David Hilbert’s Sixteenth Problem is an important open problem in mathematics. Good luck!
“I would like nuclear fusion to become a practical power source. It would provide an inexhaustible supply of energy, without pollution or global warming.”
— Stephen Hawking.
“Nothing takes place in the world whose meaning is not that of some maximum or minimum.” — Leonhard Euler.
“The conviction of the solvability of every mathematical problem is a powerful incentive to the worker. We hear within us the perpetual call: There is the problem. Seek its solution. You can find it by pure reason, for in mathematics there is no ignorabimus.” — David Hilbert.
Algorithm for the Collatz Conjecture. “… In short the Collatz problem is simple enough that anyone can understand it, and yet relates not just to number theory (as described in other answers) but to issues of decidability, chaos, and the foundations of mathematics and of computation. That’s about as good as it gets for aContinue reading “A Brief Analysis of the Collatz Conjecture”
Gauss, Riemann, Hardy, and Hilbert would have been proud of us. Amen! The central ideas behind the proof of the Riemann Hypothesis are deceptively simple. The proof depends on the very important Harmonic Series and the following important fact. For every positive integer, n > 1, there exists a prime number, p, that divides nContinue reading “We (mathematicians) have a valid proof of the Riemann Hypothesis that we can celebrate on the great Bernhard Riemann’s 194th birthday, September 17, 2020.”