Can we have overlooked short solutions to major problems?
Efim Geller was a Soviet chess grandmaster, author, and teacher. Between 1953 and 1973 he reached the late stages of contention for the world championship many times but was stopped short of a match for the title. The Italian-American grandmaster Fabiano Caruana was similarly stopped last week in the World Chess Federation Candidates Tournament in Moscow. He was beaten in the last round by Sergey Karjakin of Russia, who will challenge world champion Magnus Carlsen of Norway in a title match that is scheduled for November 11–30 in New York City.
Today we salute a famous move by Geller that was missed by an entire team of analysts preparing for the world championship in 1955, and ask how often similar things happen in mathematics and theory.
Casinos beware—the primes are not random
|Quanta source (K.S. at left)|
Robert Lemke Oliver and Kannan Soundararajan have observed that the primes fail some simple tests of randomness in senses that are both concrete and theoretical.
Today we discuss this wonderful work and what it means both for properties of the primes and for asymptotics.
A trick of language and echoing
Neil L. is a Leprechaun. He has been visiting me once every year since I started GLL. I had never seen a leprechaun before I began the blog—there must be some connection.
Today I want to share the experience I had with him this morning of St. Patrick’s Day.
Another coins on a chessboard puzzle
|Cropped from Ashley’s TwiCopy source|
Hou Yifan and Maurice Ashley are champions of chess in several senses. Hou just regained the Women’s World Champion title by defeating Mariya Muzychuk of Ukraine 3-0-6 in their match which ended today in Lviv. Along with her male Chinese compatriots who reign as Olympiad team champions, she headlines an extraordinary growth of the game in southeast Asia. Ashley became the first ever grandmaster to play a tournament in Jamaica where he was born and has been one of the game’s premier video commentators and ambassadors for over two decades. The past two years he teamed with entrepreneur Amy Lee of Vancouver to create and run the Millionaire Chess open tournaments in Las Vegas, to raise the professional profile of the game.
Will there be any man left standing?
|Sensei’s Library player bio source|
Lee Sedol of South Korea, who is currently ranked #4 on the unofficial GoRatings list, may be on his way to being #5. AlphaGo, a computer project sponsored by Google DeepMind, is ahead 2-0 in their five-game match.
Today I take stock, explain some of what has happened, and briefly discuss the prospects for AI and human ingenuity.
David just passed away
David Johnson was a computer theorist who worked on many things, with special emphasis on the care and treatment of hard computational problems.
Ken and I are sad today to hear that David just passed away.
Many will announce this sad event; we expect that the whole community will express how much they miss David. He was unique among theorists in his dedication to see how hard so-called “intractable” problems really are. He dedicated much of his career to building challenges: A typical one asked you to design an algorithm that solved some hard problem, often an NP-complete one. These challenges were of great importance in pushing forward the field of attacking difficult but important problems.