# Combinatorics and More’s Greatest Hits

## First Month

Combinatorics, Mathematics, Academics, Polemics, …

Helly’s Theorem, “Hypertrees”, and Strange Enumeration I (There were 3 follow up posts:)

Extremal Combinatorics I: Extremal Problems on Set Systems (There were 4 follow up posts II ; III; IV; VI)

Drachmas

Rationality, Economics and Games

## Open problems

Five Open Problems Regarding Convex Polytopes

Seven Problems Around Tverberg’s Theorem

F ≤ 4E

The AC0 Prime Number Conjecture

Coloring Simple Polytopes and Triangulations

Some old and new problems in combinatorics and geometry

Noise Stability and Threshold Circuits

## Taxi and other Stories

Cosmonaut: Michal Linial

Michal Linial: No Witches in Portugal

Tel-Aviv’s “Jerusalem Beach”

Coffee, Cigarettes, and Aggression

## Polytopes

Ziegler´s Lecture on the Associahedron

The Simplex, the Cyclic polytope, the Positroidron, the Amplituhedron, and Beyond

Satoshi Murai and Eran Nevo proved the Generalized Lower Bound Conjecture.

Telling a Simple Polytope From its Graph

## Combinatorics

When Do a Few Colors Suffice?

Fractional Sylvester-Gallai

My Mathematical Dialogue with Jürgen Eckhoff

Influence, Threshold, and Noise

## Quantum

A Few Slides and a Few Comments From My MIT Lecture on Quantum Computers

Why Quantum Computers Cannot Work: The Movie!

Symplectic Geometry, Quantization, and Quantum Noise

Aaronson and Arkhipov’s Result on Hierarchy Collapse

## Computing

Is Backgammon in P?

Four Derandomization Problems

Navier-Stokes Fluid Computers

Subexponential Lower Bound for Randomized Pivot Rules!

Impagliazzo’s Multiverse

## Economics and Rationality

Arrow’s Economics 1

Social Choice Talk

## Sex, football, and other sports

Academic Degrees and Sex

The Intermediate Value Theorem Applied to Football

Is More Sex Safe? A book review.

## Guests posts

Emmanuel Abbe: Erdal Arıkan’s Polar Codes

János Pach: Guth and Katz’s Solution of Erdős’s Distinct Distances Problem

Amir Ban on Deep Junior

About Conjectures: Shmuel Weinberger

(Eran Nevo) The g-Conjecture I

Christine Bjorner: The Golden Room and the Golden Mountain

## Polls

What does “beyond a reasonable doubt” practically mean?

Would you decide the election if you could?

The Generation Gap

## People

Oded

Happy Birthday Richard Stanley!

Happy Birthday Ron Aharoni!

Nati’s Influence

## Polymath and online research

The Polynomial Hirsch Conjecture: A proposal for Polymath3

Polymath 8 – a Success!

Polymath8: Bounded Gaps Between Primes

Mathematics, Science, and Blogs

Polymath1: Success!

## Opinions

Chess can be a Game of Luck

Amy Triumphs* at the Shtetl

## Test your intuition

Test Your Intuition (17): What does it Take to Win Tic-Tac-Toe

Mittag-Leffler Institute and Yale, Winter 2005; Test your intuition: Who Played the Piano?

## Mathematics

The Amitsur-Levitzki Theorem for a Non Mathematician.

About Mathematics

Can Category Theory Serve as the Foundation of Mathematics?

Buffon’s Needle and the Perimeter of Planar Sets of Constant Width

A Few Mathematical Snapshots from India (ICM2010)

The Beauty of Mathematics

## Science

Answer: Lord Kelvin, The Age of the Earth, and the Age of the Sun

Itamar Pitowsky: Probability in Physics, Where does it Come From?

## Riddles

Two Math Riddles

The Ultimate Riddle

Greg’s Dinosaurs Riddle

## Discussions of various kinds

When It Rains It Pours

Why is mathematics possible?

Chomskian Linguistics (The phrase “more or less” in various languages)

## News

The Kadison-Singer Conjecture has beed Proved by Adam Marcus, Dan Spielman, and Nikhil Srivastava

Francisco Santos Disproves the Hirsch Conjecture

Amazing: Peter Keevash Constructed General Steiner Systems and Designs

Exciting News on Three Dimensional Manifolds

Roth’s Theorem: Tom Sanders Reaches the Logarithmic Barrier

Greg Kuperberg: It is in NP to Tell if a Knot is Knotted! (under GRH!)

From Oberwolfach: The Topological Tverberg Conjecture is False

New Ramanujan Graphs!

## Updates

Celebrations in Sweden and Norway

Mabruk Elon, India, and More

## Teaching

A Proof by Induction with a Difficulty

In how many ways you can chose a committee of three students from a class of ten students?

## MathOverflow related

Fundamental Examples

Why are Planar Graphs so Exceptional

Joel David Hamkins’ 1000th MO Answer is Coming

Joe’s 100th MO question

## Gina says

My Book: “Gina Says,” Adventures in the Blogosphere String War

Anat Lotan: Who is Gina I

Anat Lotan: Who is Gina II, My Own Shocking Revelation

Praise For ‘Gina says’

## Humor (?)

Believing that the Earth is Round When it Matters

Annotating Kimmo Eriksson’s Poem

## Public service

Optimism – two quotes

The Simplified Pill Algorithm

## Useful links

Stand Clear of The Closing Doors, Please