Can Mathematicians Add up?

For some reason, whenever I speak to any maths academics or math teachers, (I know a few), I keep hearing the same anecdote about the fact that mathematicians can’t count.

To expand a little, I believe that what they mean is that many academic mathematicians don’t have a masterful and fast grasp, of basic calculation and mental arithmetic skills, such as using fractions, doing multiplications and divisions of large numbers, or deft ability in the handling of factorisation or expansion of polynomials.

I have been looking around the internet, looking for some evidence to support this urban myth / anecdote.  And, although I haven’t located any specific evidence yet, about general arithmetic skills of maths academics; I have notice some subtleties in the subject of maths, that probably lend themselves to the conclusion, that mathematicians don’t need to count, all that much.

I bought a book this week entitled Calculus, 3^rd Ed by Michael Spivak.  It is a classic text of analysis and calculus.  In his book, Spivak states that he sees mathematics as the act of ‘thinking’ about mathematical questions.  He goes on to discuss how the aim of his book, was to present mathematics, not as merely a collection of tools; but as a framework of ideas on which to form a view of mathematics as a holistic subject, interlinked in all ways.

I agree with this hypothesis, and that led me to postulate that perhaps, as mathematicians develop in their field; they become more detached from ‘numbers’ and more involved with ‘ideas’.  Hence, perhaps, the anecdote ‘those academics can’t count’.  Perhaps they don’t actually need to?

My only problem with this approach is that having studied maths recently, and as part of an attempt to apply it to physics; I have discovered that each mathematical skill or tool, builds on the ones that preceded it.  By mastering the basics I believe that you can do them on automatic, allowing one to concentrate on the ‘ideas’ that Spivak describes so beautifully.

An example:

Want to fly your private jet across the globe?

Need to think about continuous vector forces…

Want to work out those vectors?

Gotta know calculus…

Want to use calculus?

Gotta know differentials, integrals, functions and limits…

Want to work out limits?

Gotta know how to simplify, factorise or expand…

Want to factorise?

Gotta know your algebra…

Want to be an algebra God?

Gotta practice, lots…

Want to practice algebraic manipulation?

Gotta know the fundamental properties of numbers…

Want to know those properties?

You need to know ‘four operations’, fractions and factors…

As Newton stated in his ’Principa’;     ‘ 1+1=2, is a very important sum’.

You MUST be able to count!

There are so many rules and methods that are used in manipulating numbers, to arrive at a model such as the one you would need to plot your aircraft’s path around the world; that mastering as many of the early steps as possible, must make it easier to concentrate on the bigger questions such as, ‘What colour should my private jet , be’?  Or ‘what wine should I serve, as we fly over Paris?’

Of course, you could always use Mathcad or Maple, computer packages.  But even then, as good as they are, you still need to know that the answer that they provide is the right one.