- Mathematical news to cheer you up
- To Cheer You Up in Difficult Times 28: Math On the Beach (Alef’s Corner)
- To cheer you up in difficult times 27: A major recent “Lean” proof verification
- To cheer you up in difficult times 26: Two real-life lectures yesterday at the Technion
- To Cheer You Up in Difficult times 24: Borodin’s colouring conjecture!
- To cheer you up in difficult times 25: some mathematical news! (Part 2)
- To cheer you up in difficult times 23: the original hand-written slides of Terry Tao’s 2015 Einstein Lecture in Jerusalem
- Alef Corner: ICM2022
- The probabilistic proof that 2^400-593 is a prime: a revolutionary new type of mathematical proof, or not a proof at all?
Top Posts & Pages
- Mathematical news to cheer you up
- The Argument Against Quantum Computers - A Very Short Introduction
- A sensation in the morning news - Yaroslav Shitov: Counterexamples to Hedetniemi's conjecture.
- To cheer you up in difficult times 27: A major recent "Lean" proof verification
- Zur Luria on the n-Queens Problem
- To Cheer You Up in Difficult Times 28: Math On the Beach (Alef's Corner)
- The Quantum Fault-Tolerance Debate Updates
- Around Borsuk’s Conjecture 3: How to Save Borsuk's conjecture
- To cheer you up in difficult times 5: A New Elementary Proof of the Prime Number Theorem by Florian K. Richter
Category Archives: Number theory
Topology Quasi-polynomial algorithms for telling if a knot is trivial Marc Lackenby announced a quasi-polynomial time algorithm to decide whether a given knot is the unknot! This is a big breakthrough. This question is known to be both in NP … Continue reading
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)
What will be the next polymath project? click here for our post about it. New lower bounds for van der Waerden numbers by Ben Green Abstract: We show that there is a red-blue colouring of [N] with no blue 3-term … Continue reading
Prologue Consider the following problems: P3: What is the maximum density of a set A in without a 3-term AP? (AP=arithmetic progression.) This is the celebrated Cap Set problem and we reported here in 2016 the breakthrough results by … Continue reading
For the previous post “quantum matters” click here. Noam D. Elkies piano improvisations Every day since March 27, 2020 Noam Elkies (Noam’s home page) uploaded a new piece of piano improvisation. The Hebrew title of his page is “Music will … Continue reading
To cheer you up in difficult times 5: A New Elementary Proof of the Prime Number Theorem by Florian K. Richter
Here is a piece of news that will certainly cheer you up: Florian Richter found A new elementary proof of the prime number theorem. (I thank Tami Ziegler for telling me about the new result.) From left to right: Atle Selberg, … Continue reading
Hoi Nguyen and Melanie Wood: Remarkable Formulas for the Probability that Projections of Lattices are Surjective
Following a lecture by Hoi Nguyen at Oberwolfach, I would like to tell you a little about the paper: Random integral matrices: universality of surjectivity and the cokernel by Hoi Nguyen and Melanie Wood. Two background questions: Hoi started with … Continue reading
The result on Paley Graphs by Hanson and Petridis On May 2019, Brandon Hanson and Giorgis Petridis posed a paper on the arXive: Refined Estimates Concerning Sumsets Contained in the Roots of Unity. The abstract was almost as short as … Continue reading
This post, about the Riemann zeta function, which is among the most important and mysterious mathematical objects was kindly written by Dan Romik. It is related to his paper Orthogonal polynomial expansions for the Riemann xi function, that we mentioned … Continue reading
Update: The result was achieved by Andrew Booker from Bristol. Here is the preprint Cracking the problem with 33. It is a notoriously difficult open problem which integers can be written as the sum of three integer cubes. Such integers … Continue reading
How much is The product ranges over all primes. In other words, Just heard it from Avinoam Mann.