Often people ask me what is new
in mathematics, in your view?
Have mathematicians become astuter?
Not really, they've just learned to use the computer.
We haev all kinds of new hardware
to help us with the load we bear
so now when we want to solve an equation
we just head for the nearest workstation.
Whatever the mathematical task,
whatever question you care to ask,
we can give you the answer then and there
if only we have the right software.
We now have
Suns,
Apollos and
VAX's
(all paid for with your taxes)
and the software we receive
can do some things you wouldn't believe.
Inverse a matrix? It's a snap.
Iteratte the Henon map.
Any large integer we can factor
or show the world a strange attractor.
In now takes hardly any time
for the number theorists to find a prime.
The topologists program for the purpose
of making pictures of some strange surface.
The numerical analysts are having a ball.
Computing's their business, after all.
They are happy to use what they know
to show the rest of us the way to go.
THere's lesson here that's quite instructive.
The finite element group is more productive.
They all do more than they ever did
using a computer generated grid.
Then there are dynamics boys
who are going wild with their new toys.
They use computer graphics to get
color pictures of a julia set.
Their computations are so exact they'll
reveal patterns which are clearly fractal.
They can now shock and dismay us
with even more exmaples of chaos.
So I would say there's no dispute.
Mathematicians must learn to compute.
Computers have changed the rules of the game
and mathamatics will never be the same.
