ABC conjecture: Difference between revisions
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*[http://sbseminar.wordpress.com/2012/06/12/abc-conjecture-rumor-2/ ABC conjecture rumor], Secret Blogging Seminar, June 12, 2012 | *[http://sbseminar.wordpress.com/2012/06/12/abc-conjecture-rumor-2/ ABC conjecture rumor], Secret Blogging Seminar, June 12, 2012 | ||
*[https://plus.google.com/103703080789076472131/posts/j1sEGnPyiRu Timothy Gowers Google+], 4 Sept 2012 | *[https://plus.google.com/103703080789076472131/posts/j1sEGnPyiRu Timothy Gowers Google+], 4 Sept 2012 | ||
*[https://plus.google.com/117663015413546257905/posts/Npu7xDniXMS John Baez Google+], 4 Sept 2012 | *[https://plus.google.com/117663015413546257905/posts/Npu7xDniXMS John Baez Google+], 4 Sept 2012, see also a [https://plus.google.com/117663015413546257905/posts/2vTzJJSueRb repost] | ||
**[https://plus.google.com/117663015413546257905/posts/hzqBCeujWEg John Baez Google+], 5 Sept 2012 | **[https://plus.google.com/117663015413546257905/posts/hzqBCeujWEg John Baez Google+], 5 Sept 2012 | ||
**[https://plus.google.com/117663015413546257905/posts/d1RsN4KnCUs John Baez Google+], 12 Sept 2012, comments by Minhyong Kim. | |||
*[https://plus.google.com/114134834346472219368/posts/c7LkaWV69KL Terence Tao Google+], 4 Sept 2012 | *[https://plus.google.com/114134834346472219368/posts/c7LkaWV69KL Terence Tao Google+], 4 Sept 2012 | ||
*[http://bit-player.org/2012/the-abc-game The abc game], bit-player, 7 Sept 2012 | *[http://bit-player.org/2012/the-abc-game The abc game], bit-player, 7 Sept 2012 | ||
Revision as of 03:05, 12 September 2012
The abc conjecture asserts, roughly speaking, that if a+b=c and a,b,c are coprime, then a,b,c cannot all be too smooth; in particular, the product of all the primes dividing a, b, or c has to exceed [math]\displaystyle{ c^{1-\varepsilon} }[/math] for any fixed [math]\displaystyle{ \varepsilon \gt 0 }[/math] (if a,b,c are smooth).
This shows for instance that [math]\displaystyle{ (1-\varepsilon) \log N / 3 }[/math]-smooth a,b,c of size N which are coprime cannot sum to form a+b=c. This unfortunately seems to be too weak to be of much use for the finding primes project.
Mochizuki's proof
The paper: INTER-UNIVERSAL TEICHMULLER THEORY IV: LOG-VOLUME COMPUTATIONS AND SET-THEORETIC FOUNDATIONS, Shinichi Mochizuki, 30 August 2012
The previous papers:Shinichi Mochizuki's papers
Blogs
- Mochizuki on ABC, Quomodocumque, Jordan Ellenberg, 3 Sept 2012
- As easy as 123…, Simple City, Richard Elwes' Blog, 4 Sept 2012
- ABC conjecture rumor, Secret Blogging Seminar, June 12, 2012
- Timothy Gowers Google+, 4 Sept 2012
- John Baez Google+, 4 Sept 2012, see also a repost
- John Baez Google+, 5 Sept 2012
- John Baez Google+, 12 Sept 2012, comments by Minhyong Kim.
- Terence Tao Google+, 4 Sept 2012
- The abc game, bit-player, 7 Sept 2012
- The Ax-Grothendieck Theorem According to Category Theory, The n-Category Café, September 10, 2012
Q & A
- Mochizuki’s proof and Siegel zeros, Mathoverflow, 4 Sept 2012
- Philosophy behind Mochizuki’s work on the ABC conjecture, Mathoverflow, 7 Sept 2012
- Implications of proof of abc conjecture for cs theory, Theoretical Computer Science Stackexchange, September 11, 2012
Discussions
- Shin Mochizuki has released his long-rumored proof of the ABC conjecture , Hacker News, 5 Sept 2012
- Proof Claimed for Deep Connection between Prime Numbers, Hacker News, 11 Sept 212
- Possible Proof of ABC Conjecture, Slashdot, September 10, 2012
News Media
- Proof claimed for deep connection between primes, Nature News, 10 September 2012
- Fiendish 'ABC proof' heralds new mathematical universe, New Scientist, 10 September 2012
- Mathematician Claims Proof of Connection between Prime Numbers, Yahoo News, 11 Sept 2012
