The Fields Medal is widely regarded as the highest honour a young mathematician can attain
and is especially hard to win because the medals are only awarded every four years
to mathematicians under the age of 40. so James congratulations on being awarded the Fields medal . How did you find out?
Thanks so much so I was actually at the top of a ladder decorating
my house and uh I came down to get my phone to use it as a torch and I saw that I got an email
then from the IMU President asking for a Zoom call so I wasn't totally sure what it was but I
certainly had a pretty strong suspicion then about what this might be because there's no
other reason for him to contact me so that's the main time when I found out, although
it's only in the Zoom call that I found out for sure.
And so tell the many billions of us who will never win anything, how did it feel to win something so prestigious? What did you do next?
Obviously it feels amazing there's a huge adrenaline rush, but it takes also, it feels
very bizarre or at least it felt bizarre to me. It took a while for it to sink in. I remember
the IMU President asked me after he told me that I'd won it if I would accept the medal or not and
because emotions were going all over the place and I had this huge adrenaline rush I think I
responded very very slowly and deliberately saying yes I would accept it because I was so nervous
that I'd accidentally say no I don't accept it, just because my emotions were going all
over the place. But even now I think it's still taking a while to actually sink in that I've won.
Now you won the medal for your work in the field of Number Theory; so could you explain what that is?
So Number Theory is really the study of whole numbers and how they interact with one another
mainly under addition when you add numbers together and multiplication when you multiply
numbers together; and lots of my research is in how this operation of addition and multiplication
interact with one another which turns out to be an exceptionally complicated and poorly understood
mathematical phenomenon even though these seem like the most basic mathematical objects.
And in particular you've been recognized for your work on prime numbers. What are the primes
and what's the fascination? So prime numbers are essentially these atoms of multiplication that
every whole number can be written uniquely as a product of prime numbers multiplied together
so six is two times three which means that from the point of view of multiplication six can be
understood by the properties of the numbers two and three but two and three are prime
numbers which can't be broken down any further. So there's lots of fascinating questions about prime
numbers which really underlie how whole numbers interact with one another under multiplication
but even some of the most basic properties about prime numbers are still poorly understood
And so why do we know so little about the primes given we've been studying them for millennia?
This is still one of the great mysteries to me that, to me somehow the prime numbers
seem like some of the most fundamental and basic building blocks of mathematics and of the Universe
and yet we really don't understand the mysteries of the primes very well and it's this combination
of them being so fundamental but so mysterious and these seemingly very simple operations of addition
and multiplication having this huge amount of complexity that we really haven't fully grasped
which is really what motivates me to study the primes. Now you won the medal for quote "incredible
advances" in the field. What have you done that's so far advanced our understanding of the primes?
So one question that I've been very interested in prime numbers is about the small scale
distribution: how close prime numbers can come together and how far prime numbers can be
apart from one another. And this is one of these very basic questions that mathematicians
would study if they're interested in trying to understand the distribution of any sequence
But for the prime numbers this still remains very mysterious but in some of my
work and work with collaborators we showed that infinitely often primes come clustered unusually
closely together and infinitely often primes become very far apart and there's big gaps
between the prime numbers and so that was a major theme of my research so far in my
career has been investigating these small-scale distributions and the gaps between prime numbers.
And what did you learn about that, if you like, irregularity or regularity?
Yeah, so it fitted very much with some of our guesses as to how the prime numbers
should be disputed. So we have this huge web of conjectures about what we think
should be true about the prime numbers and this was maybe a baby step towards
making progress on this whole theory that we, where we have guessed answers for what should
happen but no mathematical proof for how to prove that it really does happen like that.
And so how does it feel to be the first person in human history to work these things out?
Yeah, in various pieces of my work you, I really have had a single Eureka moment
where I've spent maybe months or years toying with a problem, trying to understand
what's going on and spending a long time not understanding it and then suddenly everything
seems clear and everything, you can see how everything should fit together and
you can see the way to a solution of the problem; and this sudden moment of insight
and clarity is absolutely euphoric, there's a huge adrenaline rush, you're very excited,
there's often then a huge urge to sort of write down the details and make sure what you see is
how they fit together really does work out in the way that you think it should do and check all
the details. But yeah, there's this one euphoric Eureka moment which is really incredible .
And tell me about your working practices. Lots of computer time? Long walks? What are the tricks
of the number theorist? So my day-to-day time spent doing research would mainly be me at my
desk with pen and paper doing it in a sort of fairly old school style, but I definitely
use computers quite a lot as an assistant to help try out things and to test lots of individual
cases. So computers are certainly growing in their importance in mathematics but despite
the fact that most of my day-to-day work is maybe spent at a desk working with a pen and paper ,often
it's exceptionally important for understanding these objects to mull it over in your subconscious.
So there's been many days when I've worked very hard on a problem but made no progress during
the day and got very frustrated and then when I go on the walk home and I'm trying not to think
about maths at all suddenly the solution becomes clear to me. So a bizarre amount of progress has
really been made on, on walks home just wandering around or things like in the shower in the morning.
Now the Fields Medal is given to mathematicians under the age of 40 to encourage them to go on
to even greater things. Where next for you? So my main interests are still very much to
do with Number Theory and prime numbers and how integers interact with one another. So I really
hope this can be a launching pad for lots more discoveries in the area of Number Theory. It's
a very exciting time, there's lots of other people making exciting advances, particularly
in Analytic Number Theory at the moment and I'm really hoping that this momentum in the
field can continue because there's lots of exciting discoveries to be made out there.
Well, good luck James we'll be in touch when you win your next prize. One last question: I
understand you have just moved to a new house but number 16. Was 17 not available? Unfortunately
not a prime but at least it is a power of a prime. It's a prime power so it's close enough for me