14 DAY TRIAL // The Kervaire invariant problem is one of the long-standing mysteries of topological science, and many researchers alive today didn't even imagine that the solution could be found within their lifetime. The formula managed to keep its secrets for more than 45 years, but now a team of three mathematical researchers, from the prestigious US universities, have succeeded in cracking it.
The Kervaire is “one of the major outstanding problems in algebraic and geometric topology,” Nick Kuhn, a fellow mathematician at the University of Virginia, in Charlottesville, explains. “Most people thought it would never be solved in their lifetime. Many people have thought they've solved it but have been wrong,” algebraic topologist Mark Hovey, who is also an expert at the Wesleyan University, in Middletown, Connecticut, adds.
“The solution to this problem seems to indicate new and deep connections between topology on the one hand, and algebra and number theory on the other. The exploration of these new connections will enrich the subject for years to come,” Allen Hatcher, who is also a mathematician at the Cornell University, in Ithaca, New York, argues. These three experts have not been involved in the study.
The mathematicians who solved the 45-year-old problem, Mike Hopkins, of Harvard University, Douglas Ravenel, of the University of Rochester in New York, and Mike Hill, of the University of Virginia in Charlottesville, made their solution public on April 21st, at a conference held in Edinburgh, UK. “In some respects, the solution of the Kervaire invariant problem is like the proof of Fermat's last theorem in the 1990s. The importance lies with the new tools, techniques and insights that were developed to get the solution,” Hatcher says, as quoted by Nature.
The experts went as far as saying that their calculations, which successfully cracked the Kervaire invariant, could also be used in quantum physics, as well as in brane cosmology. The latter field of research is a new area of science, which has been created to explain some of the things that are not fully understood by using the Big Bang and the inflationary Universe theories.