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Jan
26 |
comment |
The P VS NP problem as relates to factoring
Correction: The constant 2(2/3)^(2/3) in the preceding formula is valid (heuristically) only for integers of a special form. I think the best known constant for the general number field sieve is given in D. Coppersmith, "Modifications to the number field sieve," J. Cryptology 6 (1993), no. 3, 169-180. This too is only heuristic. |
Jan
26 |
comment |
The P VS NP problem as relates to factoring
@Adam P. Goucher: Incidentally, the expected running time exp( (2(2/3)^(2/3) + o(1)) (log n)^(1/3) (log(log n))^(2/3) ) of the number field sieve, is, to the best of my knowledge, heuristic and has not actually been proved. Also worth noting: the number field sieve is not a deterministic algorithm. |
Oct
28 |
awarded | Good Answer |
Oct
15 |
awarded | Nice Answer |
Sep
24 |
awarded | Autobiographer |
Jul
15 |
awarded | Nice Answer |
Jul
13 |
answered | How does one justify funding for mathematics research? |
Jun
2 |
awarded | Yearling |
Oct
19 |
awarded | Necromancer |
Sep
13 |
comment |
What is the expected number of random numbers (generated uniformly) such that their sum of numbers exceeds one?
This question was Problem A3 of the 1958 Putnam Competition (and as such is not research-level mathematics). |
Sep
13 |
awarded | Informed |
Aug
20 |
answered | Proof a Weyl Algebra isn't isomorphic to a matrix ring over a division ring |
Jul
29 |
answered | Subgroups of finite index of fields |
Jun
25 |
awarded | Revival |
Jun
2 |
awarded | Yearling |
Jul
6 |
comment |
How do you present a non-existence theorem?
This story implicitly answers the problem of the student who shrugs upon hearing the theorem on bounded entire functions. By the time it occurs in a class it's very natural, but presented with it cold, the reaction of any student of normal inquisitiveness would be astonishment and an attempt at a counterexample. A student who isn't excited about celebrated classical results is perhaps best advised to find a field of study more to his liking. Incidentally, a result that has allured many a student into mathematics is, so to speak, a non-existence non-theorem: the continuum hypothesis. |
Jul
6 |
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How do you present a non-existence theorem?
My first reaction on seeing the title of this question was to recall Rota's "Ten Lessons I Wish I Had Been Taught": completely erase the blackboard, begin writing in the upper left corner, .... |
Jun
17 |
awarded | Nice Answer |
Jun
13 |
answered | When is a topological group Hausdorff (separated)? |
Jun
2 |
awarded | Yearling |