Have students lost the ability to do hard math problems?

Let’s say I give my students a challenging problem in mechanics — one that involves a complicated mathematical technique like Fourier analysis. They can type the problem word for word into Google, and there is a chance they’ll find the solution. They will at least find a solution to a problem much like it. And where the internet falls short, they can use a host of amazing software packages like Mathematica or MATLAB to solve the problem.

Now before you think I’m just an old guy complaining about “these kids today with their fancy computers,” I want you to know that I use the same Google searches and amazing software packages to help me solve my problems. Right now, I’m climbing up the MATLAB learning curve to help me solve a complex set of partial differential equations. The package does in a few minutes what it took me months to program when I was a wee grad student. MATLAB is a godsend.

But there was a power to the old way which I fear we may be losing. That is because the old way was really, really old. Since the time of Pythagoras, 2,500 years ago, mathematics has been done by staring down a problem with a pencil and paper, or a quill and parchment. You were forced to think your way through the silent world of mathematical forms and relationships. There was nothing you could do until your journey led to an insight that you could apply to your problem. With software and the internet, though, there is always something you can do. Press buttons, tweak code, run another search. While the approach saves huge amounts of time and allows a wider exploration, I am afraid that it does not teach the kind of depth of thinking that the Theoretical Minimum was meant to test.