Professor Stephen Hawking, 68, is a theoretical physicist and cosmologist. He studied physics at Oxford, went on to do research at Cambridge and was the Lucasian professor of mathematics at Cambridge for 30 years. His books include A Brief History Of Time (1988), The Universe In A Nutshell (2001) and The Grand Design, published this month. Professor Brian Cox, 42, is a physicist and broadcaster. While studying at Manchester University, where he is now a research fellow, he joined the pop group D:Ream, best known for the Labour 1997 election anthem Things Can Only Get Better. He is a researcher on the Large Hadron Collider and this March presented Wonders Of The Solar System on BBC2. The accompanying book is out next month.

What is the one bit of science from your field that you think everyone should know?

Stephen Hawking: Science can explain the universe without the need for a Creator.

Brian Cox: That's a wonderfully provocative sentence, actually. A beautiful answer. It's interesting, because you have previously used the word God in a similar way, in my view, to Einstein. I am thinking of phrases like "knowing the mind of God", which you used in A Brief History Of Time. In my opinion, Einstein was using the word God as a shorthand to convey the majesty and beauty of the laws of physics, and did not intend this to be taken as a sign that he subscribed to a particular religious doctrine. Is this the sense in which you have used the term before, and are you trying to clear up any misunderstandings caused by your previous use of the word "God", or have I read too much into your answer?

SH: In A Brief History Of Time I used the word "God" like Einstein did as a shorthand for the laws of physics. However, this is not what most people mean by God, so I have decided not to use the term. The laws of physics can explain the universe without the need for a God.

BC: As for my answer, I think everyone should know a few basic facts about the universe. It began 13.7 billion years ago; our sun and solar system formed just under five billion years ago; there are 200 billion stars in our Milky Way galaxy, and 100 billion galaxies in the observable universe. These are wonderful discoveries, and it's quite astonishing we've been able to find these things out from our vantage point on our tiny Earth.

Where and when do you do your best thinking?

SH: It can be anywhere I have time to think. I'm never any good in the morning. It is only after four in the afternoon that I get going.

BC: I say that actually, and my wife thinks it's an affectation, I just don't want to get out of bed. I don't think at any particular time of day or night, or in any particular place. If I have the time and I'm not totally overwhelmed with things to do, then my mind constantly and gently chews over problems and often an answer or idea will pop into my head almost at random. Having the space to think is a genuine luxury, and vitally important if we want people to be creative in any job.

What distracts you?

SH: People asking me questions. I can concentrate and ignore everything else.

BC: For me, it's TV. If I had more willpower, I would limit the amount I watch. When I was studying for my PhD in Hamburg, I only had German channels, and watched them very little. This was probably the most productive time of my life.

What problem do you hope scientists will have solved by the end of the century?

SH: Nuclear fusion. It would provide an inexhaustible supply of energy without pollution or global warming.

BC: I share that view, that the provision of clean energy is of overwhelming importance. What frustrates me is that we know how to do it as physicists, how it works. It is an engineering solution that is within our grasp. I don't understand why we don't seem to want it enough at the moment. As a society, do you think we invest enough in scientific education and research?

SH: I don't think we invest enough. They are why we are not still in the Middle Ages. Many badly needed goals, like fusion and cancer cure, would be achieved much sooner if we invested more.

BC: I think the most important practical problem, which may be more of an engineering challenge than a scientific one, is to build economically viable nuclear fusion power stations. If we haven't dealt with our world's increasing appetite for energy by the end of this century, I think we will be in very deep trouble indeed. In physics, understanding why gravity is such an astonishingly weak force compared with the other three forces of nature is probably the great challenge. Also, understanding why the universe began in such a highly ordered state.

Can you remember the moment you decided to become a scientist?

SH: My father was a research scientist in tropical medicine so I always assumed I would be a scientist, too. I felt that medicine was too vague and inexact, so I chose physics.

BC: I always wanted to be one – particularly an astronomer. I can't remember wanting to be anything else.

What is the most common misconception about your work?

SH: People think I'm a Simpsons character.

BC: For me, the most common misconception is that particle physics, which is the quest to understand the forces of nature and the building blocks of matter, is a luxury and has no purpose other than to satisfy our curiosity. I understand why people think this about many areas of modern science, but it is a deeply flawed view of how progress happens. The great "useful" scientific discoveries – electricity, penicillin, the structure of atoms, the transistor – have rarely been a response to what governments or societies considered "useful" questions, whatever that meant at the time. History shows us that simply being curious about the universe and allowing ourselves to explore is by far the best way to make discoveries that eventually change everybody's lives.

Which living scientist do you most admire, and why?

SH: There are plenty of dead scientists I admire, but I can't think of any living ones. This is probably because it is only in retrospect that one can see who made the important contributions.

BC: I think that's a very important point. It's like, because you're judged against whether your theories agree with nature, whether what you say measures up against experiment, that means there's a delay in the award of the accolade great. I'd ask whether you think someone like Richard Feynman achieved greatness in his lifetime?

SH: Yes.

BC: The scientist I most admire would be you. You have combined a world class scientific career with a world class career in science communication. This is very difficult to do, but it is vitally important that our great researchers can also be great teachers.

What keeps you awake at night?

SH: If I have questions about the universe on my mind when I go to bed, I can't turn off. I dream equations all night.

BC: Do you remember them?

SH: No, I don't.

BC: I worry about the lack of funding for research in the UK. I think it stems from a misunderstanding about the value to society of our science base and our universities. The university system really is the foundation upon which our economy rests – not to mention an industry that is immensely successful and in which the UK is genuinely world class. While all research and development in our economy doesn't come from universities, all the researchers do. This is something the government would do very well to remember when it comes to the spending review next month.

What has been the most exciting moment of your career?

SH: When I visited Antarctica in 1997. The Chilean air force flew a group of theoretical physicists to their base on King George Island off the Antarctic peninsula. My wheelchair did have snow chains, but they took me round on a snowmobile.

BC: I think my early research career, when I actually sat down for days and months and analysed data from the Hera particle accelerator in Hamburg, was the most exciting time for me. I spent three or four years working on data 24/7, and there is nothing quite like it. Becoming successful as a science communicator is a double-edged sword in that, necessarily, your time for research diminishes. This is why I admire people like you who get the balance right – I aspire to do the same!

Who is your favourite fictional scientist?

SH: My mother used to tell me and my sisters stories she made up about a Professor Henbrain, who had all sorts of weird inventions. I'm trying to persuade her to write down some of these and other stories.

BC: I thought Jodie Foster's character Ellie Arroway in Contact was superbly written and wonderfully acted. But she was created by Carl Sagan after all.

What is the most difficult ethical dilemma facing science today?

SH: It is over genetic engineering. It should soon be possible dramatically to increase the intelligence and life span of a few individuals. They and their offspring could become a master race. Evolution pays no regard to social justice. It was not fair on the Neanderthals they were replaced by modern humans.

BC: I think one of the great challenges for the scientific community is how to deal with arguments from people with genuinely held views that are demonstrably wrong and potentially damaging. I'm thinking of issues like the vaccination of children or the imperative to reduce greenhouse gas emissions. The science is very clear on these issues, and science really is the best guide we have to facing global challenges. The dilemma is how to convince quite vocal minorities that a rational and scientific approach is no threat to their political or religious beliefs – it's just the best approach. You see the problem immediately, of course, because this sounds rather arrogant and nobody thinks they are irrational! But we have to achieve the right outcomes in certain important areas.

Another dilemma we face at the moment is how to lobby against possible dramatic funding cuts for science in the autumn. I strongly believe that a healthy science base is necessary for a healthy economy and vital for our society, but that can feel like special pleading in hard times. What do you think would be the consequences for the UK if we were forced to pull out of a major project like Cern because of science budget cuts?

SH: It would discourage and damage the academic community whose task is to train the nation's next generation of scientists.

BC: How can we make the case for an increase in spending in areas such as physics and cosmology?

SH: Maintaining high standards in physics and mathematics is important for British industry. We don't have large natural resources. Our success depends on technical ability.. • The Grand Design, by Stephen Hawking, is published by Bantam Press at £18.99. Wonders Of The Solar System, by Brian Cox, is published by Collins at £20. Both titles can be ordered from the Guardian Bookshop.