaristic than the norm"."

Sounds like a guy you could have a couple pints of Hoegarden with.


Consider writing about a specific point in the history of mathematical economics rather than a broad summary. For example, the marginal revolution, history of general equilibrium analysis, or Paul Samuelson's role in modern mathematical economics (I believe there are several books on this topic).
I had considered doing something about the marginal revolution and the various angles that the different schools of thought viewed marginal utility, focusing on Mashall and the more quantitative approaches.

Golden Rule
09-03-2008, 03:12 AM
I want to do something related to economics, history of economic thought/anaylsis, etc.. Anyone have any suggestions?
I think that's entirely reasonable.

Put more simply, I was considering doing some kind of paper that has a lot to do with proofs, so I can get more exposure to that kind of thinking. Maybe it can help me later on down the road. Any ideas with respect to that?
This could work, but my initial reaction is that a history of math class isn't the best place to gain an introdution to the kind of theoretical math skills you'll need in grad school, which sounds like what you're looking for here. There are courses better designed to help you do this as an undergrad.

I'm mentioning this because the choice of economic topics that are feasible for me are rather limited as I don't know any advanced economic analysis at this point.
I don't think you need to worry too much. Any economics you should be able to figure out what the problem was, and what the technique introduced solved, even if you might understand every detail of the proofs.


Might try skimming through David Warsh's Knowledge and the Wealth of Nations. Knowledge and the Wealth of Nations » Reviews (http://kwonbook.com/reviews-2/) It's a very accessible history of economic thought, with a relative narrow theme, and you could use that as a starting point. I think the contributions of the Cowles Foundation might be something to look at, and that's discussed well in there. You can still write about economics pretty well, since the nature of economic systems and the lack of experimental data require that you solve problems that are often unique to the field.

Harry Lime
09-03-2008, 08:47 PM
This could work, but my initial reaction is that a history of math class isn't the best place to gain an introdution to the kind of theoretical math skills you'll need in grad school, which sounds like what you're looking for here. There are courses better designed to help you do this as an undergrad.
Yeah, you're quite right. Although the syllabus is written by the department and claims to focus on studying dusty old proofs from antiquity, the professor doesn't seem very committed to it.

Thanks for the other suggestion I'll look into it.


One other idea that had crossed my mind occurred when the professor was lecturing on Chinese mathematics (he's Chinese born). He mentioned that during the Cultural Revolution, officially, the only mathematical research that was allowed had to in some way or another confirm or support Marxist/Maoist economic theories. I think it might be interesting to see if Chinese mathematicians at the time would either make up zany theories in order to tow the party line, or if they might have employed strategies to disguise legitimate research as somehow supporting Maoism.

The problem is that I feel like every young non-native Chinese person (like myself), who I've met or read about, that has studied Chinese history inevitably writes about the Cultural Revolution. Every thesis title is "X within the context of the Cultural Revolution", where X is anything from "aesthetics of park statues" to "woman's footwear". It's an annoying trend and I don't want to be part of the problem. I think it's just easy to write about because the Cultural Revolution was a nine ring circus, every crazy thing that happened at the time seems interesting and worthy of study.