Greatest Hits 2015-2022, Part I

In February 2015 I wrote a post on the blog’s greatest hits in the first seven years, and its time to write a similar post for the eight years that followed.

Quick updates: In recent months I took part in two unusual conferences (for me). One conference in the city of Nazareth was about “free will” and the participants included neurologists, brain scientists, biologists, philosophers, psychologists, physicists, and experts in law and ethics. The other conference was at Tel Aviv about the Many Worlds Interpretation to quantum mechanics with a variety of researchers interested in the foundations of physics. In the last few weeks I gave (by Zoom) two physics colloquiums, one in Rutgers University and one in the Perimeter Institute at Waterloo, and in both cases the lecture was followed by very nice discussions. The lecture and discussion at the Perimeter Institute was videotaped and uploaded to PIRSA (Perimeter Institute Recorded Seminars Archive) and can be found in this link. The very interesting discussion included Ray Laflamme, Lee Smolin, Debbie Leung, Latham Boyle (my host, who, against all odds, perfectly pronounced my name 🙂 ) and Dominique.

Here is a link to the (Hebrew) lectures and discussions from the Free Will conference. I gave there a short response to Yakir Aharonov’s lecture. And here is the You Tube link to the Many worlds interpretation conference.

Before we start: Happy new year 2023 to all!   

2015-2022: The blockbusters

Not many great hits in 2015 (since March) and the most viewed post from 2015 was the opening post for Polymath10: Polymath10: The Erdos Rado Delta System Conjecture.

The most viewed post from 2016 and one of the most viewed posts ever was A Breakthrough by Maryna Viazovska Leading to the Long Awaited Solutions for the Densest Packing Problem in Dimensions 8 and 24.


The most popular post in 2017 (and among the most popular ever) was Elchanan Mossel’s Amazing Dice Paradox (your answers to TYI 30). (The post posing the question was also very popular.)


2018’s blockbuster was: Aubrey de Grey: The chromatic number of the plane is at least 5. A 2018/2019 blockbuster was Amazing: Karim Adiprasito proved the g-conjecture for spheres!

2019 was the year with maximum views ever. There were many posts with news about breakthroughs, and the most popular one was Amazing: Hao Huang Proved the Sensitivity Conjecture! Another hit was my first post about Google’s quantum supremacy claims: Quantum computers: amazing progress (Google & IBM), and extraordinary but probably false supremacy claims (Google).

The most popular post in 2020 was also about quantum computers  The Argument Against Quantum Computers – A Very Short Introduction. In April 2020 we introduced a new corner “To cheer you up in difficult times”.

The 2021 post with most views was a little debate between Avi Wigderson and me The probabilistic proof that 2^400-593 is a prime: a revolutionary new type of mathematical proof, or not a proof at all?

The most viewed post in 2022 was: Amazing: Jinyoung Park and Huy Tuan Pham settled the expectation threshold conjecture!

Here are other popular and favorite posts 2015-2018,  the second part will be devoted to 2019-2022.

2015 – polymath10, Israeli politics

The post Updates and plans III, contains a lot of startling mathematical and personal news. Among the mathematical news was the Adiprasito-Huh-Katz solution to the Heron-Rota conjecture. On the personal side are pictures from my 60th birthday conference.

The most viewed post from 2015 was the opening post for Polymath10: Polymath10: The Erdos Rado Delta System Conjecture, Polymath10, which started on November 2017 and was concluded in January 2017. In the second post Polymath10, Post 2: Homological Approach, I proposed a homological approach to the conjecture and we discussed (and improved) it, among other things, in several subsequent posts.

Another popular post was NogaFest, NogaFormulas, and Amazing Cash Prizes announcing Noga’s birthday conference.

For the first (and last) time I used the blog as a political platform:  I wrote a few posts in Hebrew criticizing our (then) prime minister Netanyahu and endorsing the labor opposition party for the 2015 elections. There were interesting comments (mostly negative).

I reported about several advances in combinatorics and computer science. Choongbum Lee proved the Burr-Erdős conjecture, More Reasons for Small Influence, New Isoperimetric Results for Testing Monotonicity, and The Simplex, the Cyclic polytope, the Positroidron, the Amplituhedron, and Beyond.  The last three posts are a mixture of reporting new results, explaining some classical results and raising some ideas of my own. Also in 2015 was a detailed report on Midrasha Mathematicae #18: In And Around Combinatorics, and a celebration following the solution of Erdos discrepancy problem EDP Reflections and Celebrations.

On the skeptical side we had a post with Angry Birds Update

In 2015, my beloved mother Carmela Kalai passed away and I devoted a post to her and her art.


2016 – Densest packing in dimensions 8 and 16, and the polynomial method

The most viewed post from 2016 and one of the most viewed posts ever was A Breakthrough by Maryna Viazovska Leading to the Long Awaited Solutions for the Densest Packing Problem in Dimensions 8 and 24. The second most popular post in 2016 involved the US elections, influence, noise sensitivity, social choice and Hex. The US Elections and Nate Silver: Information Aggregation, Noise Sensitivity, HEX, and Quantum Elections.

The startling news on the cup set problem came in 2016. Mind Boggling: Following the work of Croot, Lev, and Pach, Jordan Ellenberg settled the cap set problem! Dion Gijswijt also reached the same result. This post followed an earlier one: More Math from Facebook where we talked about Croot, Lev and Pach’s paper and other results. In December 2016 Jordan and I ran a Polynomial Method Workshop in Jerusalem. Also in 2016: The Erdős Szekeres polygon problem – Solved asymptotically by Andrew Suk.

Also in 2016, a beautiful guest post Stefan Steinerberger: The Ulam Sequence, and a report on my Notices paper The Quantum Computer Puzzle @ Notices of the AMS. Imre Barany’s beautiful presentation on Jiří Matoušek is given in Jirka.

2017 – Elchanan Mossel’s dice problem and lovely mathematical proofs

2017 marked new attempts for humorous stories. Layish – a true story from 1995 about Avi W. and me. Proofs that will make you smile: The seventeen camels riddle, and Noga Alon’s camel proof and algorithms; From camels to lice: Micha A. Perles’ Proof By Lice!; Touching Simplices and Polytopes: Perles’ argument (with additional mathematical fantasies and humor);  Micha Perles’ Geometric Proof of the Erdos-Sos Conjecture for Caterpillars; Test Your Intuition 33: The Great Free Will Poll; and a humorous quantum cartoons post: If Quantum Computers are not Possible Why are Classical Computers Possible?


A favorite post of mine was: The World of Michael Burt: When Architecture, Mathematics, and Art meet. As already mentioned the most popular posts featured Elchanan Mossel’s dice problem. 2017’s most viewed mathematical news was R(5,5) ≤ 48.  Also popular was a thorough discussion Around the Garsia-Stanley’s Partitioning Conjecture. We discussed the question Is Heads-Up Poker in P? And here is a post on Edmund Landau and the Early Days of the Hebrew University of Jerusalem.

The post Where were we? described several updates including, most excitingly, a nice personal greeting by Benjamin Netanyahu (Israeli PM in 2017) to a talk I gave in the Technion. Another nice eclectic mathematical update was Updates (belated) Between New Haven, Jerusalem, and Tel-Aviv.

2018 The g-conjecture; Rio ICM2018

Many startling mathematical news: In December 2018 definite progress on the problem I worked the most:  Amazing: Karim Adiprasito proved the g-conjecture for spheres! In January, Subhash Khot, Dor Minzer and Muli Safra completed the proof of the 2-to-2 Games Conjecture, Also in January, Cody Murray and Ryan Williams’ new ACC breakthrough: Updates from Oded Goldreich’s Choices. In February Serge Vlăduţ : Lattices with exponentially large kissing numbers. In April, Aubrey de Grey: The chromatic number of the plane is at least 5. Also in April,  Cohen, Haeupler, and Schulman: Explicit Binary Tree-Codes & Cancellations, and Nathan Rubin Improved the Bound for Planar Weak ε-Nets and Other News From Ein-Gedi;  In May, Duncan Dauvergne and Bálint Virág Settled the Random Sorting Networks Conjectures, and Zur Luria on the n-Queens Problem. Also in December, Nima Anari, Kuikui Liu, Shayan Oveis Gharan, and Cynthia Vinzant Solved the Mihail-Vazirani Conjecture for Matroids!

Toward the g-conjecture announcement I wrote about “what’s next”: Beyond the g-conjecture – algebraic combinatorics of cellular spaces I. I wrote another related post A Mysterious Duality Relation for 4-dimensional Polytopes.

Blogging from ICM 2018 Rio: I gave a plenary lecture at ICM 2018, and I was not the only Kalai in the congress: Yael Tauman Kalai’s ICM2018 Paper, My Paper, and Cryptography. I also slowly blogged about various events and lectures from the Rio congress. The most popular post from Rio was ICM 2018 Rio (3) – Coifman, Goldstein, Kronheimer and Mrowka, and the Four Color Theorem. I devoted much effort writing ICM 2018 Rio (4): Huh; Balog & Morris; Wormald.

Also in 2018, Ricky and Branko was an obituary to Ricky Pollack and Branko Grünbaum, and Coloring Problems for Arrangements of Circles (and Pseudocircles), was a post much in Ricky and Branko’s spirit.

2018 was the year of the first post in Alef’s corner: Alef’s Corner: There is Still a Small Gap in the Proof. Other popular posts were: Test Your Intuition 35: What is the Limiting Distance?; Conference in Singapore, Vietnam, Appeasement, Restorative Justice, Laws of History, and Neutrinos

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3 Responses to Greatest Hits 2015-2022, Part I

  1. Jon Awbrey says:

    Happy New Year 2023 !!! Hope You Have A Great One !!!

    Riffs and Rotes • Happy New Year 2023

  2. Happy new year Gil, that in 2023 we can dive deeper and deeper into the subspace dimensions of mathematics! Lots of health and creativity!

  3. Pingback: Greatest Hits 2015-2022, Part II | Combinatorics and more

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