Contemporary Math - written assignment

Written assignment #1 for Contemporary Math, Fall 2009

Prof. Mark Janeba

Brief summary: Write a 600-800 word paper responding to at least two of the web pages linked below, which address the question: "Is mathematics discovered or invented?" The question is whether mathematics (and the various rules, theorems, and so on of mathematics) already existed in any sense before humans first wrote them down, or if mathematics is, in some sense, a game for which humans have written the rules, rules which they could have written entirely differently.

Some articles to respond to:

A review of a book by Reuben Hersh on the subject, which has some nice overview: http://www.maa.org/reviews/whatis.html

An interview with Hersch (see first article): http://www.edge.org/3rd_culture/hersh/hersh_p2.html
A more intellectually dense (in the good sense) review of Hersh's book: http://www.ams.org/notices/199909/rev-dubinsky.pdf
Here's an actual excerpt from another Hersch book: The Mathematical Experience.
What is Mathematics?, a review-essay of "John D. Barrow's 1994 book Pi in the Sky: Counting, Thinking, and Being which has as one of its primary themes the idea that mathematics has much in common with religion." http://members.cox.net/mathmistakes/what_is_mathematics1.htm
A relatively sophisticated philosophical essay that comes down on the formalist side; be sure to look up the technical meanings of phenomenal and noumena before reading.
A student essay which is very broad for the first 80%, then takes an interesting religious twist (you can include or exclude the latter part of the article, per your interests): http://www.infohatter.com/node/6/print
The Stanford Encyclopedia of Philosophy's entry is heavy going, but it has many clearer gems for the determined reader: http://plato.stanford.edu/entries/philosophy-mathematics/#MatLogFouMat

The question itself [is math discovered or invented] is difficult, and stumps many philosophers and mathematicians, so the goal of the paper is not to give an answer to the question, though you are welcome to tell which way you lean. I am much more interested in your response to what the articles have to say about the question. You should certainly discuss both key thoughts or ideas you get out of the articles (i.e. some summarization), and questions or conclusions that arise in your mind in response (i.e. some reflection). Some areas you might choose to discuss are:

Any rephrasings of the question that you find that seem to clarify what it is asking
What seem to be the main "schools of thought" on the question (and which schools seem to be established or have a large following, versus those which seem new or peripheral, etc.)
What evidence or arguments, if any, you see presented by those schools,
Whether the question seems to be considered important or not (and why), and whether that has changed over the last century or so,
How are different cultures' approaches similar or different (For this point I have less material above than last year, some of the more relevant sources I had last year are no longer available)
Just about any other issues raised by some of the articles that you would care to discuss, in ways that show you have read the article carefully and thought about it at least somewhat thoroughly. I also welcome your finding another article if you don't like any of these, but do get my approval in advance in that case. Note: while I am generally pleasantly surprised by the quality of Wikipedia, I'm not so impressed with their articles on this subject.

Grading will be based on the amount and quality of thinking shown in the paper, overall coherence, and yes, grammar and spelling. This paper counts for 30 class points. 600-800 words is around 2-2.5 pages double spaced, depending on font and margins, but it's the word count I'll check.

Papers are to be submitted electronically to Turnitin.com by 4 p.m. Thursday, December 3. To submit your paper, go to the Turnitin site and log in with an account and password I will provide no later than Monday, Nov. 30. A word on academic honesty: Plagiarism, which is the presentation of other's words, thoughts, or ideas as your own, will result in a failing grade for the paper. Along with allowing convenient online paper submission, Turnitin also detects the use of material from web pages and previously submitted papers (both properly cited and uncited), so take care. If you are uncertain about what constitutes plagiarism, it is your responsibility to seek clarification, which I am glad to give.

Last Modified November 23, 2009.
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