Who comes up “unsolvable” problems like the Navier Stokes problem, and why is solving such unsolvable equations so important?
In: Mathematics
Sometimes when trying to determine how something moves, it’s easier to describe how motion changes over time than it is to describe the complete trajectory of how something moves.
This is the realm of differential equations.
How a leaf moves around in the wind is a good example. Who knows where it will end up. But if we know the direction of the wind at a bunch of points, then we can determine what direction the leaf will go for a short distance, and then determine what the direction of the wind is at the new location, and repeat this process.
The Navier Stokes Equation is one such scenario, in this case dealing with fluid flow. It takes into account the momentum of a fluid, the energy and pressure of the fluid, as well as the viscosity of the fluid, in all three directions, as well as the fact that fluid is incompressible. All this information can be used to determine what fluid will do in the next split second, which will provide information that can be used again to find the next split second, and so on. This gives approximate solutions that are usually sufficient for engineering purposes.
The key takeaway is that the answers we get from doing this apply to the specific conditions present (Energy, momentum, pressure, etc), and cannot be solved “generally”
Physicists and mathematicians looking for answers to questions like is faster than light travel possible and so on.
They are unsolvable, generally because our understanding of the subjects is insufficient in some way so by solving them, science advances.
[deleted]
Really really high level math is insanely hard and also commonly used. When people who are good at math and are applying it find something that current math doesn’t seem to explain well enough, but just solving this equation would explain it, and nobody solved it yet, boom. New question arises. People try to solve it.
This is basically the story of all of the problems
Latest Answers