This is a link to a history of the Taniyama conjecture we were discussing in class, it describes the conjecture, the attempts to prove it and finally Wiles's proof. I found it interesting and helpful.

http://fermat.workjoke.com/flt8.htm

Angela Rogers

- Thanks for this link! It's a really good exposition that says much of what I tried to say in class today, much more clearly. Read the section you point to, and the next one. Ethan

http://www.flickr.com/photos/93582379@N06/8508995604/in/photostream

Over the weekend i went to Syracuse, New York to visit my older sister who is currently at Syracuse University getting her masters degree in Biomedical engineering. She has an apartment that is off of Euclid Street. I took a picture and thought i would share this with the class. I got to tell my Mom as we drove by on our way to my sisters apartment why Euclid Ave was relevant to math.

Nicole Nocera

- Can you find out if the Euclid after whom this street was names was in fact the mathematician? Ethan
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- when I was reading the statement:
- x^2+y^2=p where p is an odd prime number, conditions under which this is true:

Either x or y is odd and either x or y is even, they cannot both be odd or even

When you divide the prime by 4 the remainder is 1. Written 1(mod 4). (Gauss introduced modular arithmetic)

I was trying to prove it by my self,

1, suppose x=2n, and y=2m, then, x^2+y^2=4(m^2+n^2)=p, so p is not an prime number

2, suppose x=2n+1, and y=2m+1, then x^2+y^2=2(2m^2+2m^2+2m+2n+1)=p, so p is not an odd prime number,

3, suppose x=2n, and y=2m+1,then x^2+y^2=4(n^2+m^2+m)+1=p. so when we divide p, the remainder is 1..