Leading scientists gather at Cambridge University to pay tribute to Hawking and take stock of our understanding of the universe

"Bold", "provocative", "relentless", "witty" and "an inspiration" – tributes to Prof Stephen Hawking have not been hard to come by at a gathering of more than a hundred of the world's top cosmologists.

The planet's most famous living physicist turns 70 on Sunday and scientists began to assemble in his honour at Cambridge University on Thursday and Friday to raise a toast. They are also here to take stock of the scientific fields to which he has applied his considerable brain power during his career.

The meeting, entitled "The State of the Universe", is charting the theoretical frontiers of our understanding of black holes, cosmology and fundamental physics. But the event, which culminates in a public symposium that Hawking will address on Sunday, is also a tribute to a career that many feared would be short-lived after he was diagnosed with motor neurone disease at the age of 21.

Hawking has worked on the inflation of the early universe, a quantum theory of gravity, and famously showed that black holes emit radiation and so slowly disappear. His fame has also brought his field to a vast audience outside academic circles. A Brief History of Time has reportedly sold over 10m copies worldwide and Hawking has made guest appearances on The Simpsons and Star Trek.

"He's a very witty, humourous guy. It's amazing, under the circumstances, how he keeps his spirits up and brightens the atmosphere," said Nobel laureate and long time friend Frank Wilczek at the Massachusetts Institute of Technology. "It's an inspiration that he's been able to control his world and make genuine scientific contributions under very difficult situations and keep up his good work. It's a fantastic human story."

Prof Hawking himself was too unwell to attend on Thursday but Peter Haynes, head of the department of applied mathematics and theoretical physics at the University of Cambridge, warned the illustrious attendees to be on their best behaviour because "Stephen was watching online".

Gary Gibbons, a professor of theoretical physics at the University of Cambridge and former PhD student of Hawking's in the early 1970s who has worked with him for several decades, said the aim of the symposium was to "summarise where we are now and where we go in future. Are the ideas we've had supported by observation? If theoretical conjectures have been made have they been proved or disproved? The particular topics that we're discussing here are very close to Prof Hawking's heart and, in many cases, he's made conjectures or worked in these subjects so it is an assessment of where we stand today."

Hawking has "a wry sense of humour", he added. "You can always tell when he's cracking a joke because his face will light up. He likes to be provocative, what he will say will provoke people to respond."

Prof Hawking's most compelling trait, said Gibbons, was his "imagination and his desire to get to the bottom of things. In physics, that's the thing that will really characterise you – he makes bold conjectures, some of which have turned out to be correct, and he's relentless."

Wilczek opened the scientific part of the symposium by presenting one of his own most recent theoretical concepts, known as time crystals. Everyday crystals, such as diamond or ice, are periodic arrangements of atoms and usually exist when the matter in question is in its lowest energy state.

Albert Einstein's theories of relativity, however, show that time can be thought of as another dimension of space. Wilczek has combined these ideas to investigate whether matter could therefore have periodic structures in time, just as it does in space. "At first I thought it would be very easy to arrange, then I thought it was impossible but now I think that it's barely possible, which makes it interesting," he said.

Wilczek said that he had had some results and was about to submit a research paper on his idea for peer review. "I don't know where this is going to lead but I've landed on a new continent and there's a big world of things to explore."

Further discussions on the nature of symmetry (this time in subatomic particles) and the latest mathematical thinking behind the properties of black holes followed Wilczek. As a gale threatened to blow down the walls of the Centre for Mathematical Sciences in Cambridge, presentations flew by in a whirl of differential equations and charts describing everything from supergravity to non-Gaussian distributions to set theory.

Sandwiched between the algebra were probing questions from the expert audience about the finer points of each speaker's work, whether on black holes or the expansion of the universe after the big bang.

David Spergel of Princeton University presented the latest "baby picture of the universe", results of the WMAP project to analyse the microwave background radiation of the universe, an afterglow of the state of our cosmos just a few hundred thousand years after the big bang.

Spergel, like many of the day's speakers, ended his presentation of high-end cosmology with a tongue-in-cheek slide wishing Prof Hawking a happy birthday.

The scientific meeting will continue until Saturday evening, with scheduled talks by a galaxy of the stars of theoretical cosmology. The bill includes string theorist Michael Green, Hawking's successor in the Lucasian chair of mathematics at Cambridge; Neil Turok, director of the Perimeter Institute in Canada; and Andrei Linde of Stanford University, one of the scientists who formulated inflation theory, which says that, minutes after the big bang, the rate of expansion of the universe jumped to gargantuan levels for a very short period.

On Sunday, the birthday celebrations go public, with talks on cosmology by the Astronomer Royal Martin Rees, Nobel laureate Saul Perlmutter, one of the discoverers of dark energy, and long-time Hawking collaborator Kip Thorne. The day will be topped off by a rare public lecture by Hawking himself, entitled "A Brief History of Mine".