[SOUND].
I think in mathematics, writing is probably more central than it is to other
fields, and that's because of the nature of the discipline,
which is centered on proof argumentation, and perspective,
convincing convincing people and making them understand is central to mathematics.
And it's also the difficulty of writing mathematics which makes it very important.
And as a result probably it's the only subject where
elegance with the writing is, is central to how we see the subject.
One of the most famous books in mathematics is called
Proofs From the Book.
It's one of these concepts from the mathematician Paul Erdős.
Where he collected proofs and arguments that were so
beautiful they would be in God's book.
And I think the idea of things being able to be in God's book is something peculiar
to mathematics.
So there's an idea if you hear a proof then that is so beautiful then you'd say
it's from the book, and there'd be collections of such things.
And the reason it's so important is because mathematics is
not just about finding out what is true and telling people what is true,
we wanna know why it's true, and you need to convince them that it's true, and
also why in retrospect it's obviously true.
So as a result the greatest mathematicians have tended to be,
although not always the greatest writers, and what absolutely is true,
is that the terrible writers have really hurt themselves as mathematicians.
If you have a fantastic idea and no one understand you, it doesn't count.
If you have a fantastic idea and you don't get across why it's so beautiful,
it doesn't count.
So, writing mathematics is, is central for that reason.
And it's central for a second somewhat surprising reason.
Because once you have an idea you have to write it down.
And when you write it down clearly, concisely and convincingly,
that's when you find out where the flaws in your thinking actually are.
It's in the revision, revision, revision process, that really,
you actually learn some of the most important mathematics.
When you find a gap in your argument, and you realize that that is where, the heart
really is, and that takes you back to days or weeks, of further thinking.
That's where the real mathematics happens.
[SOUND].
I think communicating with people who speak a different language is very
important and it's a similar skill, and shouldn't be,
shouldn't be separated from the idea of writing to to fellow mathematicians.
And the key thing is to know your audience and to speak to your audience.
And that means being able to speak to your audience,
being able to speak to the person who is taking the same class,
the person in the same research group, but also to the granting agency, and
also to your grandparents when you tell them what you are doing.
You don't need to get across the precise detail of the latest idea of what you had,
but you should be able to convey the, the spirit of what you are doing.
If you can't explain why you're doing what you're doing, then, well,
that's fairly said, and you're not gonna be able to convince a grant agency, but
more importantly, you're not gonna have a fulfilling life.
And I think the process of thinking through
doing what you're doing is very important.
And secondly, there's some times when you want to convince
someone without a technical background of some technical fact, and
that's a new skill, a difficult skill.
When that we see happening with budget negotiations in Washington.
In, in when when thinking about issues in the tech industry.
They're, they're often things where they're issues of fundamental things that
are true or false.
And it's subtle as to why they are true or false.
Why does Wall Street do what it does?
Who's responsible for certain actions?
You need to really understand what's going on to be able to explain things to people,
who really not only don't speak the language, but don't have the background.
So this takes practice, and there's no, there's no wrong road to that as,
to that as well.
[SOUND].
The point I'd like to make is, the kinds of mistakes people make when they learn
mathematics and either become mathematicians, or
at least learn to think in a very sophisticated mathema, way mathematically.
And I mean this of, of our best students.
And a good example is where people are writing either senior thesis or
a PhD thesis, where they do the work, they have the idea, and
they say now all I have to do is write it up.
And they leave remarkably little time for the writing.
And those who plan out in advance and write, and write, and write, and revise,
and revise, and revise, write great theses.
[SOUND].
I guess I would say it's not true that a good writer's a good mathematician, or
that a good mathematician's a good writer, but there is a surprising correlation.
There are great, great mathematicians who are terrible, terrible writers.
Who are famous in spite of their ability
to communicate because their ideas are just so great.
That's not the person you want to be.
If you are that person, that's great, but there are also many great mathematicians
whose ideas have changed at least the mathematical world.
And in many cases the world period, who changed the world
because of their ability to have incredibly powerful ideas,
and to get them across in an incredibly powerful way.
So I think to speak precisely there's a high correlation between the ability to
write well as a mathematician, and the ability to be a good mathematician.
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