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
Solve problems, that’s the essence of it. Some of them can be stated simply, like the Collatz Conjecture (iterate a function: on even numbers, divide by 2; on odd numbers, multiply by 3 then add 1; for any positive integer starting point, does it eventually reach the loop 4-2–1-4-2-1-etc.?), and some of them require more advanced knowledge, like the Reimann hypothesis (do all the non-trivial zeros of the analytic extended Reimann function satisfy Re(z)=-1/2?).
It might not be apparent why these problems are important, but their applications can be hidden in the real world and not known for years or decades or centuries. Fermat’s Little Theorem, for example, is why encryption on your computer works. Or, finding solutions of the Navier-Stokes equation is useful for fluid dynamics, which affects engineering of planes, cars, etc. On the flip side, we might never know if there’s a practical use for the Goldbach Conjecture or the Twin Primes Conjecture, but even if there isn’t there’s still the pursuit of knowledge, applying those methods to other problems.
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