What is better than how (?)

 History of filters source.

Wilhelm Cauer was a German mathematician and engineer who worked in Göttingen and the US between the two world wars. He is associated with the term “black box,” although he apparently did not use it in his published papers, and others are said to have used it before. What Cauer did do was conceive a computing device based on electrical principles. According to this essay by Hartmut Petzold, Cauer’s device was markedly more advanced and mathematically general than other ‘analog devices’ of the same decades. He returned to Germany in the early 1930′s, stayed despite attention being drawn to some Jewish ancestry, and was killed in the last days of Berlin despite being on the Red Army’s list of scientists whose safety they’d wished to assure.

Today Ken and I wish to talk about black boxes and white boxes, no matter who invented them, and their relation to computing.

How far can trivial ideas go?

Klaus Roth is famous for many results, but two stand out above all others.
One sets limits on Diophantine approximations to algebraic numbers, and the other sets limits on how dense a set can be and have no length-three arithmetic progression. He has won many awards for his work, including a Fields Medal and the Sylvester Medal.

Today I want to try and amuse you with a simple proof that is related to his work on progressions.

It snowed in Atlanta, and we are closed, for the foreseeable future—where is global warming?

Atlanta is frozen. Here is what we looked like the other night.

Today I thought I might talk about the weather in Atlanta, and its connection to mathematical paradoxes. Read more…

More on the crypto approach to the Jacobian Conjecture

Arno van Essen is one of the world experts on the Jacobian conjecture (JC)—we have discussed his work before here. He has made many contributions to it, with my favorite being: To Believe Or Not To Believe: The Jacobian Conjecture. I like his attitude about conjectures: I think we should be more skeptical about our own. Oh well, few of my colleagues feel this way about ${\mathsf{P \neq NP}}$, for example.

Today I want to update a previous discussion on the JC, and prove a new theorem. Read more…

A puzzle with a story

Dick Karp needs no introduction. So I will give him none. Okay I will say that it has been an honor to know him for many years—we met right after I graduated from CMU, a pleasure to work with him on a few projects, and always fun to see.

Today I wish to talk about a recent dinner conversation I had with Dick and Noga Alon. Read more…

Applications of social networks to arbitrary graphs

Tim Roughgarden is a faculty member at Stanford, with interests in modern algorithms—my term. So his research is all about auctions, game theory, microeconomics, and social networks. You can see his visible hand here, from time to time. Read more…

COLT deadline is Fri. Feb. 7

 Columbia University source.

Vladimir Vapnik is one of the founding visionaries of Computational Learning Theory. His papers in 1963 with his advisor Aleksandr Lerner and in 1964 with Aleksey Chervonenkis are considered foundational for the Support Vector Machine model, which Vapnik himself ushered into its modern form in 1995 in joint work with Corinna Cortes. Vapnik and Chervonenkis got their initials into the theory walk of fame with the concept of VC-dimension in statistical classification. A 2008 interview with him titled “Learning Has Just Started” is still featured on the permanent page of the Computational Learning Theory (COLT) conferences and association.

Today Ken and I wish to note that my colleague Nina Balcan is chairing the COLT 2014 program committee, and talk about ways we might simplify learning—at least learning our field. Read more…