"No object in the equations makes any sense classically," said Jeremy Quastel, a professor of mathematics at the University of Toronto.
For decades, mathematicians strove for a rigorous method of operating on distributions in order to solve SPDEs but made little headway.
There are even published books that present incorrect procedures for doing so, Quastel
said, "which is not something you would normally have in mathematics."
Hairer's big idea came to him in October 2011 while he
was walking from the common room of the Warwick math department back to his
office and thinking about nothing in particular.
suddenly realized that he
could tame the distributions in SPDEs using an approach modeled on the mathematical properties of "wavelets" - brief, heartbeatlike oscillations that encode information in JPEG and MP3 files.
"There is a worry that it won't have the impact it deserves, not through any fault of Martin's but just because the simplest way that one can deal with this type of problem is just too difficult to be popularizable," said Quastel
, who joked to colleagues that the theory must have been a dispatch from aliens.
The power of regularity structures is easily understood, but when Hairer
actually delves into how the theory works in talks and papers, Quastel
said, "he loses his audience a little bit."