Navier Stokes

February 1, 2018

 

In physics’ continued attempts to mathematically model the physical world, models that are at best rough approximations are accepted as uncontested fact. This is a limitation of physics itself, as approximations work just fine for any intents and purposes. This can be seen in the lack of precision calculations physicists use in their efforts to explain every occurence in the universe. NASA only uses 13 digits of Pi in its most precise interplanetary calculations, and only 40 digits are needed to calculate the size of the universe within the width of a hydrogen atom. So why are mathematicians interested in finding, and currently working to, finding and analyzing trillions of digits of Pi?

 

The goals of mathematics and physicists, while similar, are only coincidental. Physicists use mathematics as a tool in their goal of explaining the universe, while mathematics conduct their work for the sake of making progress within the field of mathematics. This explains the divide between physicists and mathematicians on the issue of the Navier-Stokes equations; for physicists, they are working equations to determine the position and movement of turbulent fluids, while mathematicians refuse to accept them as fact without sufficient proof. As of yet, the equations have not been proven to be consistent mathematically, and new research appears to find an instance in which the same set of inputs can lead to multiple outputs.

 

Since the equations were first discovered in the 1800’s, no case has disproved their validity. As important as that fact is, equally significant is the fact that nobody has been able to prove them to be true. This discrepancy is another one of the 7 millenium problems, and the first person to either prove or disprove the equations mathematically will win a prize of one million dollars.

 

 

Works Cited

https://www.quantamagazine.org/mathematicians-find-wrinkle-in-famed-fluid-equations-20171221/

https://www.jpl.nasa.gov/edu/news/2016/3/16/how-many-decimals-of-pi-do-we-really-need/

http://web.gps.caltech.edu/~cdp/Desktop/Navier-Stokes%20Eqn.pdf

 

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