The man who took on Stephen Hawking's prestigious post at Cambridge University has won $1.5m (£918,000) for pioneering work on string theory, an idea that describes the world as tiny strings in eleven-dimensional space-time.

Michael Green, who became the Lucasian professor of mathematics at Cambridge when Hawking stepped down in 2009, shares the $3m Fundamental Physics prize with fellow theorist John Schwarz at California Institute of Technology.

The award, worth more than double the $1.2m Nobel prize, was set up last year by Yuri Milner, a Russian investor and self-described "failed physicist" who made a billion from investments in Facebook, Twitter and other internet companies.

The prize winners were announced on Thursday night at a glitzy ceremony hosted by Kevin Spacey in Hangar One, an enormous former airship station managed by Nasa in Silicon Valley. It is the second of Milner's prizes to reward the Cambridge lab: Hawking won $3m last year for a lifetime of achievements.

The prize is one of a string of annual awards set up by Milner and other Silicon Valley stars to raise the profile of scientists and put them on a par – in some sense, at least – with film and sports celebrities. Earlier this year, Milner joined forces with Mark Zuckerberg, founder of Facebook, and Sergey Brin, who co-founded Google, to launch the $3m Breakthrough prize in life sciences. At Thursday's ceremony, Milner and Zuckerberg unveiled yet another $3m prize: this time for advances in mathematics.

Zuckerberg, 29, who dropped out of Harvard and became one of the world's youngest self-made billionaires, said he hoped the new prize would allow top mathematicians to focus their energies on their work, raise the profile of mathematics and encourage children to see it as a great career to pursue. The first winners are expected to be announced next year.

"Mathematics is the language the universe is written in. Pythagoras said 'All things are numbers', and anyone who's ever written code has probably reached the same conclusion," Zuckerberg said.

"The Breakthrough prize is about recognizing the heroes in our society in physics, life sciences and now math. There is nothing more fundamental than math. The greatest minds in mathematics should be celebrated," he added.

Milner wants the prizes to encourage people to think more about the biggest questions in life. "If you take the largest scales possible, there are a number of scientists, individuals, who operate at that scale, they think about the whole universe. I think that we focus too much on small scales as human beings, and not enough at larger scales. That's really the problem we're trying to address here," he told the Guardian. "We have responsibilities beyond our own little problems. We have a much greater responsibility, to figure out how the world works, and pass this knowledge on to future generations."

Green said he was "delighted and flattered" to have won. "I feel really fortunate to have been able to contribute, along with many others, to developments in string theory, which has provided such an inspiring succession of novel insights into fundamental physics and mathematics," he said.

Six other researchers, each named a winner of the life sciences prize on Thursday, saw $3m land in their bank accounts. Mahlon DeLong at Emory University discovered neural circuits that malfunction in Parkinson's disease. Bob Langer at MIT won for his work on biomaterials and systems to release drugs into the body.

"It's wonderful that the Breakthrough prize is recognising science, particularly life sciences, which is making the world a better place. I feel tremendously humbled and appreciative to be among those to receive this remarkable award," he said.

Another winner, Michael Hall at Basel University in Switzerland, discovered how the immunosuppresant drug rapamycin controls cell growth. "My immediate reaction was disbelief," he said. "Milner and the other creators of the prize are visionaries, as the general public needs to appreciate the importance of basic science. I hope it works. Where would, and will, we be without science?" Hall said he had not thought about how to spend the money. "My daughters want me to buy a Harley," he said.

The new prizes have not won universal support in the academic community. Peter Woit, a mathematician at Columbia University in New York, said the physics prize should not be awarded for work on string theory because the theory does not seem to work.

"Heavily rewarding failure is not good for science. If someone is writing huge cheques to everyone involved, they'll say this is great, rather than face up to the fact that it isn't working," he said.

One prominent physicist who did not wish to be named said the huge sums of money could be used better: "The great philanthropists of the 19th and 20th centuries, like the Rockefellers and the Carnegies, did not create prizes – they created universities and research institutes that have enabled thousands of scientists to make great breakthroughs over the succeeding decades.

"By contrast, giving a prize has a negligible effect on the progress of science. A few already well-recognised people get enriched, but there is little value added in terms of the progress of science compared to the multiplier effect of creating new institutions for scientific research."

Not all of the prize money dished out to the winners stays with the winners. Some have set up funds to help struggling students, or established their own prizes to award the best young researchers in their labs.

Three New York-based scientists – Charles Sawyers, Cornelia Bargmann and Lewis C Cantley – each won the $3m life sciences prizes last time around. They have each contributed $100,000, which will be added to by their institutions, to fund annual prizes for gifted post-docs. Sawyers said the prize value had yet to be confirmed but would be "eye-popping".

The scientists who led the Large Hadron Collider project shared one of the $3m physics prizes last year. Fabiola Gianotti and Peter Jenni on the Atlas team at Cern donated their entire $1.5m share to humanitarian and educational causes, including a PhD grant scheme. Joe Incandela on the CMS team at Cern used all of his share to fund young researcher prizes and a scholarship programme. Jim Virdee, another Cern researcher, used his to support science teachers in Africa.

Others winners of the latest life sciences prize are James Allison at the University of Texas, who pioneered immunotherapy for cancer; Alexander Varshavsky at the California Institute of Technology for work on protein degradation; and Richard Lifton at Yale University, who discovered biological mechanisms that cause hypertension.

Thursday's ceremony will be shown on the Science Channel on 27 January 2014.