by Peter Wolfe
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 have 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.
Iterate 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.
- 一首数学诗：新数学（英文）
- It looks to me as if trying to do this without making heavy use of computer-assisted proofs is like tying one or possibly two hands behind your back, – Charles Fefferman -> Computer Proof ‘Blows Up’ Centuries-Old Fluid Equations
- A computer is used by a pure mathematician in much the same way that a telescope is used by a theoretical astronomer. … When computers first appeared in mathematicians’ environments the almost universal reaction was that they would never be useful for proving theorems since a computer can never investigate infinitely many cases, no matter how fast it is. But computers are useful for proving theorems despite that handicap. We have seen several examples of how a mathematician can act in concert with a computer to explore a world within mathematics. From such explorations there can grow understanding, and conjectures, and roads to proofs, and phenomena that would not have been imaginable in the pre-computer era. This role of computation within pure mathematics seems destined only to expand over the coming years and to be imbued into our students along with euclid’s axioms and other staples of mathematical education. (The Princeton Companion to Mathematics - VIII.5 Mathematics: An Experimental Science, by Herbert S. Wilf)
- If Gauss were alive today, he would be a hacker. — Peter Sarnak