bio | website | gilkalai.wordpress.com |
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location | Jerusalem | |
age | 58 | |
visits | member for | 4 years, 5 months |
seen | 3 hours ago | |
stats | profile views | 16,413 |
Professor of Mathematics at the Hebrew University of Jerusalem and at Yale University
Dec 24 |
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Examples of major theorems with very hard proofs that have NOT dramatically improved over time
From my perspective, the Feit-Thompson theorem is "very hard" on its own, and it will be great if a simpler proof will be found. Strangely, I am not entirely sure if I regard the proof of the four-color theorem as "very hard" but certinly a different shorter proof that we can understand in details will be absolutely great! |
Dec 23 |
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Ultrafilter-based Fourier-Walsh-like Functions
Dear Bjorn, many thanks x2 |
Dec 23 |
awarded | Good Question |
Dec 22 |
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Intersecting Family of Triangulations
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Dec 22 |
asked | Ultrafilter-based Fourier-Walsh-like Functions |
Dec 22 |
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Generalization of Darboux's Theorem
Very nice question! Related MO question mathoverflow.net/questions/135946/… related blog post gilkalai.wordpress.com/2008/08/20/… |
Dec 22 |
answered | Examples of major theorems with very hard proofs that have NOT dramatically improved over time |
Dec 22 |
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Intersection homology for toric varieties
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Dec 22 |
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Intersecting Family of Triangulations
edited tags |
Dec 22 |
revised |
Intersecting Family of Triangulations
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Dec 22 |
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Examples of major theorems with very hard proofs that have NOT dramatically improved over time
Dear Daniel, Is the "Dehn's lemma" proved by Christos Papakyriakopoulos (and his "loop and sphere theorems,") an example of a hard proof that was not substantially simplified? For all I know (but I am not sure) , it is still a necessary piece of the proof of Poincare conjecture. |
Dec 21 |
answered | Is Euclid dead? |
Dec 21 |
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Is Euclid dead?
Very interesting answer! |
Dec 21 |
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Examples of major theorems with very hard proofs that have NOT dramatically improved over time
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Dec 21 |
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Examples of major theorems with very hard proofs that have NOT dramatically improved over time
No no, Furstenberg's proof is indeed simpler (and there is a further simplification of his approach); The proof based on hypergraph regularity is also simpler than Endre's original proof. So is the polymath1 proof. (The last two are easier than the ergodic theoretic proof) So we do have several dramatic simplifications but none that can be presented in 4 hours. |
Dec 21 |
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Examples of major theorems with very hard proofs that have NOT dramatically improved over time
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Dec 21 |
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Examples of major theorems with very hard proofs that have NOT dramatically improved over time
The 2002 Perfect Graph theorem of Chudnovsky, Robertson, Seymour, and Thomas is another very hard major theorem and thus a good contender for a future answer, unless simplified dramatically before 2027. |
Dec 21 |
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Examples of major theorems with very hard proofs that have NOT dramatically improved over time
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Dec 21 |
answered | Examples of major theorems with very hard proofs that have NOT dramatically improved over time |
Dec 21 |
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Examples of major theorems with very hard proofs that have NOT dramatically improved over time
Dear Vit, many thanks for your answer (which was certainly correct for more than a decade). I think it is a good and useful answer (while incorrect). Like in the case of Szemeredi's theorem an even simpler proof of Carleson's theorem is much desirable. In some sense, reasonable incorrect answers to the question can be as educating as correct ones. (And we do hope that most answers will become incorrect before they fit the 100-years twin MO question.) |