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me I consumed every outlet of science I could get my hands on.

      I persuaded my parents to buy me a subscription to New Scientist. I devoured Scientific American in our local library. I hogged the television each week to watch episodes of my favourite science programmes: Horizon and Tomorrow’s World. I was captivated by Jacob Bronowski’s Ascent of Man, Carl Sagan’s Cosmos, Jonathan Miller’s Body in Question. Every Christmas the Royal Institution Christmas Lectures provided a good dollop of science alongside our family turkey. My stocking was stuffed with books by Gamow and Feynman. It was a heady time, with new breakthroughs being announced each week.

      Alongside reading these stories of the discovery of things we know, I began to get more fired up by the untold tales. What we knew lay in the past but what we didn’t yet know was the future, my future. I became obsessed with the puzzle books of mathematician Martin Gardner that my maths teacher gave me. The excitement of wrestling with a conundrum and the sudden release of euphoria as I cracked each puzzle got me addicted to the drug of discovery. Those puzzles were my training ground for the greater challenge of tackling questions that didn’t have an answer in the back of the book. It was the unanswered questions, the mathematical mysteries and scientific puzzles that no one had cracked that would become the fuel for my life as a scientist.

       WHAT WE KNOW

      If I look back to the Seventies when I was at school and compare the things that we knew then to what we know now, it is quite extraordinary how much more we have understood about the universe even in the half century that I’ve been alive. Technology has extended our senses so we can see things that were beyond the conception of the scientists who excited me as a kid.

      The new range of telescopes that look out at the night sky have discovered planets like the Earth that could be home to intelligent life. They have revealed the amazing fact that three-quarters of the way into the lifetime of our universe the expansion of the universe started to accelerate. I remember reading as a kid that we were in for a big crunch, but now it seems that we have a completely different future waiting for us.

      The particle colliders like the Large Hadron Collider at CERN (the European Organization for Nuclear Research in Switzerland) have allowed us to penetrate the inner workings of matter itself, revealing new particles – like the top quark discovered in 1994 and the Higgs boson discovered in 2012 – that were bits of speculative mathematics when I was reading my New Scientist at school.

      And since the early Nineties the fMRI scanner has allowed us to look inside the brain and discover things that in the Seventies were frankly not even considered part of the remit of scientists. The brain was the preserve of philosophers and theologians, but today the technology can reveal when you are thinking about Jennifer Aniston or predict what you are going to do next even before you know.

      Biology has seen an explosion of breakthroughs. In 2003 it was announced that scientists had mapped one whole human DNA sequence consisting of 3 billion letters of genetic code. In 2011 the complete neuronal network of the C. elegans worm was published, providing a complete picture of how the 302 neurons in the worm are connected.

      Chemists too have been breaking new territory. A totally new form of carbon was discovered in 1985, which binds together like a football, and chemists surprised us again in 2003 by creating the first examples of graphene, showing how carbon can form a honeycomb lattice one atom thick.

      And in my lifetime the subject to which I would eventually dedicate myself, mathematics, has seen some of the great enigmas finally resolved: Fermat’s Last Theorem and the Poincaré conjecture, two challenges that had outfoxed generations of mathematicians. New mathematical tools and insights have opened up hidden pathways to navigate the mathematical universe.

      Keeping up with all these new advances, let alone making your own contribution, is a challenge in its own right.

       THE KNOW-IT-ALL PROFESSORSHIP

      A few years ago I got a new job title to add to my role as a professor of mathematics at the University of Oxford. It often makes me laugh: the Simonyi Professor for the Public Understanding of Science. There seems to be a belief that with such a title I should know it all. People ring me up expecting that I know the answers to every question of science. Shortly after I’d taken on the job, the Nobel Prize for medicine was announced. A journalist called, hoping for an explanation of the breakthrough that was being rewarded: the discovery of telomeres.

      Biology has never been my strong point, but I was sitting in front of my computer screen and so I’m embarrassed to admit I got the Wikipedia page up on telomeres and, after a quick scan, proceeded to explain authoritatively that they are the bit of genetic code at the end of our chromosomes that controls ageing among other things. The technology we have at our fingertips has increased that sense that we have the potential to know anything. Just tap my question into a search engine and the device seems to predict, even before I’ve finished typing, what it is I want to know and provides a list of places to find the answer.

      But understanding is different from a list of facts. Is it possible for any scientist to know it all? To know how to solve non-linear partial differential equations? To know how SU(3) governs the connection between fundamental particles? To know how cosmological inflation gives rise to the state of the universe? To know how to solve Einstein’s equations of general relativity or Schrödinger’s wave equation? To know how neurons and synapses trigger thought? Newton, Leibniz and Galileo were perhaps the last scientists to know all that was known.

      I must admit that the arrogance of youth infused me with the belief that I could understand anything that was known. If someone’s human brain out there has found a way to navigate a path to new knowledge, then if the proof works in their brain it should work in mine. With enough time, I thought, I could crack the mysteries of mathematics and the universe, or at least master the current lie of the land. But increasingly I am beginning to question that belief, to worry that some things will forever remain beyond my reach. Often my brain struggles to navigate the science we currently know. Time is running out to know it all.

      My own mathematical research is already pushing the limits of what my human brain feels capable of understanding. I have been working for over ten years on a conjecture that remains stubbornly resistant to my attempts to crack it. But my new role as the Professor for the Public Understanding of Science has pushed me outside the comfort zone of mathematics into the messy concepts of neuroscience, the slippery ideas of philosophy, the unfounded theories of physics. It has required a different way of thinking that is alien to my mathematical mode of thought, which deals in certainties, proofs and precision. My attempts to understand everything that is currently regarded as scientific knowledge has severely tested the limits of my own ability to understand.

      The process of attaining knowledge necessarily relies on our standing on the shoulders of giants, as Newton famously declared about his own breakthroughs. And so my own journey to the edges of knowledge has involved reading how others have articulated the current state of knowledge, listening to lectures and seminars by those immersed in the field I’m trying to understand, talking to those pushing the boundaries, questioning contradictory stories, consulting the evidence and data recorded in the scientific journals that support a theory, even at times looking up an idea on Wikipedia. Although we teach students to question any information that pops up from a Google search, research has revealed that Wikipedia’s accounts of topics at the less controversial end of the scientific spectrum, like the theory of general relativity, are regarded as on a par with accounts in the scientific literature. Choose a more contested issue, like climate change, and the content might depend on what day you look.

      This raises the question of how much can you trust any of these stories. Just because the scientific community accepts a story as the current best fit, this doesn’t mean it is true. Time and again, history reveals the opposite to be the case, and this must always act as a warning that current scientific knowledge is provisional. Mathematics perhaps has a slightly different quality, as I will discuss in the final two chapters. Mathematical proof provides the chance to establish

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