I meet Prof Hugh Montgomery the day after the heatwave reaches its sticky, stultifying peak, a day when Londoners are red-eyed, over-caffeinated and on a hair trigger. It’s business as usual, however, for Montgomery. With an expansive enthusiasm that cuts through the clammy torpor, he’s fine: he rarely tops five hours a night. “I get up between 4 and 5am. But I wouldn’t want to promulgate the idea that not sleeping is a good thing.”

It might not be recommended, but in his case, it’s essential. You need those extra hours when you’re chair of Intensive Care Medicine at UCL, a practising clinician, a groundbreaking genetic researcher (Montgomery is director of the Institute for Human Health and Performance and discovered the ACE gene that influences physical fitness and endurance) and founder member of the UK Climate and Health Council. He has also conducted research on Everest, run three ultramarathons, skydived naked for charity and holds the world record for playing piano underwater (110 hours, as part of a team during his medical school days. He persuaded Yamaha to create a keyboard that would work underwater and “dumped it in a swimming pool”.)

This is a mere scattering of career highlights. Montgomery learns a new skill each year, of which more later, and we are meeting to mark the publication of his novel, Control, a dark, twisty thriller set – naturally – in a hospital. It’s pleasingly medical, with visceral descriptions of surgery and a wealth of jargon. “There’s a drama to medicine for people who’ve never seen a crash intubation or a kid on an operating table who’s dying,” he says.

Control is not Montgomery’s first book. In addition to the 477 academic publications listed on his CV, he wrote a children’s book as a Christmas present for his godchildren. “I was working long hours and the shops were shut” (not a £5 note in an envelope for him). He has also collaborated on TV scripts and is writing a screenplay. Lynda La Plante prodded him to start the novel during a boozy dinner. “You don’t usually get asked to write something by Lynda, so I tried to sober up, poured myself lots of coffee and sent her the first chapter in the morning.” He “smashed through the first draft in about six weeks”.

Facebook Twitter Pinterest ‘People say, I want to relax – losing the point that learning something is really relaxing’: Hugh Montgomery. Photograph: Pål Hansen/The Observer

I wrote a book, too. It took me two years of listless crying, during which I procrastinated/watched 13 series of Grey’s Anatomy. I’m so lazy that the night before meeting him, rather than going upstairs to change my trousers when a button fell off, I went to the chip shop wearing a shoelace as a belt.

Like a 21st-century Alexander Hamilton, he does everything as if he’s running out of time because he’s acutely conscious that he is. “I’ve got this frustrating, peculiar awareness of my mortality. I know I’m going to die unfulfilled, because I don’t think there’s anything I can ever do that will make me feel as if my life’s been worthwhile.” For a 56-year-old research pioneer who also saves lives daily, this seems borderline pathological. Has he always been like this? He remembers an incident when he was seven or eight. “We were on holiday and I remember looking at the sea and thinking ‘Oh my God, all this will end and it won’t be in very long’. It’s obviously completely pathological, isn’t it?”

A career in intensive care has increased that awareness. “A quarter of our patients die, that’s just the nature of critical illness. There’s a myth about why people die and how… because they’re very bad or very good. It isn’t like that. It’s a roll of the dice. We get 21-year-olds who were super fit gym bunnies in the morning and dead a day or two later.”

Partly to keep death at bay, and partly because he is, as he describes himself, “rapaciously interested,” Montgomery keeps outlandishly busy. He loves new things, hard things and the constant flow of information. “I like puzzles, so it’s partly trying to work out how to learn something.” The claim that he learns a skill a year, I realise, is an understatement to make people like me feel better. This year he’s learning the guitar, but also to swim. Not the basic mechanics, you understand – he was “a county-level swimmer” in his teens – but learning proper technique with a triathlon coach.

What has been the hardest of his new skills? “I did a year of particle physics and that was appallingly hard. I struggled because I don’t see the world in terms of mathematics.” And the most fun? “Close-up magic. There’s no purpose at all, but it’s fabulous.”

How on earth does he fit it all in? There’s that Thatcherite sleep regime, but it’s also, he says, a question of perspective. For him, work time is “tiles” and other time is “grouting”. “You look at a bathroom wall and you see an awful lot of tile. But if you worked out the area covered with grouting it’s probably tankloads.” He packs his “grouting” with activity, inevitably renouncing my own pastimes, becoming consumed with envy on Instagram and rage on Twitter. “I must be the only person in the world who has never read a Harry Potter book or seen a Facebook page… I dally with Twitter, but quickly learned I was just in this massive echo chamber. I’d much rather do than spectate in life.” His two teenage sons share lots of his sporting and outdoorsy interests, which helps with squeezing in family time, though he admits it’s tricky to find time to spend with his wife, also a doctor: “Life is hectic.”

It must be hard for him to understand people without his formidable drive. “People say: ‘I want to relax, I don’t want to have to do something else!’ They lose the point that learning or doing something is really relaxing.”

Decide you are going to live life, not observe it. Don’t watch reality TV

Montgomery is also evangelical about learning as a way to make life feel longer. That impression we have that life goes faster as we age, he believes, is because for many of us, getting older means we are rarely surprised by life. “New experiences make things seem to run slower. You go on a holiday to somewhere you’ve never been and everything is amazing and interesting and a week away seems like you’ve been away for a month. Trying to learn new stuff every day and surprising yourself slows time down a bit.”

It’s a lovely idea – curiosity and novelty tricking us into feeling that time expands. Does he have advice for people like me, in our shoelace belts, lethargically slumped on our sofas, staring at the internet?

“The first thing is to decide that you’re going to live life, not observe it. Don’t watch reality TV shows about other people living life – go and live it yourself. And if you love a good television drama, write one as opposed to watch one?” (Despite this, he asks: “Did you see Fleabag? I thought it was absolutely magnificent.”)

Montgomery recommends setting targets – “Tell everyone so you can’t back out” – and picking social activities. “Have a big smorgasbord of experience and find the thing that makes you go ‘ooh’.”

I need to ask for my own mental equilibrium: is he bad at anything? His initial response is a grave disappointment. “I’m not a good climber,” says the man who has scaled the world’s sixth highest peak. No, I say, firmly. I mean properly bad. Are you a terrible cook? Do you sing like a wounded moose? Finally he takes pity on me, sort of. Following “an experiment on a mountain” that went wrong, he lost his sense of direction. “I have absolutely no idea where I am. Even simple visual-spatial stuff I can’t do.”

It could be crushing meeting someone so extraordinarily accomplished, but I’m buoyed. Montgomery’s enthusiasm is unforced and infectious. He’s currently working out what’s next – drawing, sculpture, perhaps architectural history. That’s on top of finishing his screenplay and other books he’s planning. “There are four more fully worked out… Then I’ve got the magnum opus ones, that I really want to write.”

I have to let him go. He’s had an idea for an ingenious piece of medical engineering and needs to discuss its feasibility. I email him later with a proposal for a new skill I could assist with. Niksen, the newly fashionable Dutch art of doing absolutely nothing. “I suspect that it must be very good for one indeed. But I just can’t see myself doing this.”

Control by Hugh Montgomery is published by Zaffre at £7.99. Order it for £7.03 from guardianbookshop.com