## A Brilliant Book on Combinatorics

*And Razborov’s brilliant proof method*

Stasys Jukna is the author of the book *Extremal Combinatorics With Applications in Computer Science*.

Today we talk about Jukna’s book on extremal combinatorics.

## Mathematical Search

*A flying start from nearby Rochester*

Anurag Agarwal and Richard Zanibbi are tenured faculty in Mathematics and Computer Science, respectively, at RIT. They partner with Clyde Lee Giles of Penn State and Douglas Oard of U.Md. on the MathSeer project. If the name reminds you of CiteSeer, no surprise: Giles co-originated that and still directs it.

Today we note last month’s release of a major piece of MathSeer called MathDeck and show how to have fun with it.

## Ron Graham, 1935–2020

*Ron Graham passed away, but he lives on…*

Cropped from tribute by Tom Leighton |

Ron Graham just passed away Monday at the age of in La Jolla near UCSD.

Today Ken and I wish to say a few words about Ron.

## Intellectual Fireworks?

*Some different ideas for marking the Fourth*

“Founding Frenemies” source |

John Adams and Thomas Jefferson did not use Zoom. Their correspondence, from 1777 up to their deaths hours apart on July 4, 1826, fills a 600-page book.

Today, Independence Day in the US, we consider the kind of intellectual fireworks represented by the correspondence.

## Taking a Problem Down a Peg

*By blowing up its objects*

Composite crop of src1, src2 |

Joshua Greene and Andrew Lobb proved last month that every *smooth* Jordan curve in the plane and real , there are four points on the curve that form a rectangle with sides of ratio .

Today we explain how this result relates to Otto Toeplitz’s famous “square peg conjecture,” which is the case when the curve need not be smooth.

## Some Real and Some Virtual News

*Gossip and more.*

Composite of , src1, src3 |

Jessica Deters, Izabel Aguiar, and Jacqueline Feuerborn are the authors of the paper, “The Mathematics of Gossip.” They use infection models—specifically the Susceptible-Infected-Recovered (SIR) model—to discuss gossip. Their work was done *before* the present pandemic, in 2017–2019. It is also described in a nice profile of Aguiar. Their analogy is expressed by a drawing in their paper:

Not just for today, but for the summer at least, Ken and I want to share some gossip, share some problems, and ask our readers a question.

## P<NP

*Some thoughts on P versus NP*

Norbert Blum is a computer science theorist at the University of Bonn, Germany. He has made important contributions to theory over his career. Another claim to fame is he was a student of Kurt Mehlhorn, indeed the third of Mehlhorn’s eighty-eight listed students.

Today I wish to discuss a new paper by Blum.

## The Doomsday Argument in Chess

*Framing a controversial conversation piece as a conservation law*

Snip from Closer to Truth video on DA |

John Gott III is an emeritus professor of astrophysical sciences at Princeton. He was one of several independent inventors of the controversial Doomsday Argument (DA). He may have been the first to think of it but the last to expound it in a paper or presentation.

Today we expound DA as a defense against thought experiments that require unreasonable lengths of time.