The Clay Mathematics Institute is a global organisation dedicated to furthering the beauty, power and universality of mathematical thought.
Navier-Stokes Equation
This is the equation which governs the flow of fluids such as water and air. However, for many decades no proof was found answering the most basic questions one can ask: do solutions exist, and are they unique? Why ask for a proof? Because a proof gives not only certitude, but also understanding.
Riemann Hypothesis
The prime number theorem determines the average distribution of the primes. The Riemann hypothesis tells us about the deviation from the average. Formulated in Riemann’s 1859 paper, it asserts that all the ‘non-obvious’ zeros of the zeta function are complex numbers with real part 1/2.
Yang-Mills & the Mass Gap
Experiment and computer simulations suggest the existence of a “mass gap” in the solution to the quantum versions of the Yang-Mills equations. But no proof of this property is known.
