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10103189
bio website gilkalai.wordpress.com
location Jerusalem
age 58
visits member for 4 years, 5 months
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Professor of Mathematics at the Hebrew University of Jerusalem and at Yale University

Dec
24
comment 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
comment Ultrafilter-based Fourier-Walsh-like Functions
Dear Bjorn, many thanks x2
Dec
23
awarded  Good Question
Dec
22
revised Intersecting Family of Triangulations
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Dec
22
asked Ultrafilter-based Fourier-Walsh-like Functions
Dec
22
comment 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
revised Intersection homology for toric varieties
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Dec
22
revised Intersecting Family of Triangulations
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Dec
22
revised Intersecting Family of Triangulations
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Dec
22
comment 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
comment Is Euclid dead?
Very interesting answer!
Dec
21
revised Examples of major theorems with very hard proofs that have NOT dramatically improved over time
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Dec
21
comment 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
revised Examples of major theorems with very hard proofs that have NOT dramatically improved over time
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Dec
21
comment 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
revised 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
comment 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.)