Monthly Archives: January 2021

Possible future Polymath projects (2009, 2021)

Posted on January 29, 2021 by Gil Kalai

What will be our next polymath project? A polymath project (Wikipedia) is a collaboration among mathematicians to solve important and difficult mathematical problems by coordinating many mathematicians to communicate with each other on finding the best route to the solution. … Continue reading →

Posted in Combinatorics, Mathematics over the Internet, Open discussion | Tagged , , | 32 Comments

Peter Cameron: Doing research

Posted on January 27, 2021 by Gil Kalai

Originally posted on Peter Cameron's Blog:
Probably every research mathematician has been asked the question, “How do you do mathematical research?” Some lay people think we simply figure out ways of doing bigger and bigger long multiplications. Many more…

Posted in What is Mathematics | Tagged | Leave a comment

To cheer you up in difficult times 18: Beautiful drawings by Neta Kalai for my book: “Gina Says”

Posted on January 25, 2021 by Gil Kalai

In 2009 I wrote a book “Gina Says” that appeared here on the blog, about the adventures of “Gina” in the blogsphere. In 2017 the book (edited and shortened a little) appeared in “world scientific.” The most important additions were … Continue reading →

Posted in Art, Gina Says | Tagged | Leave a comment

Amazing: Simpler and more general proofs for the g-theorem by Stavros Argyrios Papadakis and Vasiliki Petrotou, and by Karim Adiprasito, Stavros Argyrios Papadakis, and Vasiliki Petrotou.

Posted on January 21, 2021 by Gil Kalai

Stavros Argyrios Papadakis, Vasiliki Petrotou, and Karim Adiprasito In 2018, I reported here about Karim Adiprasito’s proof of the g-conjecture for simplicial spheres.  This conjecture by McMullen from 1970 was considered a holy grail of algebraic combinatorics and it resisted … Continue reading →

Posted in Algebra, Combinatorics, Geometry | Tagged , , , , | 7 Comments

Igor Pak: What if they are all wrong?

Posted on January 19, 2021 by Gil Kalai

Originally posted on Igor Pak's blog:
Conjectures are a staple of mathematics. They are everywhere, permeating every area, subarea and subsubarea. They are diverse enough to avoid a single general adjective. They come in al shapes and sizes. Some…

Posted in Combinatorics, Computer Science and Optimization, Geometry, What is Mathematics | Tagged | 7 Comments

To cheer you up in difficult times 17: Amazing! The Erdős-Faber-Lovász conjecture (for large n) was proved by Dong Yeap Kang, Tom Kelly, Daniela Kühn, Abhishek Methuku, and Deryk Osthus!

Posted on January 14, 2021 by Gil Kalai

Dong Yeap Kang, Tom Kelly, Daniela Kühn, Abhishek Methuku, and Deryk Osthus have just uploaded a paper to the arXive, A proof of the Erdős-Faber-Lovász conjecture. (I am thankful to Nati Linial and Ryan Alweiss for telling me about it.) … Continue reading →

Posted in Combinatorics, Updates | Tagged , , , , , | 4 Comments

Open problem session of HUJI-COMBSEM: Problem #5, Gil Kalai – the 3ᵈ problem

Posted on January 10, 2021 by Gil Kalai

This post continues to describe problems presented at our open problems session back in November 2020. Here is the first post in the series.  Today’s problem was presented by me, and it was an old 1989 conjecture of mine. A … Continue reading →

Posted in Combinatorics, Computer Science and Optimization, Geometry, Open problems | 7 Comments

To cheer you up in difficult times 16: Optimism, two quotes

Posted on January 7, 2021 by Gil Kalai

A timely quote “If there’s so much shit around, there has to be a pony somewhere.” Arundhati Roy, The God of Small Things and Give me a couple of years free from other duties, and I shall complete the task … Continue reading →

Posted in Art, Poetry | Tagged , , | Leave a comment