Conrad Wolfram (http://en.wikipedia.org/wiki/Conrad_Wolfram) has been giving talks on how to make mathematics more beautiful https://www.youtube.com/watch?v=gsWKyFg9IdM.

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

1. Posing the Right Question

2. Real world -> maths formulation

3. Computation

4. Maths formulation -> Real world / verification.

and that mathematical education over emphasize computation.

Though I applaud Conrad 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. In 2001, I was honoured to get my name published for solving one of these problems https://www.ems-ph.org/journals/newsletter/pdf/2001-03-39.pdf (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.