What are the biggest problems that researchers are working on
now? I'm not talking about cancer research or health care.
I'm talking about the Millennium Problems. They were posed in the
year 2000 and they were seven in number. Another set of 23
problems were posed in 1900, hence the name Millennium. There is a
$1,000,000 US prize attached to each problem and one has been solved
already. One of the problems carries the name 'The NavierStokes"
Equations and it involves what is known as fluid flow. Most
experts understand the equations, but nobody to date has solved them.
Navier was a famous French Engineer and Stokes the Lucasian Professor of
Mathematics at Cambridge (held by Newton and Hawking) What is the
origin of such problems? The Bernoulli family and in particular
Daniel became interested in studying the way gases and fluids flow over
and around objects. Their work was extended by Leonard Euler. Navier added a 'tweek' to the equations to make the problem complete and
Stokes proved that Navier was correct (next column)
23/07/2009 12:11 AM

So why is a solution important? After all planes fly, pumps
pump and ships glide through the water. Well, yes that's right
because engineers have become adept at making things work and they have
approximation techniques that help them a lot. The problem really
revolves around finding the theoretical best solution. Ah, you
say.... "Those guys are just playing and things work well without
perfection"
This is true, but nobody knows where perfection stands. That
is, it might be a long way from where we are now. If it was very
close, then no matter, let the theoreticians play, but it may be a long
way away and things might be quite different. Can you imagine what
might happen? The exact shape of a hull that was optimal could be
designed right away. The NavierStokes equations are very complicated
and the best minds have worked on them to no avail. Maybe just
around the corner there is a young person who will have an insight.
It would be fun to be alive to see what things would look like after the
$1,000,000 was awarded and people understood the solution. You can
bet that computers would be active as part of the roll out of the new
technology
