The most lucrative prize in science has been awarded to three researchers for a landmark theory that married particle physics with Einstein’s description of gravity, and proposed a candidate for the mysterious cosmic goo known as dark matter to boot.

Daniel Freedman, Peter van Nieuwenhuizen and Sergio Ferrara, from the US, the Netherlands and Italy respectively, developed “supergravity” in the 1970s, a mathematical feat that wrapped Einstein’s general relativity into a speculative theory of all the known particles in the universe.

The work has been credited as a driving force in string theory, physicists’ most popular model of reality, in which tiny, vibrating strings of energy moving through 10 or 11-dimensional spacetime form the fundamental fabric of nature.

In honour of their achievement, the physicists share the $3m (£2.5m) Special Breakthrough prize in fundamental physics, an award founded by the internet billionaire Yuri Milner and backed by Silicon Valley entrepreneurs such as Sergei Brin and Mark Zuckerberg. The trio will receive the prize at a glitzy ceremony nicknamed “the Oscars of science” in California in November.

Freedman, 80, had just got home from a gym class when a physicist on the prize committee called with the news. “It was a complete surprise. I put down the phone and cried,” he told the Guardian. So far, the MIT and Stanford University scientist has only decided what he won’t do with the windfall: “I’m not going to Las Vegas,” he said.

Ferrara, 74, who works at Cern near Geneva, was heading for bed when he got the call. “We knew that we did some important work, but we didn’t expect the prize,” he said. “It’s very hard to think you can get it.”

Van Nieuwenhuizen, 80, a physicist at Stony Brook University in New York, was in the kitchen paying bills when he spotted an email from the physicist Ed Witten, chair of the selection committee, asking for his number. “I was afraid he might have a difficult question about supergravity,” Van Nieuwenhuizen said. “I was totally speechless. It is outside any size of money I have ever encountered. I like sitting in my office doing equations. That’s my life. It’s a number I don’t know how to handle.”

The trio met in the 1970s when particle physics faced a particular problem. Decades of work had led to the so-called Standard Model, a quantum theory that described how the building blocks of matter, such as electrons and quarks (known collectively as fermions), worked with force particles such as photons and gluons (known as bosons).

But the model was incomplete. It said nothing about gravity, nor the weird dark matter that appeared to clump around galaxies like invisible goo. When physicists tried to combine the Standard Model and gravity they repeatedly met with failure: the calculations turned up infinities that made a nonsense of the mathematics.

But around the same time, physicists developed another theory called supersymmetry. The elegant, if speculative, idea postulated that all known particles had an unseen, heavy partner. The partners of fermions were bosons and vice versa.

Freedman, Ferrara and Van Nieuwenhuizen set out to marry gravity with supersymmetry, an arduous task that culminated in Van Nieuwenhuizen sitting up late one night waiting for a powerful computer to churn out results. If the infinities that plagued previous attempts at unification cancelled out, the computer would return 2,000 zeroes, and the theory would be on good footing.

“The computer gave the results in batches and with each new batch I crossed my fingers that it was zero. The first batch was zero, the second batch was zero. And then it was over: all came back as zero,” Van Nieuwenhuizen said. “I wasn’t elated at that point. I was extremely tired and even a little depressed. But over the next few days I realised something very nice had happened.”

The theory, published in 1976, became physicists’ first bridge between the quantum field theory of the Standard Model and Einstein’s theory of gravity, in which mass curves spacetime. In supergravity, the “gravitino”, the unseen partner of the particle said to carry the gravitational force, is a potential constituent of dark matter.

Supergravity has become a powerful mathematical tool and is effectively a low-energy version of string theory. But despite its undeniable value, there is no evidence yet that it exists in nature. Searches for supersymmetric particles at the Large Hadron Collider at Cern have found nothing so far, leading many physicists to go off the theory.

With the next generation of more powerful colliders some decades away, it is not clear when more concrete answers may be found. “We’re going through a very tough time,” Freedman told the Guardian. “I’m not optimistic. I no longer encourage students to go into theoretical particle physics. And happily, they don’t listen to me.”