Win 1 million dollars!

No one who cannot rejoice in the discovery of his own mistakes deserves to be called a scholar.

Donald Foster

I've received an email asking for the truth of the Riemman hypothesis from the last post. I'm glad to read those kind of questions.

In Mathematics, and in every science, there are several steps from an idea to become an Universal Law. First, the scientist discovers something that can't be explained with the current science, so he or she designs an idea to explain that situation. If the supposition is not backed by observation is known as a conjecture, and if backed by observation it is a hypothesis.

It's important to note that every hypothesis must be testable and based on previous observations or extensions of scientific theories.

Then, the scientist develops a theory, which is an explanatory statement of what has been observed, explaining the why and how. Most theory evolves from hypotheses, but the reverse is not true: many hypotheses turn out to be false and so do not evolve into theory.

If the theory can be logically deducted from a set of axioms, it's called a theorem. An axiom is an idea that it's true or we assume that, for example A=A.

Finally, a physical law is a model of reality, which not only explains the observed data, but also predicts future observations.

We have presented some mathematical hypothesis in this blog, like Riemman hypothesis or the normality of pi. Both are really interesting, but the first one is more... profitable.

Six years ago, the Clay Mathematics Institute (CMI) named seven Prize Problems. The Board of Directors of CMI designated a $7 million prize fund for the solution to these problems, with $1 million allocated to each. They became the Millennium Prize Problems.

1. Birch and Swinnerton-Dyer Conjecture
2. Hodge Conjecture
3. Navier-Stokes Equations
4. P vs NP
5. Poincaré Conjecture
6. Riemann Hypothesis
7. Yang-Mills Theory

There are 3 conjetures, 1 hypothesis, 1 problem, 1 (currently irresoluble) equation and 1 physics theory with a mathematical problems.

Solve it, and you'll win 1 million dollar for each one.