This is the second part of Greatest Hits 2015-2022, Part I. Here are popular and favorite posts published in 2019-2022.
2019 Supremacy and Sensitivity (and Sunflowers)
Test your intuition 38 was contributed in March 2019 by my youngest son Lior. TYI38 Lior Kalai: Monty Hall Meets Survivor. Aside from the problem itself, the post contained beautiful pictures of my family, and, two days after the post was published, I added the startling breaking news about Karen Uhlenbeck being awarded the Abel Prize.
Also in March 2019, the post 10 Milestones in the History of Mathematics according to Nati and Me drew many views and many comments. And in April 2019 I made an unusual invitation: An Invitation to a Conference: Visions in Mathematics towards 2000, with links to videos and many pictures of us 20 years younger. This followed by a post discussing a bold statement made at the conference by Misha Gromov Are Natural Mathematical Problems Bad Problems?
In August 2019 I presented a new paper and a CERN colloquium: The Argument against Quantum Computers – a CERN Colloquium and a New Paper, a month later on September 22, 2019, a paper by a team from Google was leaked with a demonstration of quantum supremacy, which, if true, would refute my argument. I found the leaked paper rather unconvincing and raised some concerns about it in this post: Quantum computers: amazing progress (Google & IBM), and extraordinary but probably false supremacy claims (Google).
Two weeks later I wrote The story of Poincaré and his friend the baker, where I raised another concern regarding the calibration process of the paper, and this concern was amply discussed in the comment section. Following the appearance of the Google paper itself on October 21, 2019, and some responses from the Google team, I wrote on November 11, 2019 a new post Gil’s Collegial Quantum Supremacy Skepticism FAQ. Some further updates and discussion can be found in the Dec. 27 post The Google Quantum Supremacy Demo and the Jerusalem HQCA debate.
2019 mathematical news
The mathematical news that was most exciting to me in 2019 was reported in August. Amazing: Ryan Alweiss, Shachar Lovett, Kewen Wu, Jiapeng Zhang made dramatic progress on the Sunflower Conjecture. This was a problem I had first heard about as an undergraduate, I thought about it over the years, and we ran polymath 10 for attacking it. I also was excited about other possible applications, but did not imagine it would be related to Jeff Kahn and mine expectation threshold conjecture. But indeed it was related: Amazing! Keith Frankston, Jeff Kahn, Bhargav Narayanan, Jinyoung Park: Thresholds versus fractional expectation-thresholds;
Other great results were: Amazing: Hao Huang Proved the Sensitivity Conjecture! (July); A sensation in the morning news – Yaroslav Shitov: Counterexamples to Hedetniemi’s conjecture (May); Another sensation – Annika Heckel: Non-concentration of the chromatic number of a random graph (June); Konstantin Tikhomirov: The Probability that a Bernoulli Matrix is Singular (February); Jeff Kahn and Jinyoung Park: Maximal independent sets and a new isoperimetric inequality for the Hamming cube; Matan Harel, Frank Mousset, and Wojciech Samotij and the “the infamous upper tail” problem; Attila Por’s Universality Result for Tverberg Partitions; Isabella Novik and Hailun Zheng: Neighborly centrally symmetric spheres exist in all dimensions!; Danny Nguyen and Igor Pak: Presburger Arithmetic Problem Solved! And in number theory 8866128975287528³+(-8778405442862239)³+(-2736111468807040)³;
We had two great guest posts: Dan Romik on the Riemann zeta function, and Imre Bárány: Limit shape.
In 2019 I also wrote about Jean Bourgain and about The last paper of Catherine Rényi and Alfréd Rényi: Counting k-Trees.
A drawing explaining Attila Por’s construction
Jean Bourgain and Joram Lindenstrauss
2020 To cheer you up in difficult times
The post about mathematical news that excited both the readers and me the most appeared in January: Amazing: Zhengfeng Ji, Anand Natarajan, Thomas Vidick, John Wright, and Henry Yuen proved that MIP* = RE and thus disproved Connes 1976 Embedding Conjecture, and provided a negative answer to Tsirelson’s problem. My final correspondence with Boris Tsirelson was about this breakthrough and I wrote about him in this post Trees not Cubes! Memories of Boris Tsirelson.
Two other exciting and popular posts with 2020 major mathematical news came in July and December. The July post was To cheer you up in difficult times 7: Bloom and Sisask just broke the logarithm barrier for Roth’s theorem!; And in December To Cheer You Up in Difficult Times 15: Yuansi Chen Achieved a Major Breakthrough on Bourgain’s Slicing Problem and the Kannan, Lovász and Simonovits Conjecture
To cheer you up in difficult times (Math news, and fun)
To cheer you up in difficult times 3: A guest post by Noam Lifshitz on the new hypercontractivity inequality of Peter Keevash, Noam Lifshitz, Eoin Long and Dor Minzer; To cheer you up in difficult times 5: A New Elementary Proof of the Prime Number Theorem by Florian K. Richter; To cheer you up in difficult times 6: Play Rani Sharim’s two-player games of life, read Maya Bar-Hillel presentation on catching lies with statistics, and more.;To Cheer you up in Difficult Times 8: Nathan Keller and Ohad Klein Proved Tomaszewski’s Conjecture on Randomly Signed Sums; To cheer you up in difficult times 9: Alexey Pokrovskiy proved that Rota’s Basis Conjecture holds asymptotically; To cheer you up in difficult times 12: Asaf Ferber and David Conlon found new lower bounds for diagonal Ramsey numbers; Three games to cheer you up.
The first post which explicitly aimed cheering up our readers was from mid-March when it had become clear that the Corvid outbreak is going to overshadow our lives. To cheer you up in complicated times – A book proof by Rom Pinchasi and Alexandr Polyanskii for a 1978 Conjecture by Erdős and Purdy!
Other mathematical news from 2019 were Ringel Conjecture, Solved! Congratulations to Richard Montgomery, Alexey Pokrovskiy, and Benny Sudakov; In February Remarkable New Stochastic Methods in ABF: Ronen Eldan and Renan Gross Found a New Proof for KKL and Settled a Conjecture by Talagrand; Kelman, Kindler, Lifshitz, Minzer, and Safra: Towards the Entropy-Influence Conjecture; Noam Lifshitz: A new hypercontractivity inequality — The proof!
Quantum news and matters
In December 2020 I wrote about an attempt to establish quantum supremacy using a photonic device: Photonic Huge Quantum Advantage ???, This time, an algorithm from a 2014 paper by Guy Kindler and me sufficed to refute the fantastic claims. A few days later I wrote The Argument Against Quantum Computers – A Very Short Introduction, which has become one of the blog’s blockbusters.
2021 Erdős-Faber-Lovász and Diverse Matters
Discussion about Diversity: the post To Cheer You Up in Difficult Times 31: Federico Ardila’s Four Axioms for Cultivating Diversity, led to heated discussions mainly on Facebook.
Celebrations and discussions: The post Cheerful News in Difficult Times: The Abel Prize is Awarded to László Lovász and Avi Wigderson, contains a lot of pictures of Avi and Laci and their families (and in a few cases of my family), and it was followed by the most viewed 2021 post presenting a debate between Avi Wigderson and me, which goes deeply into the connection between (computer science) theory, practice, and mathematics: The probabilistic proof that 2^400-593 is a prime: a revolutionary new type of mathematical proof, or not a proof at all?
Mathematical news from 2021: 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!; To cheer you up in difficult times 20: Ben Green presents super-polynomial lower bounds for off-diagonal van der Waerden numbers W(3,k);To cheer you up in difficult times 21: Giles Gardam lecture and new result on Kaplansky’s conjectures; To Cheer you up in difficult times 30: Irit Dinur, Shai Evra, Ron Livne, Alex Lubotzky, and Shahar Mozes Constructed Locally Testable Codes with Constant Rate, Distance, and Locality. To cheer you up in difficult times 34: Ringel Circle Problem solved by James Davies, Chaya Keller, Linda Kleist, Shakhar Smorodinsky, and Bartosz Walczak; 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.
Two collections of startling mathematical news: To cheer you up in difficult times 25: some mathematical news! (Part 2) and To cheer you up in difficult times 22: some mathematical news! (Part 1)
Memorabilia: Nostalgia corner: John Riordan’s referee report of my first paper; To cheer you up in difficult times 23: the original hand-written slides of Terry Tao’s 2015 Einstein Lecture in Jerusalem
Quantum matters: Amazing: Feng Pan and Pan Zhang Announced a Way to “Spoof” (Classically Simulate) the Google’s Quantum Supremacy Circuit!; This work and several related works largely (but not fully) refuted Google’s 2019 quantum supremacy claim.
Free will: To cheer you up in difficult times 29: Free will, predictability and quantum computers
A post about my papers: Let me tell you about three of my recent papers;
Open problems: The 3ᵈ problem; Turan type theorems for simplicial complexes.
Are we up for a new polymath project?: Possible future Polymath projects (2009, 2021)
2022 The expectation threshold conjecture
Blogging from ICM 2022: I slowly blogged about various events and lectures from ICM 2022. The most popular post about ICM2022 was about verifying mathematical proofs using computers and especially LEAN: ICM 2022. Kevin Buzzard: The Rise of Formalism in Mathematics. I attempted to report on ICM 2022: Langlands Day which I followed on Zoom, and I gave a live report from Helsinki on ICM 2022 awarding ceremonies (1).
Because of Russia’s invasion of Ukraine, the ICM originally planned for St. Petersburg turned into a virtual event, but the opening ceremonies and lectures of the medalists took place with live audience in Helsinki.
The Israeli delegation to the 2022 general assembly of the IMU. With Tammy Ziegler and Mina Teicher.
The mathematical news that caught most attention: A conjecture of Jeff Kahn and me is now fully resolved: Amazing: Jinyoung Park and Huy Tuan Pham settled the expectation threshold conjecture! … and major progress on Frankl’s conjecture: Amazing: Justin Gilmer gave a constant lower bound for the union-closed sets conjecture
Other news: Oliver Janzer and Benny Sudakov Settled the Erdős-Sauer Problem; Bo’az Klartag and Joseph Lehec: The Slice Conjecture Up to Polylogarithmic Factor! ;
News about polytopes and combinatorial geometry: Joshua Hinman proved Bárány’s conjecture on face numbers of polytopes, and Lei Xue proved a lower bound conjecture by Grünbaum; James Davies: Every finite colouring of the plane contains a monochromatic pair of points at an odd distance from each other.; Chaim Even-Zohar, Tsviqa Lakrec, and Ran Tessler present: The Amplituhedron BCFW Triangulation; Alexander A. Gaifullin: Many 27-vertex Triangulations of Manifolds Like the Octonionic Projective Plane (Not Even One Was Known Before).
Quantum matters: Inaugural address at the Hungarian Academy of Science: The Quantum Computer – A Miracle or Mirage;