Reputation
3,783
Next privilege 5,000 Rep.
Approve tag wiki edits
Badges
1 26 33
Newest
 Enlightened
Impact
~136k people reached

  • 0 posts edited
  • 0 helpful flags
  • 96 votes cast
May
5
awarded  Enlightened
May
5
awarded  Nice Answer
May
4
answered Random projection and finite fields
May
4
awarded  Scholar
May
4
comment Translation of Goldbach's 1742 letter to Euler
Brilliant. And we could all learn from his style...
May
4
accepted Translation of Goldbach's 1742 letter to Euler
May
4
awarded  Nice Question
May
3
awarded  Commentator
May
3
comment Translation of Goldbach's 1742 letter to Euler
Franz: that might be helpful?
May
3
comment Translation of Goldbach's 1742 letter to Euler
Ha! I wish. No, I'm preparing for a public lecture at the Radcliffe Institute.
May
3
comment Translation of Goldbach's 1742 letter to Euler
What is "the conjecture"? Something like every number $n$ being the sum of exactly $m$ "primes" for each $3 \leq m \leq n$, counting $1$ as prime? That's my guess just looking at the formulae in his letter. In the case $n = 2k + 2$ even and $m = 3$ it implies the usual Goldbach conjecture for $2k$, unless $2k - 1$ is prime.
May
3
comment Historical question concerning Jordan's theorem
Jim: I agree completely. I'd still like an actual reference to the argument I sketched above though, if there is one earlier than Tao's blog.
May
3
comment Historical question concerning Jordan's theorem
Yes indeed - and this paper has proved very useful indeed to many of us working in additive combinatorics recently. The paper also contains a proof in characteristic zero, but it is certainly a bit more complicated than the one I described above.
May
3
comment Translation of Goldbach's 1742 letter to Euler
Brilliant - now we just need someone who reads German to take a look at the footnote at the bottom of page 127.
May
3
asked Translation of Goldbach's 1742 letter to Euler
May
2
comment Historical question concerning Jordan's theorem
I should also point out that by $j(n)$ I think you mean the index of the biggest normal abelian subgroup of $A$; so your $j(n)$ is at most $F(n)!$, but they need not be the same.
May
2
comment Historical question concerning Jordan's theorem
Igor, I believe this issue is comprehensively despatched in this paper of M. J. Collins: On Jordan's theorem for complex linear groups. J. Group Theory 10 (2007), no. 4, 411--423. He evaluates $j(n)$ for all $n$ and shows that $(n+1)!$ is the truth for $n \geq 71$ (and not for $n = 70$). But my interest is more in finding the simplest argument that gives some bound.
May
2
awarded  Student
May
2
asked Historical question concerning Jordan's theorem
May
2
awarded  Critic