“Scientists and mathematicians, we always begin with disbelief.”

Not so!

Scientist and mathematicians, while they often do not believe in the sort of stories that involve bearded fellows floating in the sky, do have strong beliefs of their own.

For the scientists there is the belief that the Universe is ultimately comprehensible. That Nature is governed by simple and universal laws, which it is our job to discover and elucidate.

The beliefs of the mathematicians are more complex. Mathematicians believe in pattern and generalization. They always look for patterns and generalizations, and delight in those they find. They believe in the beauty of logical structures.

Mathematics has nothing to do with reality. This sort of statement is likely to confound the non-mathematician --- but it is, nevertheless, correct. Two mathematical theories might make entirely contradictory statements about the nature of “space”, for example, but they will still be recognized as being perfectly logical and consistent within their own individual realms. They will coexist, neither being discounted in the favor of the other.

Bertrand Russell famously wrote that "mathematics is the subject in which we know neither what we are talking about, nor whether what we say is true."

So far as the formula C = 2 pi R is concerned, it is often introduced to children in their sixth or seventh grades as a formula that defines the circumference of a circle; and pi is, at the same time, introduced as a magic number that comes in pretty much from nowhere.

That is not a good way to look at this equation.

What needs be done is to introduce pi = C/(2R) as the expression that defines the number pi. From there, then, it follows that C = 2 pi R.

It is a wonderful property of circles that the ratio of the circumference to the diameter of any circle (drawn on a flat two-dimensional surface) is always this strange and wonderful number pi.

The moral of the story is: Never put the cart before the horse!

(To be continued)