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Sep
24
awarded  Autobiographer
Sep
18
comment Examples of intuition from fields other than Physics to solve math problems
@Olivier - It has been a while since I read the Aczel book, but the impression I got from it was that Bourbaki was part of the Structuralist movement, and that the influence went in both directions simultaneously. I may be misremembering -- and even if I am remembering correctly, I can't vouch for the accuracy of Aczel's account. It did seem to me at the time that Aczel was exaggerating the connection between Bourbaki and the Structuralists to make a better story.
Sep
17
awarded  Teacher
Sep
17
answered Examples of intuition from fields other than Physics to solve math problems
Mar
31
awarded  Quorum
Mar
22
awarded  Yearling
Mar
21
awarded  Nice Question
Mar
21
awarded  Supporter
Mar
21
accepted Rings for which no polynomial induces the zero function
Mar
21
comment Rings for which no polynomial induces the zero function
Let $R$ be the ring $\mathbb{Z}/p \mathbb{Z}$ with infinitely many elements $u_i$ adjoined, each satisfying the relation $u_i^p -u_i = 0$. Then the polynomial $p=x^p-x$ satisfies $\hat{p}=0$.
Mar
21
comment Rings for which no polynomial induces the zero function
P Vanchinathan, yes, that was one of my examples. More precisely if $R$ is a ring that has my desired property, than $R \times R$ also has the desired property, even though it is not a domain. So that shows that "infinite domain" is not necessary for this property.
Mar
21
awarded  Editor
Mar
21
revised Rings for which no polynomial induces the zero function
added 10 characters in body
Mar
21
asked Rings for which no polynomial induces the zero function
Oct
21
comment Lost soul: loneliness in pursing math. Advice needed.
When I was in my 1st year of grad school I got married; in my 3rd year we had our first child. I missed a lot of classes, and a lot of deadlines, and was worried that he consequences might be dire. But my professors all -- all, without exception -- told me not to worry: "Some things are more important than math", said one, and that advice has kept me (reasonably) sane and balanced. I hope it helps you too.
Oct
15
comment A weird function related to the denominators of rational squares
Only in the most elementary case: \sigma (a) = 2 iff $a=n^2 + n$ for some $n$.
Oct
12
awarded  Scholar
Oct
12
comment A weird function related to the denominators of rational squares
Thanks -- those citations will be very helpful, I think. I am a total newbie when it comes to the OEIS; is there a way to search for papers / pages that discuss or reference a specific OEIS sequence?
Oct
12
accepted A weird function related to the denominators of rational squares
Oct
12
comment A weird function related to the denominators of rational squares
Plus I've got a list of 20 special cases that have the form: If $a=n^2 + $ [something], then $\sigma (a) = $ [some specific linear polynomial in n with simple coefficiets]. But I can't find a way to tie those 20 special cases together into a general statement.