BERNARD CARR

Professor of mathematics and astronomy, Queen Mary, University of London. Stephen Hawking's PhD student 1972-75

Stephen's discovery in 1974 that black holes emit thermal radiation due to quantum effects was one of the most important results in 20th-century physics. This is because it unified three previously disparate areas of physics – quantum theory, general relativity and thermodynamics. Like all such unifying ideas, it is so beautiful that it almost has to be true, even though it has still not been experimentally confirmed. The renowned physicist John Wheeler once told me that just talking about it was like "rolling candy on the tongue".

At the time of the discovery, I was working with him as a PhD student in Cambridge and I count myself as very fortunate to have had a ringside seat during these developments. It also enabled me to be one of the first people to study the cosmological consequences of the effect and thereby make my own small contribution to the subject.

I was one of Stephen's first PhD students and people often ask me what it was like having him as a supervisor. He was not so famous in those days but his brilliance was already clear to his peers and I found it rather daunting when, on becoming his research student, I was informed by one of my tutors that he was the brightest person in the department. Students are probably always in awe of their supervisors but with Stephen the awe was even greater. Indeed, on matters of physics, I always regarded him as an oracle, just a few words from him yielding insights that would have taken weeks to work out on my own.

However, Stephen is only human and not all encounters led to illumination. Once, while sharing an office with him at Caltech [California Institute of Technology], I asked a question about something that was puzzling me. He thought about it silently for several minutes and I was quite impressed with myself for asking something that Stephen couldn't answer immediately. His eyes then closed and I was even more impressed with myself because he was clearly having to think about it very deeply. Only after some time did it become clear that he had fallen asleep! Nowadays I also sometimes fall asleep while talking to students, so I recall this incident with amusement.

The other human side of Stephen is that he does occasionally get annoyed. One of the myths put around is that he sometimes vents his frustration by running over the toes of students. This never happened to me – he didn't have a motorised wheelchair in those days – but I well recall one occasion when I made a remark in the maths common room at tea-time that showed that I had misunderstood what he'd been saying. Stephen screamed "No" so loudly that his wheelchair shot back halfway across the room under the recoil. I was most impressed that a single word from him could have such dramatic consequences.

My relationship with Stephen was not the usual type of supervisor-student relationship. In those days, before he had his entourage of nurses and assistants, students would necessarily have to help him in various ways on account of his disability. This was not an arduous task but it did mean that one's relationship with him became quite intimate. I shared an office with him, lived with his family for a year in California, and accompanied him as he travelled around the world, giving talks and collecting medals.

As an impressionable young student, it was a tremendous thrill to meet so many celebrities and renowned physicists. One of the great excitements of visiting Caltech, where Stephen was a Fairchild scholar in 1975, was meeting the brilliant physicist Richard Feynman, who was regarded almost like a god there. He used to visit our office quite often and, since Stephen's voice was already quite weak, I would act as interpreter.

I also travelled around China with him in 1985. During a long train journey, I recall reading the first draft of a popular book he was writing at the time. My initial impression that it would never sell proved inaccurate since it eventually turned into A Brief History of Time!

Shortly after his return from China he fell seriously ill with pneumonia and lost his voice. Ever since, he has had to communicate through his computer, which is painfully slow, so it's ironic that he has still managed to become one of the great science popularisers of our age. He has even written books for children with his daughter, Lucy, and it is sobering to reflect that a contribution I wrote for their most recent one has probably been read by more people than any of my scientific articles. His inspiration of public interest in some of the deepest questions of physics is certainly one reason why he has become such an iconic figure.

MARTIN REES

Astronomer royal and master of Trinity College, Cambridge. Like Hawking, he studied under Dennis Sciama in the 1960s

I first met Stephen in 1964. I was in my first week as a Cambridge graduate student. He was two years ahead of me in his studies – but already unsteady on his feet and speaking with difficulty. I learned that he might not live long enough even to finish his PhD.

Astronomers are used to large numbers. But few could be as huge as the odds I'd have given, back then, against him reaching his 70th birthday – after astonishing achievements that have made him the most famous living scientist.

In his first few years of research, he came up with a succession of insights into the nature of black holes (then a very new idea) and how our universe began. These earned him election to the Royal Society at the exceptionally early age of 32.

He was by then so frail that we guessed he could scale no further heights. But this was still just the beginning. He then worked, as I did, at the Institute of Astronomy in Cambridge. I would often push his wheelchair into his office. He would sit motionless for hours reading a book on quantum field theory – not a subject that he had hitherto engaged with. He couldn't even turn the pages without help. I wondered what was going through his mind, and if his powers were failing. But within a year he had his greatest "eureka moment" – encapsulated in an equation that he wants on his gravestone. He discovered a profound and unexpected link between gravity and quantum theory that has helped set the agenda for fundamental physics ever since.

He has probably done as much as anyone else since Einstein to extend our grasp of gravity, space and time. And he continues to write technical papers and attend premier conferences – doubly remarkable in a subject where few healthy researchers stay so long at the frontiers.

But the second half of Stephen's life has been a crescendo of fame and celebrity. When A Brief History of Time appeared, the printers made some errors (a picture was upside down), and the publishers tried to recall the stock. To their amazement, all copies had already been sold. This was the first inkling that the book was destined for runaway success. The concept of an imprisoned mind roaming the cosmos grabbed people's imagination. Had he achieved equal distinction in, say, genetics rather than cosmology, his triumph of intellect against adversity probably wouldn't have achieved such worldwide acclaim.

After his disease was diagnosed [amyotrophic lateral sclerosis] Stephen's expectations dropped to zero. He says that everything that happened since then was a bonus.

And what a triumph his life has been. His name will live in the annals of science; millions around the world have had their cosmic horizons widened by his books and TV appearances; and even more have been inspired by a unique human achievement against all the odds.

RAYMOND LAFLAMME

Executive director, Institute for Quantum Computing, University of Waterloo, Canada. In 1988 he earned his PhD at Cambridge under the direction of Hawking

I recently gave Stephen a boomerang. That might seem like a peculiar gift to give the world's most famous scientist but Stephen instantly understood its significance. He grinned when he saw it, as I hoped he would. He grinned the same wise, slightly mischievous grin that I frequently sought – and was occasionally rewarded with – when I was a nervous young doctoral student under his supervision at Cambridge 27 years earlier.

It was during that doctoral year that Stephen suggested I tackle an idea inspired by his "no-boundary proposal" about the origins of the universe. Specifically, he assigned me to mathematically confirm his theory that time would reverse in a contracting universe. I was 24 and ready for a challenge, so I got to work. But there was a problem: try as I might, I couldn't prove Stephen's theory. In fact, I could only prove it wrong.

My maths seemed airtight, but Stephen needed convincing. Many afternoons were spent with me at a blackboard, nervously writing out my equations for Stephen, who insisted I had oversimplified this or failed to consider that. Finally, after countless blackboard sessions, and with the help of postdoctoral fellow Don Page, I convinced Stephen that time indeed marches eternally forward, even when the universe itself does an about-face.

Little did I know this cosmological titbit would find its way into a book that would eventually sell 10m copies and make Stephen a scientific superstar, A Brief History of Time. Stephen personalised my copy of the book with a printed note (he was unable to write longhand by then) inside the front cover. It reads: "To Raymond, who showed me that the arrow of time is not a boomerang. Thank you for all your help. Stephen." I love that little dedication. It so nicely conveys the wit and warmth Stephen always exudes.

In 2010, Stephen spent a summer in Waterloo, Canada. I invited him to drop by the institute for a look around, and he happily obliged. He spent the day visiting labs, meeting researchers and, I think, learning some new things about quantum information science. That's when I gave him the boomerang.

It was an inside joke, but it was also something more. It was a way of saying that, although time is indeed an arrow, it does have a way of bringing our lives – and the people most important to us – full circle.

GEORGE ELLIS

Emeritus professor in the department of mathematics and applied mathematics at the University of Cape Town, South Africa. He co-authored The Large Scale Structure of Space-Time (1973) with Hawking

Stephen's life has been one of extraordinary achievement. His success has been because of the combination of huge technical ability and imagination, an inquiring mind always searching for answers to important issues, and extraordinary determination and focus.

I was one of his first collaborators, working with him on the issue of whether there had been a start to the universe or not. After some initial work we did together on special universe models, Stephen adapted the highly innovative work of Roger Penrose to prove a theorem able to show the universe did indeed have a start. We then jointly showed the conditions of this theorem are supported by astronomical observations: according to Einstein's theory of gravitation, there was a beginning to existence.

This technical tour de force was followed by his unique work showing black holes give off Hawking radiation. This result, based in a combination of quantum theory, gravity and thermodynamics, has been hugely influential, particularly because it was unexpected. This will always stand as a major achievement, uniquely his own.

He has made many other contributions to cosmology in his own inimitable style; like many others, I learned much from his penetrating method of analysis. And of course his scientific success has been achieved in the face of a hugely debilitating physical handicap, which would have destroyed the will of lesser people. I was able to help him with the issues of daily life at the early stages of this disease, pushing his wheelchair from the applied mathematics department to his home in Little St Mary's Lane and to the university centre for lunch. His broad grin and impish sense of humour were always present on these occasions. What a privilege it is to have been part of this epoch in his life.

THOMAS HERTOG

Professor of theoretical physics at the KU Leuven, Belgium. Co-authored a paper on "top down cosmology" while working with Hawking at Cern in 2006

Stephen was my mentor back in the 90s. I had come to Cambridge from Belgium to study theoretical cosmology, and I was delighted he took me on as his PhD student.

Cosmology is one of Stephen's favourite subjects. His goal, as he likes to put it, is to understand "why the universe is the way it is". At the deepest level this requires an understanding of the physical conditions at the time of the big bang.

To make progress on this Stephen, with his students and co-workers in the 80s, developed the subject of quantum cosmology. Roughly speaking, this involves Feynman's "multiple histories" formulation of quantum mechanics applied to the entire universe. In quantum cosmology the big bang is described in terms of a quantum mechanical state. During my years in Cambridge, Stephen introduced me to his programme and we worked together to make more explicit its predictions for the nature of the early universe.

Many years later, when I returned back to Europe after several postdoc years in the US, Stephen and I were drawn together again. We had both been thinking about the role of the observer – us – in quantum cosmology. Together with James Hartle we set out to study the implications of our existence for the predictions of quantum cosmology. This has led to a close collaboration which continues today.

It has been very exciting to work with Stephen. I have often felt that in the intense interaction of our collaboration, especially when different pieces of a puzzle fit together in a consistent picture, the chair and the difficulties with communication recede into insignificance.

I believe Stephen's genius lies in the clarity of his scientific vision. Guided by sharp intuition and insight, together with a consistent focus on the core problems and a certain boldness to discard old ideas he regards as an obstacle to progress, Stephen has produced ideas that have had a profound impact on theoretical cosmology. His quantum cosmology has brought the study of the universe's origin within the realm of the physical sciences, and with this the profound questions its study raises. Even at 70 he remains one of the world's foremost experts in this domain.

FAY DOWKER

Theoretical physicist at Imperial College London. She completed her PhD under Stephen Hawking in 1990

The epic breadth of Stephen's research makes it challenging to summarise. One concept, however, binds his entire oeuvre together: spacetime. Since the work of Einstein, we know that the stage on which the universe acts out its drama is not three-dimensional space but four-dimensional spacetime, and moreover that stage, spacetime itself, is dynamic and plays its own part in the evolving action. Stephen's achievements are such that the very form of our scientific questions about spacetime today has been framed by his discoveries. Stephen's work with Roger Penrose on the singularity theorems proves that general relativity, our current best theory of gravity and spacetime, must break down inside black holes and at the big bang, making it essential to look for a more unified theory of quantum gravity. Stephen's discovery that black holes are hot and emit thermal "Hawking radiation" unifies quantum matter and gravitational black-hole physics with thermodynamics, the science of heat. Since thermal systems are understood in terms of their microscopic constituents, Stephen's discovery immediately raised the question, "What is the microstructure of a black hole, and of spacetime itself?" We have, as yet, not agreed upon an answer, but there is a consensus that no understanding of quantum gravity will be complete without it.

The high regard in which Stephen is held globally and the widely felt appreciation of his contributions to science and society are demonstrated wherever in the world he gives a public lecture: the auditorium is always packed, the atmosphere electric and the applause thunderous. Stephen inspires people with the excitement and importance of pure scientific inquiry, and celebrating his 70th birthday with him gives us a chance to say how much we honour him for it. Happy birthday, Stephen!