And more sophisticated incarnations have allowed some physicists to venture further into the murky waters of quantum field theory, and recently string theory. A proto-version of the technique obtained exact results in quantum mechanics, which limits itself to the behavior of particles. The resurgence community is small but has made steady progress over the years. “Indeed, it works very beautifully” in many cases, said Marco Serone, a physicist who studies this strategy, which goes by the name of “resurgence.” “At some point this process ends, and what you have in front of your eyes is the exact solution to your original problem.”
If one seeks absolute precision, textbook quantum theory breaks down and yields infinite answers - nonsensical results many physicists consider to be mathematical trash.īy studying Écalle’s vintage textbooks, physicists are coming to suspect that these infinite answers contain countless treasures, and that, with sufficient effort, the mathematical tools he developed should let them take any infinity and dig out a finite and faultless answer to any quantum question. But these predictions, precise though they may be, are approximations. In that time, physicists have learned to make breathtakingly accurate predictions about the subatomic world. His visionary mathematics might be just what’s needed to overcome a profound conceptual embarrassment - one that physicists have been more or less ignoring for the past 70 years. He’s one of these visionary mathematicians.” “If you have a look at this for the first time and you don’t read it very carefully, you could think it’s a crackpot writing some crazy things,” said Marcos Mariño, a mathematical physicist at the University of Geneva who keeps what he calls the “historical documents” on his bookshelf and uses tools developed by Écalle daily. Odd-sounding terms like “trans-series,” “analyzable germs,” “alien derivations” and “accelero-summation” abound. The trilogy’s 1,110 pages brim with original mathematical objects and bizarre coinages. The mathematics itself poses another barrier. The text is also written in French, an inconvenience for researchers in the English-speaking world. Oversize mathematical symbols scrawled in thick black ink frequently interrupt the neatly typed sentences. The few physical copies that exist of Jean Écalle’s magnum opus look like little more than glorified photocopies. But physicists can be forgiven for overlooking the potentially transformative ideas within, as the volumes appear simultaneously amateurish and intimidating. The secret to fixing a fatal flaw at the heart of quantum theory may lie in three obscure textbooks from the 1980s.
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