jam sandwich, yeah

You had a sandwich? Yeah A jam sandwich? Yeah

yeah I always loved mathematics as a kid, so

one of my earliest memories is when I was like

two years old and my grandma was

cleaning the windows in our home,

and I was insisting that she put

numbers on the- she put the detergent on

windows in the form of numbers so I always

liked numbers and patterns and logic

and so forth, things are very

black-and-white where there's one right

answer and everything else is wrong. I didn't

like so subjective shades of grey type

questions, I would work on math workbooks

for fun you know my parents wanted to

shut me up she just give me a workbook

and I'll just go do sums and so forth so I

always liked mathematics, math

competitions- doing that was very

different from doing research

mathematics, the type of problems that

that you've given in a problem book and so forth

these are very canned problems,

things you can do in five minutes or ten minutes

and they don't prepare you completely

for a research problem where, you know,

you have to spend six months, you have to

read the literature, talk to people, try

something, doesn't work, modify, try it

again, and it's a very different

experience doing research but I like it a lot

better actually than– than

all the puzzles I used to do as a kid I

don't do these things very much any more.

My mother was a high school math

teacher when she was younger so she did

help me a little bit you know you know

when I was a kid you know,

just talking numbers with me and then I had a lot of

very good mentors when I was like 10 or

11 there was a retired maths professor

in Adelaide which I'd go visit on the

weekends, we'd have tea and cookies and you know

he would just discuss some some

recreational maths problem, and so forth, which was a

lot of fun. He would tell me stories

about how he'd use maths during World War Two, and so forth, you know,

to do ballistics and so forth. It was kind

of fun to actually see maths actually being used for something

"He had a PhD in maths from Princeton at

20 and was appointed professor of

mathematics at UCLA at 24"

I enjoyed it I mean

when I was a kid I mostly enjoyed

doing math and geeky things and so forth, and

you know, being accelerated and

going to going to uni that early, I was

around people who are older than me

but had similar backgrounds so we were

at sort of the same level mathematically so

you know these people five years older

maybe but we're both stuck on the same homework assignments,

we both like to talk about various math concepts and so

forth so I felt at home you know so I

did miss out on maybe sort of the

regular high school experience you know

sort of– I didn't go to many, you know,

high school social events and so forth I did a

lot of that actually once I was in grad

school in Princeton. So then I

hung around people my own age and you

know, then I partied and so forth,

so I sort of had a slightly reorganized

childhood but it worked out well for me

"And I have to say Terence Tao was

competing there and he only got one out

of seven. Let's actually cut

Terrence Tao some slack, the fields medalist, the guy

who's like coming close to solving the

twin prime conjecture. It's actually

pretty awesome because he was only 13 years old.

He holds the record as the

youngest person to ever have won a gold medal."

- It was this question six. - Oh yeah yeah yeah

it's a famous question yes.

What's your recollection of it now and why

you didn't get it right? - No I did not get it right

- How do you feel about that? - I well you know you win some

you lose some. I -- oh boy -- I have --

it was so long ago now I don't remember much

about it. I do remember once the Olympiad

was over I found out that some

Romanian woman had solved

the question and I remember searching

out for her, because it was really bugging me that

that I did not know how to solve the

question. There's a special trick to

solve it, which at the time was not a

standard trick that was taught to you. You have to use a

method of descent -- you had to... I forget the

exact question. You had to show that

something could not be a perfect square --

was always a perfect square, and show

that if it wasn't you could find a

smaller counter-example and a smaller one

and a smaller one. I think nowadays it's

become part of standard training in

its -- they all know the trick

now, but...

- Were you competitive? Were you the sort of boy

that would get upset about it or was it

just a fascination? "I just want to know

that, I want to know the answer" or

when you like angry you didn't get it?

- I think I was more obsessive than

competitive, yeah, I mean certainly I was

a bit angry at myself for not getting it

but I wanted more to know the answer

than to win, I think. - There's this

famous image of you with Erdős. - Yes.

- It was a great photograph. People want

to know what you're discussing in that

picture what's going on there. - Yes, I

think he was giving me a maths problem

which I did -- I think I even know which -- what it is

because he did send me a postcard

afterwards with what may be the same

problem. I have it somewhere. Yeah I think

it was it was some maths conference in

Adelaide, yeah I was like 10 or something

I don't know why I was there maybe

some math professor at

the University of Adelaide told me to come.

I understand, he was always very good at

at speaking to mathematically gifted kids and I don't remember much

about our conversation except that

I remember I really felt

like I was being treated like an equal

like it wasn't condescending or anything

like you know. It was a very

pleasant conversation you know I mean

now Erdős has passed you know I

mean it does have some sentimental value

for me I mean it's... Yeah, I mean I

certainly wish I'd paid more attention

to him, actually you know I mean like I'd

heard of him you know as a child for

but you know Erdős is someone...

...to me he was just someone who would

like talking math to me, and that was great. He did

write me a letter of recommendation for

Princeton later on so he did help my

career directly. - Did you ever have people

you looked up to and thought they were...

they were the top guns? Not really I mean, you

know, I would learn about Euler and

Gauss, and Newton, but these are

largely just names. I think I didn't

really have a sense of... you know so I'd learn

all these theorems and tricks and so forth

but I didn't really ever have a

good sense of what was the most

important, or what was the... yeah I

didn't learn the why of mathematics until

a lot later. I remember when I was

learning calculus, I thought that the

most important mathematician in the world must be

be Taylor, because Taylor's name appears

everywhere in

undergraduate calculus. Taylor

expansion, Taylor's rule and so forth and,

you know he was a good mathematician, but

you know, there were many other

people who did good stuff which is not

taught as much at an undergraduate level.

When you're doing mathematics do you use

any kind of visualization in your head?

What does it look like in your head when

you're doing math?

It's a bit hard to explain. It's always always a combination of

thinking inside your head and speaking

out loud and working on the board. You do

try to isolate sort of the simplest

metaphor or something for for your

problem... How can I explain it... So you know,

for instance, I do a lot of estimates

I always want X less than Y and

sometimes it helps to think of a sort of

an economics problem, like "you have a

budget of Y, and can you afford X?" and

that way you start thinking economically

like so the way you work with

inequalities like X less than Y is that

normally you maybe try to first bound

x by z and z by w and then w by y and

so forth and this is like you know

trading in you know one item for another

item and you get a sense of sort of what

inequalities are sort of good

deals for you that you're getting you're

getting you bang for your buck and which

ones are really wasting your money. Sometimes

utilizing sort of your financial

intuition can be helpful.

Algebra and topology... Those

have always been my my weakest areas.

I've only been able to get a handle

on these areas generally by translating

them into other types of mathematics,

geometry or analysis, I have better

handle on... I certainly don't claim

any mastery of all of mathematics. I think nobody can do that

not since Hilbert. (David Hilbert)

The work I'm proudest of is almost all

joint work and I think

nowadays most of my work is

joint. It is really fun to talk over a

math problem at a really high level with

a co-author who who is really on your

wavelength, understands what you're

thinking. It's actually... saying

things out loud, it almost forces

you to think, like, at a more organized level

than in your head where it can be

a bit jumbled and vague, and it's just

more fun, you know you can go back and

forth and if you're stuck maybe your

co-author has a suggestion if he or she is

stuck you can make suggestions. You at

least guarantee one other person is

interested in what you're doing. You know

when you write something, when you write

a paper by yourself you know there's

always somehow the nagging fear at the

back of your mind that maybe you know no

one will care about this... but you know

you at least have one person to talk about it

with. What do you think or feel, what's

your impression of those mathematicians

that go the opposite way, Andrew Wiles

is an obvious example, the mathematician who

works in solitude. What do you...

how does that impress you? What he did

was very impressive... you need both.

You need people who focus very very hard

on one very narrow problem working for

years, become a very deep expert. But then

you need the people who can connect

things in fragmented fields. I make

my living you know by understanding one

field X and taking some ideas from that

and applying it to field Y, but I couldn't

do that if there weren't people who are

very deeply working in in field X, and