Facebook co-founder Mark Zuckerberg figures there could be a formula that explains how people think.

During a wide-ranging online question-and-answer session on his Facebook page Tuesday, Zuckerberg told famed physicist Stephen Hawking he would like to find that equation.

"I'm most interested in questions about people," Zuckerberg said in a written chat forum response to Hawking asking what big questions in science he would like to know the answers to.

Zuckerberg responded with a list that included how the brain works and immortality.

"I'm also curious about whether there is a fundamental mathematical law underlying human social relationships that governs the balance of who and what we all care about," Zuckerberg added.

"I bet there is."

Hollywood powerhouse and fitness champion Arnold Schwarzenegger weighed in with a question about Zuckerberg's exercise routine.

"You've got to be one of the busiest guys on the planet, and younger generations can probably relate to you more than they can the Pope - so tell me how you find time to train and what is your regimen like?" the one-time California governor asked Zuckerberg.

Zuckerberg said he works out at least three times weekly, usually in the mornings.

He added that he takes his dog running whenever he can "which has the added bonus of being hilarious because that is basically like seeing a mop run."

The online question-and-answer session drew so many visitors that it stumbled technically, going offline for a few minutes due to what Facebook diagnosed to be "an overload of likes."

When asked his take on happiness, Zuckerberg said it was doing things that he believes in with people he loves.

"I think lots of people confuse happiness with fun," Zuckerberg said.

"I don't believe it is possible to have fun every day. But I do believe it is possible to do something meaningful that helps people every day."

While sharing thoughts on the future of Facebook, Zuckerberg said that immersive experiences such as virtual reality will become mainstream and that people will eventually able to share what they are sensing or feeling.

"One day, I believe we'll be able to send full rich thoughts to each other directly using technology," Zuckerberg said.

"You'll just be able to think of something and your friends will immediately be able to experience it too if you'd like."