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Three In The Room

November 12, 2014

A puzzle and a conference


Zohar Manna is an expert on the mathematical concepts behind all types of programming. For example, his 1974 book the Mathematical Theory of Computation was one of the first on the foundations of computer programming. He wrote textbooks with the late Amir Pnueli on temporal logic for software systems. As remarked by Heiko Krumm in some brief notes on temporal logic, there is a contrast between analyzing the internal logic of pre- and post-conditions as each statement in a program is executed, and analyzing sequences of events as a system interacts with its environment.

Today I want to talk about an encounter with Zohar years ago, and how it relates to a puzzle that I love.
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A Conjecture Of Ulam

November 8, 2014

A pointed question about the plane


Stanisław Ulam was one of the great mathematicians of the last century. We talked about him in a recent post on his prime spiral and other strange mathematical facts. He is associated with several famous problems, including the 3n+1 problem and the Graph Reconstruction conjecture.

Today we want to talk about one of his oldest conjectures.

The conjecture was first stated in 1945. It is simple to state, seems plausible that it is true, but so far has resisted all attempts at resolution. René Descartes could have stated in the 1600s—well almost. Read more…

DC Post

November 6, 2014

Discussing lower bounds for this blog’s 600th post


Superman, Batman, and Wonder Woman are three of the best known superheroes in DC Comics books, which were a childhood staple for many of our age. They brought us action in color before our families had color TVs. There is a new nonfiction book on Wonder Woman. She and Superman have super powers: flying, super strength, X-ray vision, magical healing, and more. It is notable that Batman does not. All of his powers come from great training, great study, great equipment, and great helpers.

Today this blog makes post number 600, DC in Roman numerals. Read more…

Reconstructing Gödel

November 1, 2014

What exactly was his “Philosophical Viewpoint”?

By permission of Renee Bolinger, artist : source

Kurt Gödel left a large amount of unpublished writings and notebooks and preserved correspondence. Called his Nachlass, German for “after-leavings” or bequest, these writings were catalogued and organized by several—including his first biographer, John Dawson, for a heroic two years. Those of highest scientific and general interest were published in volumes III, IV, and V of Kurt Gödel: Collected Works. Among them was a list of 14 numbered assertions titled “My philosophical viewpoint” but without elaboration. They are believed associated to a lecture Gödel started preparing in the early 1960s but never gave, whose draft is in the Nachlass.

Today we are delighted to have new communications from Gödel, as we have previously received around Halloween and All Saints’ Day, so we can continue our series of interviews with him.
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Rebooting Computing

October 27, 2014

How to beat the end of Moore’s Law

Screen Shot 2014-10-27 at 2.25.21 PM

Elie Track and Tom Conte were co-chairs of the recently-held Third IEEE workshop on Rebooting Computing. Tom is a computer architect at Georgia Tech. A year ago he became the 2014 President-Elect of the IEEE Computer Society, which according to both the press release and Conte’s Wikipedia page entails that he “currently serves as the 2015 President.” I guess that is one way to stay focused on the future. Track is president of the IEEE Council on Superconductivity. A year ago he founded nVizix, a startup to develop photovoltaic power, and serves as CEO. He is also a senior partner at Hypres, a superconducting electronics company.

Today I wish to relate some of what happened last week at the meeting.
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A New Twist on Flexagons?

October 22, 2014

For Martin Gardner’s 100th birthday

Martin Gardner
Global Science source

Martin Gardner introduced many including myself to the joys of Discrete Mathematics. His glorious monthly column “Mathematical Games” for Scientific American included some continuous mathematics too, of course; one could say it was on “Concrete Mathematics.” However, I conjecture—based on a quick flip of the several books I own of his columns—that the symbols {\epsilon,\delta} in a calculus context never appeared in them.

Yesterday was the 100{{}^{th}} anniversary of Gardner’s birth. Dick and I wish to join the many others marking this centennial and thanking him for all he did to make math fun for so many. Read more…

A New Provable Factoring Algorithm

October 18, 2014

Factoring, factoring, the whole day through, keeps on my mind—apologies to Hoagy Carmichael and Stuart Gorrell

Waterloo Mathematics source

Michael Rubinstein is an expert on number theory, who is on the faculty of the University of Waterloo. He is one of the organizers of a 61{^{st}}-birthday symposium being held December 15–19 in Princeton for my friend and former colleague, Peter Sarnak. I guess it is a matter of taste for a number theorist whether to observe a birthday with a lot of factors (60) or a prime (59 or 61). Rubinstein also does extensive experimental mathematics and lists several code libraries below his publications on his website, which also has interesting articles on the math, history, and practice of musical tuning.

Today Ken and I wish to discuss a paper of his on one of my favorite problems: integer factoring.
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