The Abel Prize, which is accompanied by a monetary award of approximately USD$1 million, is widely considered comparable to the Nobel Prize. It has been . . . → Read More: Endre Szemeredi wins Abel Prize for work in mathematics and computing]]> Endre Szemerédi, who has positions both at Rutgers University in the USA, and the Alfréd Rényi Institute of Mathematics in Hungary, has been awarded the 2012 Abel Prize for mathematics.

The Abel Prize, which is accompanied by a monetary award of approximately USD$1 million, is widely considered comparable to the Nobel Prize. It has been granted by the Norwegian Academy of Science and Letters since 2003. It is named for the 19th century Norwegian mathematician Niels Henrik Abel, who did groundbreaking work in algebra and analysis, including the first complete proof that a general fifth degree polynomial is not solvable in terms of radicals.

According to the Abel Prize announcement, Szemerédi was cited “for his fundamental contributions to discrete mathematics and theoretical computer science.” His work, in general terms, implies that discrete systems consisting of large numbers of components possess some identifiable structure, even if composed at “random.” What’s more, there are useful aspects of randomness even within systems that are highly structured.

His most famous result establishes the presence of arbitrarily long arithmetic progressions within any set of integers that has nonzero limiting density. This theorem, which Szemerédi proved in 1975, had been an unsolved problem for decades. It was first posed by famed Hungarian mathematicians Paul Turán and Paul Erdös.

Szemerédi has published over 200 papers, spanning five decades. At the age of 71, he continues active research work, and according to colleagues shows no signs of slowing down.

This award continues the Abel Prize committee’s catholic tradition of recognizing a wide range of mathematical accomplishments, including those that have implications and connections to fields well outside the realm of traditional theoretical mathematical research.  (See http://en.wikipedia.org/wiki/Abel_Prize for a complete list of Laureates)

For additional details, see Barry Cipra’s article on the sciencemag.org website, from which some of the above material was excerpted.

But even this feat was overshadowed by the 2011 defeat of the two most successful . . . → Read More: Computer challenges human crossword puzzle solvers]]> Many are familiar with the 1997 defeat of Garry Kasparov, the world’s reigning chess champion, by IBM’s “Deep Blue” computer [1997 NY Times article]. This feat was hailed as a major milestone in the development of artificially intelligent computer systems.

But even this feat was overshadowed by the 2011 defeat of the two most successful contestants on the American quiz show Jeopardy!, by a new IBM-developed computer system named “Watson” [2011 NY Times article]. As we explained in a previous blog article, the Watson achievement was significantly more impressive than the Deep Blue because it involved “natural language understanding,” namely the intelligent “understanding,” in some sense, of ordinary English text [Math Drudge blog #1]. Indeed, Watson more than Deep Blue well deserves the assessment of legendary Jeopardy! champ Ken Jennings, who wrote, on his computer tablet conceding victory to Watson, “I for one welcome our new computer overlords” [Math Drudge blog #2].

Now computer scientist Matthew Ginsberg has his eye on a similarly challenging problem: Defeat the world’s best human crossword puzzle solvers. Ginsberg, who has received a Ph.D. from Oxford and has written a book on artificial intelligence, is presently the Chief Executive Officer of On Time Systems in Eugene, OR. He has already tested his computer program, known as “Dr. Fill,” in a series of crossword puzzle tournaments, finishing on top in three of 15 contests.

Typical full-size newspaper crossword puzzles have roughly 140 words, and, as in Jeopardy!, the clues are often notoriously subtle. As an example, in a 2010 New York Times crossword puzzle with the theme “rabbits,” the correct answer to clue “Famous bank robbers” was “BUNNYANDCLYDE.” As another example, the correct answer for the clue “Apollo 11 and 12 (180 degrees)” was “SNOISSIWNOOW” (i.e., “MOON MISSIONS” written upside down and backwards).

Obviously such machinations require some degree of imagination and creativity. Or, at the least, the computer program’s analysis on other, more straightforward, clues must be so strong that it can still complete the puzzle in spite of its failing to “understand” some of the most subtle clues.

Will Shortz, tournament director and crossword puzzle editor for the New York Times, who has seen a demonstration of “Dr. Fill” in action, believes that the computer program may crush human opponents on easier puzzles. But on more difficult puzzles, particularly those with many subtle clues, it will be a closer match.

David Ferrucci, leader of IBM’s Watson project, agrees that “Games are a great motivator for artificial intelligence — they push things forward.” But he emphasizes that “what really matters is where it is taking us.” He is now involved with an effort to commercialize Watson’s technology in the health care field. Perhaps similar applications will be found for Dr. Fill.

For additional details, see a 2012 NY Times article, from which some of the above is excerpted.

Entitled Exploratory Experimentation in Mathematics: Selected Works, the work collects 16 articles that reflect the changing face of computer-assisted “high-performance” mathematics, wherein the computer is increasingly . . . → Read More: Bailey and Borwein publish new collection of experimental math papers]]> A collection of papers in the field of computational and experimental mathematics authored by one or both of the present bloggers has now been published by Perfectly Scientific Press.

Entitled Exploratory Experimentation in Mathematics: Selected Works, the work collects 16 articles that reflect the changing face of computer-assisted “high-performance” mathematics, wherein the computer is increasingly utilized as an active agent for exploration and discovery in the world of research mathematics.

Richard E. Crandall, a colleague of the present bloggers and Director of the Center for Advanced Computation at Reed College, comments as follows:

Refreshing always it is to have in hand a book by the pioneers of a given field. David Bailey and Jonathan Borwein have together—and along with illustrious colleagues—built the field of experimental mathematics. In this field one discovers truths in much the same way that new particles can be discovered in a physics laboratory; or in the manner by which DNA was discovered in 1953 to be of helical structure, on the basis of ball-stick models and x-ray data. Whereas Crick and Watson made hay out of their models, and Wilkinson serendipitously interpreted his data, so, too, Bailey and Borwein show how to use numerical tools and intuition to bear mathematical fruit.

A PDF copy of the book may be purchased online at Perfectly Scientific Press website.

Wain notes the successful Mathematikum in Giessen, Germany, which opened in 2002 and now attracts 150,000 visitors per year, and the Museum of Mathematics in New York City, which is slated to open . . . → Read More: Researchers seek UK home for mathematics museum]]> Geoff Wain, a mathematics educator at Leeds University, is promoting an initiative to organize a museum of mathematics in the U.K.

Wain notes the successful Mathematikum in Giessen, Germany, which opened in 2002 and now attracts 150,000 visitors per year, and the Museum of Mathematics in New York City, which is slated to open later this year. He asks “Where would you go to find out about mathematics? … There’s absolutely nowhere in this country. It’s very sad.”

Last week Wain and some supporters gathered at King’s College to discuss plans for the museum, which is tentatively known as “MathWorldUK.” They hope to provide something for persons of all ages, with a strong focus on interactivity and hands-on experimentation. Wain notes, “mathematics as a theoretical thing with no concrete side to it is what can kill it off, I think. … Having things you can actually do is really important.”

For additional details see this New Scientist article, from which the above notes were excerpted in part.

As the Crafoord Prize website . . . → Read More: Jean Bourgain and Terence Tao receive Crafoord Prize in mathematics]]> The Royal Swedish Academy of Sciences has awarded the 2012 Crafoord Prize to Jean Bourgain (Institute for Advanced Study, Princeton, USA) and Terence Tao (U.C. Los Angeles) “for their brilliant and groundbreaking work in harmonic analysis, partial differential equations, ergodic theory, number theory, combinatorics, functional analysis and theoretical computer science”.

As the Crafoord Prize website explains,

This year´s Crafoord Prize Laureates have solved an impressive number of important problems in mathematics. Their deep mathematical erudition and exceptional problem-solving ability have enabled them to discover many new and fruitful connections and to make fundamental contributions to current research in several branches of mathematics.

On their own and jointly with others, Jean Bourgain and Terence Tao have made important contributions to many fields of mathematics — from number theory to the theory of non-linear waves. The majority of their most fundamental results are in the field of mathematical analysis. They have developed and used the toolbox of analysis in groundbreaking and surprising ways. Their ability to change perspective and view problems from new angles has led to many remarkable insights, attracting a great deal of attention among researchers worldwide.

Bourgain and Tao will receive an award of SEK 4,000,000 (approximately USD 587,752) in a ceremony to be held in Lund, Sweden on 15 May 2012 hosted by the King and Queen of Sweden.

This piece briefly mentions the history of positional decimal arithmetic, from its original discovery by . . . → Read More: Magic numbers]]> The Conversation, an online forum from the Australian academic research community and aimed at the interested public, has featured an essay written by the present bloggers. Entitled “Magic numbers: the beauty of decimal notation,” it is available here: Conversation article.

This piece briefly mentions the history of positional decimal arithmetic, from its original discovery by unknown Indian mathematicians approximately 2000 years ago, to its modern incarnation (at least in binary) in computers. The article then speculates how history may have changed if either arithmetic had been discovered earlier, or it had been communicated to Greek mathematicians such as Archimedes.

It is based on an earlier blog by the present authors, available here: Math Drudge blog. This in turn has been cited by NPR in a discussion of the current  economy.