The Spirit of Math 2.0: Computational Thinking

Michel Paul's <pythonic.math@gmail.com> recent email post to mathfuture@googlegroups.com is worth reading. This is Math 2.0 thinking at its best.

Michel Paul writes:

Keith Devlin wrote the following to describe the nature of modern (20th century onward) mathematics to current undergraduates transitioning from high school (19th century and before):

"Prior to the nineteenth century, mathematicians were used to the fact that a formula such as y = x^2 + 3x - 5 specifies a function that produces a new number y from any given number x. Then the revolutionary Dirichlet came along and said to forget the formula and concentrate on what the function does in terms of input-output behavior. A function according to Dirichlet, is any rule that produces new numbers from old. The rule does not have to be specified by an algebraic formula. In fact, there's no reason to restrict your attention to numbers. A function can be any rule that takes objects of one kind and produces new objects from them."

- Keith Devlin

Introduction to Mathematical Thinking

Wow! Please read that carefully. Though he wrote this to help today's students transition from the 19th century to modern mathematical thinking, it also describes the kind of thinking one learns to do in computer science! Functions in computer science operate on objects of various types, not just numbers. 

Traditionalists lost the battle professionally in the mathematical revolution that occurred a century ag0 but won in education. Meanwhile, computer science went ahead and got created from the insights of that revolution and turned into the world we now live in. The result? Most K-12 math students and their teachers, us, are unaware of the nature of the mathematical thinking that went on in the 20th century while the technology that surrounds us was built from it! 

The ultimate irony - we use 21st century technology, made possible by 20th century math and physics, to teach students how to do 19th century mathematics that they will never use!

I think this makes it clear that the study of programming can provide a way for math students to encounter and develop some intuition regarding concepts underlying modern mathematics that the traditional high school curriculum does not provide.

-- 

Michel

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"What I cannot create, I do not understand."

- Richard Feynman

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"Computer science is the new mathematics."

- Dr. Christos Papadimitriou
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