Higgs discovery underscores effectiveness of mathematical theory

Physicists working at the Large Hadron Collider (LHC) at the CERN facility on the French-Swiss border today confirmed what many have suspected over the past few months — they have discovered a new subatomic particle that appears to be the long-sought Higgs boson, which is widely regarded as the key to why some elementary particles have mass, and thus why a universe with matter (and us) exists at all.

With the words “I think we have it,” director Rolf-Dieter Heuer signaled the longest (and most expensive!) search in the history of science. While more work needs to be done, the particles mass at 125.3 billion electron volts, is very much in line with theoretical predictions nearly 50 years ago.

The Higgs boson is named for a prediction in 1964 by six physicists, working in three independent groups: Peter Higgs of the University of Edinburgh, Tom Kibble of Imperial College in London; Carl Hagen of the University of Rochester in New York; Dr. Guralnik of Brown University in Rhode Island; and Francois Englert and Robert Brout of the Universite Libre de Bruxelles.

Brian Greene, the well-known physicist from Columbia University in New York city, speaking before the announcement, confessed that “Everything I’ve ever done, directly or indirectly, has something to do with a Higgs-like field.” He added that the discovery of the Higgs boson is the latest reminder that the universe can be well understood through mathematics.

“It makes you feel good as a theorist,” Greene continued, “Math really does provide a window on reality.”

The discovery certainly underscores the importance and unreasonable efficacy of modern mathematics. It is truly remarkable that mathematical theorems devised and proven so many years ago now been so strikingly confirmed. And it points to even more significant discoveries in the future.

Some additional details of the discovery, and its impact on the future of mathematical physics, can be had from excellent articles in the Washington Post and the New York Times, from which some of the above quotes and comments were taken.

Of related interest is a recent book by E. Brian Davies, who surveys the landscape of philosophy of science and mathematics, pointing out that “There is no way of proving that this confidence [in mathematics] is justified, but we have no choice but to rely provisionally on hard-won insights in every other sphere of investigation, and mathematics is no different.” Additional details are available in a Math Drudge blog.

The present bloggers wish to also mention a technical paper they have written that emphasizes applications of the methods of experimental mathematics, notably high-precision arithmetic computations, in mathematical physics and dynamics:

David H. Bailey, Roberto Barrio, and Jonathan M. Borwein, “High precision computation: Mathematical physics and dynamics,” Applied Mathematics and Computation, 2012, http://dx.doi.org/10.1016/j.amc.2012.03.087.  Their discussion touches on the uses of very high precision computation in particle physics settings such as at the LHC.  An online preprint copy is available here.

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