I'm Roger Penrose Emeritus Rouse Ball
Professor of Mathematics at the University of Oxford
The subject of Physics very much depends
on mathematics and we have extremely
good equations, theories to describe vast
ranges of physical activity
I mean, how particles move, how bodies move going
back to Newton most of what we know
about the dynamics of bodies including
how the planets move and so on
to very good approximation came from
Newton's ideas and that's very
mathematical theory you need to
know, see planets are attracted by each other
gravitationally by an inverse square law
and this makes the planets move around
the Sun in ellipsis and that kind
of thing which was first step in
understanding the movements of the
heavenly bodies, but it's also modern
mathematical physics we accept all that
except it's got modified by Einstein in
particular, when motions get very large,
when you want extreme accuracy or when
gravitational fields get very strong, you
have to worry about Einstein's theory of
gravity, which is a much more complicated
theory although very beautiful one
it describes the motion of planets not just
by force attracting bodies to each other
but by the fact that the whole
space and time sort of fit together
into a four dimensional structure, and Einstein has equations which tell us how
that behaves. Very difficult to work out
in practice but important if you
want to know certain things, like, well
we know now that, for example, that there are things
called black holes where gravity get so
strong that
things collapse into this hole in a sense
where nothing can escape from
and our galaxy, the Milky Way galaxy
the stars which you see, which look like almost a sort of a milky background
to the sky and across the sky. The center is the Sagittarius,  there is a
place where there lives a black hole,
which is about four million times the
mass of the Sun, and people can see stars
they can track stars going around it and
ok you don't see them move just like
that, but over a period of weeks you can
actually see the movements, and this is
something which tells us there is this
very very concentrated object as I say
about 4 million times the mass of the
Sun at the center of the galaxy. So that's
an example of the sort of thing you can
do with mathematical physics,
understanding the general principles
which tell us how things move. I've
talked about gravity, but in other
areas too. Electromagnetic effects, Maxwelll the great Scottish mathematical
physicist James Clerk Maxwell who
well a lot of the equations of electricity and
magnetism were known, but they were
incomplete, and Maxwell by theoretical
reasons realized there must be another
term in it and the whole thing fitted
together in what we now call Maxwell's equations
Maxwell's equations not only
tell you how electricity and magnetism
work but they tell us how light works. That was a fantastic realization which
came about from Maxwell's equations, he
realized that electric and magnetic
fields when they oscillate will push
each other along through space at the
speed of light, and so he postulated that
light was electric and magnetic fields
pushing each other along because he
worked out that it'd be
the speed of light and that's what light
was that was fantastic achievement
And it also requires the nuclear power
drill, which is going to be quite a challenging
thing to put on another planet
