Twenty-three.

It’s the ninth prime number. An Eisenstein prime with no imaginary part and real part of the form 3n − 1.  The first prime P for which unique factorization of cyclotomic integers based on the Pth root of unity breaks down.

It’s also the number of mathematical challenges listed here that could land you a spot in the history books (if you solve one – or more – of them).

Discovering novel mathematics will enable the development of new tools to change the way the DoD approaches analysis, modeling and prediction, new materials and physical and biological sciences.  The 23 Mathematical Challenges program involves individual researchers and small teams who are addressing one or more of the following 23 mathematical challenges.

I bet John Forbes Nash  would be interested in this for a number of reasons.  If these challenges are successfully met, they could provide revolutionary new techniques to meet the long-term needs of the DoD.

I have just three words for you:  BRING IT ON

Mathematical Challenge 1:  The Mathematics of the Brain
Develop a mathematical theory to build a functional model of the brain that is mathematically consistent and predictive rather than merely biologically inspired.

Mathematical Challenge 2:  The Dynamics of Networks
Develop the high-dimensional mathematics needed to accurately model and predict behavior in large-scale distributed networks that evolve over time occurring in communication, biology and the social sciences.

Mathematical Challenge 3:  Capture and Harness Stochasticity in Nature
Address Mumford’s call for new mathematics for the 21st century. Develop methods that capture persistence in stochastic environments.

Mathematical Challenge 4:  21st Century Fluids
Classical fluid dynamics and the Navier-Stokes Equation were extraordinarily successful in obtaining quantitative understanding of shock waves, turbulence and solitons, but new methods are needed to tackle complex fluids such as foams, suspensions, gels and liquid crystals.

Mathematical Challenge 5:  Biological Quantum Field Theory
Quantum and statistical methods have had great success modeling virus evolution. Can such techniques be used to model more complex systems such as bacteria? Can these techniques be used to control pathogen evolution?

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