Serious Logical Mind Training

Conrad Wolfram has been giving talks on how to make mathematics more beautiful (Click here to watch).

Conrad argues that mathematics should be more practical and more conceptual, but less mechanical,” and that “Calculating is the machinery of maths – a means to an end.”

He identified four phases of doing mathematics namely:

  • Posing the Right Question
  • Real world  -> maths formulation
  • Computation
  • Maths formulation -> Real world / verification.

and that mathematical education over emphasise computation.

Though I applaud Conrad’s passion, I do have a point I wish to take issue with. For  Computation, Conrad argues that we can do away with the human and replace this with computers.

Now, there is a saying “throwing out the baby with the bath water”. If we completely lose the human element of computation, we also lose an important discipline that makes us mathematicians – Serious Logical Mind Training.

Conrad states, why try solving a quadratic equation when we have computer algebra packages that can solve it with a click of a few buttons? That is like saying to an artist why paint a picture of a cathedral when you can take a photograph with a camera. Nevertheless, some computer algebra packages have a problem solving  [{x}^{x}=4]\  ( the answer is 2).

In their newsletter, the European Mathematical Society (EMS) has a problem corner section. This section poses a series of complex mathematical question for its member to solve. Back in March 2001, I was honoured to get my name published for solving one of these problems in the March 2001 Edition (page 18). To solve these problems it takes Serious Logical Mind Training with a bit of  the trusted mathematical old school – pen and paper. I believe the EMS judges would have been disappointed if solve the problems by the click of a button but in most cases this is not possible. Solving these problems in the old school way laid down the foundation for me to be  the new school mathematician I am today.