Big Problems

This column does not have a single author, but is submitted by a number of experts that contribute regularly to our news source.  Some are in Canada, some in the UK and one is in the far east


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 Navier-Stokes" 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

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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 Navier-Stokes 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

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