A coffee with...

Published on May 2nd, 2013 | by Stephanie

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Daniel Mathews

Position: Lecturer, School of Mathematical Sciences, Monash University.

How do you introduce yourself at parties?
Hi, I’m Dan. Nice to meet you. Sorry I forgot, what did you say your name was again?

Why mathematics?
Firstly, because it is how the world works. By this I partly mean that we can often model aspects of our world with mathematics. But I also mean that the world seems actually to run on mathematics. Mathematics is actually part of the nature of the universe. If science is the nature of things, we have found that mathematics is, at least to a large extent, the nature of science — it is, as Eugene Wigner once said, unreasonably effective. As James Jeans said, the architect of the universe appears to be a pure mathematician!

Secondly, because it’s true. Philosophically, mathematical statements are the closest things we have to eternal truths. When you say that two and two makes four, there’s no disputing that; and when we talk about mathematical theorems which have been proved, they may be very surprising and amazing but are just as undisputedly true.

Thirdly, because it’s challenging. If you can make progress in mathematics, you can succeed at almost any intellectual endeavour.

Finally, because it’s fun. I like doing it and it’s very rewarding to solve difficult problems.

Do you think that mathematicians deserve the “geek” tag?
When I was in high school I considered this word as a pejorative or insult. I’m not so sure now. Geeks — if by which we mean people who are enthusiastic about things like mathematics, science and computers — are probably some of the most important people in determining the future of how we live, and because of their knowledge, often quite powerful. Be kind to the geek, for they shall inherit the earth!

We see this now in culture too. Twenty years ago “geeks” only appeared in movies or television as losers, images of social repulsiveness. Nowadays we have shows like “The Big Bang Theory” and “Numb3rs” and “Criminal minds” which, although there are qualifications, largely present “geeks” as funny, quirky, and likeable. Although sometimes we may be encouraged to laugh at them rather than with them, on the whole I think this represents a positive advance in culture — there is less stigma attached to technical knowledge, intellect, and scientific intelligence.

In fact, I think that the “geek” tag has largely been reclaimed and owned by geeks, and that this is a good thing. I’m a maths geek and proud of it!

What area of mathematics and why?
All areas of mathematics are fascinating and amazing in their own way. My research has largely been in various branches of geometry and topology.

Why these? Well partly because the people I worked with at the universities where I studied did those things. But I particularly like geometry because it is visual, it comes in many different types, and because it describes the world. Etymologically, a geometer is one who measures the earth.

A lot of my recent research has been in symplectic geometry. Symplectic geometry is closely related to physics. If you’ve ever heard of Newton’s laws, or Hamiltonian mechanics, well the abstract mathematics that describes it is symplectic geometry.

Topology is an even greater abstraction again — it deals not with the size of things, but their mere shape. Don’t care how big or small, whether straight or round, something is, we just care about the shape. A donut and a coffee cup are the same thing. Well, topology leads from there into areas of enormous abstraction that are often very difficult but absolutely fascinating.

Importantly, these are areas of mathematics that seem to arise in the description of our universe at a fundamental level. We have to understand them in order to understand the world!

What has maths done for you lately?
Well, mathematical laws operated the whole universe by which 13.7 thousand million years of events happened by which we got here today and I am able to answer these questions!

I got to work today by public transport, which were scheduled by mathematical algorithms. I looked at a map on my phone, which uses incredible mathematics to tell me how to get from place to place; it connects to the internet through tricky cryptographic and communications protocols; the internet is based on layers of software upon layers of software and so on, and then down to hardware, for which their description is essentially mathematical.

And so on. The question really is, what has maths NOT done for me lately?

Do you have a favourite application or theory of maths?  If so what is it?  And why is it so?
Yes, I like symplectic geometry. It’s beautiful, it’s tricky, it’s weird and counterintuitive. It describes all of classical physics — and helps to describe quantum physics as well.[subscribe2]

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