His theory starts with cortical columns. Cortical columns are a crucial part of the neocortex, the part of the brain that handles sight, hearing, language and reason. Neuroscientists don’t agree on how the neocortex works.

Mr. Hawkins says cortical columns handle every task in the same way, a sort of computer algorithm that is repeated over and over again. It is a logical approach to the brain for a man who spent decades building new kinds of computing devices.

All he has to do is figure out the algorithm.

A number of neuroscientists like the idea, and some are pursuing similar ideas. They also praise Mr. Hawkins for his willingness to think so broadly. Being a maverick is not easily done in academia and the world of traditional research. But it’s a little easier when you can fund your own work, as Mr. Hawkins has.

Still, some wonder if his self-funded operation, isolated from the rigors of academic interaction, is a quixotic adventure. They have been researching the brain one little piece at a time for a good reason: Piecing how it all works together is a monumental, hard-to-fathom task.

“It is clear we need a better understanding of intelligence,” said Tomaso Poggio, a neuroscientist at the Massachusetts Institute of Technology who introduced Mr. Hawkins and Mr. Hassabis. “But Jeff is doing this the hard way.”

If Mr. Hawkins’s work should pan out, it could help A.I. researchers leapfrog over what exists today. In recent years, the likes of Google, Apple and Amazon have built cars that drive on their own, gadgets that answer questions from across the room and smartphone apps that instantly translate languages.