I recently saw a tweet saying most lay people have zero understanding of what high level mathematicians actually do, and would love to break ground on this one before I die. Without having to get a math PhD.
In: Mathematics
Just like medical doctors there are several different disciplines of high level math. Some of them are more abstract than others. It would be hard to truly describe them all in a simple manner. However the broadest generalization I can make is high level mathematicians use complex math equations and expressions to describe both things that exist physically and things that exist in theory alone.
An example would be, One of the most abstract fields of mathmetics is “number theory” or looking for patterns and constants in numbers. Someone working in number theory might be looking to see if they can find a definable pattern in when primes occur (so far it has been more or less impossible to put an equation to when a prime number occurs).
Now you may ask, “why work on something so abstract and purely theoretical” well sometimes that work becomes used to describe something real. For instance for hundreds of years mathematicians worked on a problem they found in the founding document of math “the elements” by Euclid. One part of it seemed to mostly apply, but their intuition told them something was wrong. Generations worked on this problem without being able to prove Euclid wrong. Eventually they realized the issue. Euclid was describing geometry on a perfectly flat surface. If we curve that surface and create spherical and hyperbolic geometry the assumption Euclid made was wrong, and our Intuition was right. Later we learned we can apply that geometry to how gravity warps space and time. Thus the theoretical came to describe reality.
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