THE MUSEUM OF MATHEMATICS
Harold Brochmann

 

Those of us who subscribe to Internet have access to discussion groups called lists. The general idea is that someone submits a proposition or an idea via e-mail to a computer called alit server which distributes the message to subscribers. Responses are similarly distributed. There are lists for a wide variety of topics.

For some time I took part in a list called CALC-REFORM. The other participants were mostly university mathematics instructors and professors. As the title implies, the question under discussion was "What should a universal calculus curriculum look like?"

 

One day last fall someone posted this question:

If the steam engine belongs in the Museum of Technology, then what should we put in the Museum of Mathematics?

No one seemed to have a good answer to this one because no suggestions were forthcoming in the next few days.

Then, out of cyberspace came this:

If Newton had had a computer would he have invented calculus?

The silence was deafening.

Consider:

If Watt had had a diesel, would he have invented the steam engine?

I propose the answer is:

Perhaps. But what would have been his purpose?

And the answer to this one:

If Newton had had a computer would he have invented calculus?

is:

Perhaps. But what would have been his purpose?

The steam engine represents a stage in the evolution of a technology that led to more practical, efficient and economical ways of converting fossil fuels to mechanical energy. It was developed in an era when precision engineering and manufacturing technologies were not available. Improvements in these technologies eventually made internal combustion engines possible. The steam engine is of historical interest; but now there are better alternatives. The steam engine belongs in a museum.

We don't teach our children how to operate steam engines.

The classical approqches to problems dealt with in calculus classes represents a stage in the evolution of a mathematics that led to more practical, efficient and economical ways of finding areas enclosed by, and tangents to, curves. It was developed in an era when computer technologies were not available. Improvements in these technology eventually made numerical techniques possible. Calculus is of historical interest; but now there are better alternatives. Calculus belongs in a museum.

We still teach our children "traditional" calculus. Do we know why?

Well, maybe there is an answer; but I'm not at all sure that all of us know what it is. Anyone care to care to explain?