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The Art and Elegance of Mathematics: In Problem Solving and Applied Game Theory
I have never been very good at math and yet I use applied game theory daily in my work as a teacher and writer on personal development and life coaching. How can this be? Most people think of math as essential in creating game-based strategies. Most of us think of math as a dry, logical system for ordering the world, but that’s not really accurate. It can be basic mathematics applied to understand a rigid mechanistic universe. Mathematics, when done at the highest level, is a deeply artistic and creative process. It transcends the simple precision of numbers, arithmetic, geometry, trigonometry, calculation.
The gap between theory and practice is often large (potential energy and kinetic energy). When we were taught math in school, we were taught to do math by those who already knew the answers to the questions asked. But there is another kind of math. This is a process calculation where the problem has not even been answered and the person asking the question may need to ask a different question.
This way of thinking is described by Andrew Wiles on the PBS program Nova. Wiles is an acclaimed mathematician who solved Fermat’s theorem, a concept first conjectured by Pierre de Fermat in 1637 that had not been solved until Wiles found the solution.
It’s about conceptually walking through a series of dark rooms and getting your bearings. Yes, he knows what he’s doing and can feel his way, but he’s still blind. Then one day, someone turns on the light. It’s the difference between just doing math and knowing math.
Many of us say we did poorly in math at school or “knew nothing about math.” To say that is to misunderstand what mathematics is. When you drive a car, sing a song, wash the dishes, make your bed, or color coordinate your clothes, you’re practicing math. It’s a math akin to Wiles’ description of making your way around furniture in a dark room. It’s one thing to find your way around in the dark and quite another to see the furniture with the lights on.
Having an advanced degree in mathematics does not mean that one has “turned on the light”. One can have a very advanced knowledge of mathematics. These people know formulas, equations and algorithms, but they don’t really understand what they know.
When the switch is turned on, we have an epiphany, a zen realization, an “Aha” moment. It is a deep knowledge of what “is”. What the Taoists call the “One”.
For many mathematicians there is often a separation between what seems mathematical, artistic and spiritual, but the three are not separate entities.
If one wants to talk about mathematics in a way that transcends pure logic, the scientific method, the writing of formulas and the study of complex algorithms, one must change one’s view of mathematics to include creativity. and deep “tacit knowledge”. This way of looking at mathematics is not about solving problems, but like a painter working with oils on a canvas, one examines and engages in a process where mathematics is about creating and understanding how a new creation occurs.
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