Monthly Archives: October 2011

Hypatia

The history of mathematics seems to have a scarcity of women’s names before the 19th century — and even since then, math seems to be predominantly a male domain. There are a few exceptions in ancient times, notably Hypatia of (guess where?) Alexandria.

Does the shortage of women reflect a cultural bias and lack of opportunity for women? Or are males naturally more mathematical? Does your own experience shed any light?

Euclid

In your own mathematical education, did you learn to regard math as a set of rules to follow (algorithms) or as a body of knowledge that needed to be proved? When you apply math in your career as, say, an accountant, will you be using algorithms or proofs?

And why were the ancient Greeks so obsessed with the need to prove everything? Maybe they took us up a 2000-year blind alley?

Mayan mathematics included a sort-of-positional notation (with base 20) and a zero. The Mayans almost certainly developed it independently, without any contact with the Old World civilizations.

If some mathematical ideas are culturally contingent (see “Draw a Triangle”), what mathematical concepts are universal? What ideas must develop in any society that has some kind of advanced math, and what ideas could we do without? For example, we think of math as based on proof and logic, but perhaps that’s just a cultural legacy from the ancient Greeks, and not really necessary at all?

Writing can be considered as a kind of technology. The physical form varies according to local circumstances (availability of clay for tablets, say, or of papyrus, or of light-emitting diodes), but the conceptual advance was far-reaching. How did this new technology enable the development of mathematics in particular?

Eleanor Robson tells us that practically all (97%) of written documents from southern Iraq 4000 years ago were accounts. Thus the twin births of writing and of mathematics both came about together due (largely) to accounting. Was this just a reflection of the bureaucratic nature of early Mesopotamian civilization, or is accounting the only possible stimulus for these crucial advances?