1. Making a million dollars: an exploration of the millennium prize problems
Darius Mattson

2. CMI
May 24, Clay Mathematics Institute of Cambridge Massachusetts announced they would create a $7 million prize fund; $1 million for each problem
Inspire and inform the general public
recognize the historic achievement of those who solve the problems

3. The rules Publish Wait a minimum of two years SAB of CMI
Possible division of the prize
Counterexamples

4. P vs np P is how easily an equation can be solved
NP is how easily a solution can be verified
If P=NP
Efficiency problems, protein structure prediction etc. positively affected
Cryptography, place of mathematicians, bit coins etc. negatively affected
If P≠NP
Focus on partial solutions

5. Navier-stokes equations
Describe flow of viscous fluids
Begins with Fnet=ma
Incorporates the three components of velocity, density, pressure, temperature, and viscosity as well as the conservation laws
Results in partial differential equations; sometimes an answer “blows up”
CMI doesn’t require gravity or other extra forces and only uses incompressible fluids
Given any smooth initial conditions show that you can determine the pressure and velocity of any point at anytime in the future

6. Yang-mills and mass gap
U(1), SU(2), and SU(3) are the matrices that describe the qualities of a quark; produce 12 fields and particles total
E2=p2c2+m2c4
Minimum value
p can approach infinity
Rigorously prove the mass gap while successfully renormalizing for U(1)xSU(2) and SU(3)

7. Poincaré conjecture Topology and rules for morphing
Any shape with the topology of a sphere can be morphed into a sphere; true for all dimensions
By the ‘70s it had been proven for 5 dimensions and up
Richard Hamilton proposed using Ricci flow to solve for the 4th dimension
Grigori Perelman devised a method for dealing with singularities

8. Hodge conjecture Geometric shapes can be modeled by equations
Applying to higher dimensions produces an algebraic cycle/ manifold
Topologists morphed shapes on manifolds
Algebraists produced more algebraic cycles within manifolds
Homology classes = algebraic cycles
Prove you can draw any shape and morph it into a simple algebraic cycle

9. Riemann hypothesis
Predicted vs Actual distribution of primes

10. Birch and swinnerton-dyer conjecture
Elliptic curves can be analyzed using the L-series
The conjecture compares the L-series and its derivative to determine the number of solutions
If proven, this could make finite number of non-trivial answers from curves with infinite solutions
New systems of encryption based on elliptic curves

11. research P vs NP: http://en.wikipedia.org/wiki/P_versus_NP_problem
Navier-Stokes Equations: layperson/ ;
Yang-Mills and Mass Gap: problems/yang%E2%80%93mills-and-mass-gap
Poincaré Conjecture:
Hodge Conjecture: maths-hodge-conjecture
Reimann Hypothesis:
B-S-D Conjecture: