### The Language of Mathematics is English

25Oct06

Today there was a talk on “how to write a Part III essay.” Essays are literature reviews on a topic in mathematics that may segue into PhD topic. One essay may be written during the course of Part III to count as a three unit exam. The speaker addressed the concern that at an institution such as Cambridge, some students may be concerned that speaking English as a second/third/nth language may be a disadvantage: (rough paraphrase from memory)

Writing an essay would still be good practice since English is the language that mathematics is conducted in. That’s just the way the world is. It could have been German, but Germany decided to take part in two rather ill-advised World Wars.

The room had a good chuckle at this, including to my German neighbor, Steffen, who offered a lighthearted, “It’s true.”

(As a side note: did you ever notice that physicists use the word ‘ansatz’ while mathematicians use the word ‘conjecture’? One professor suggested that this may be reflective of the geographic history of physics.)

#### 4 Responses to “The Language of Mathematics is English”

1. 1 Steffen

I’m not quite sure if an ‘ansatz’ is really the same as a conjecture. The German word ‘Ansatz’ means something like ‘attempt, approach, proposal’ (apart from various other meanings). It can describe, in a calculation, what you expect the solution to look like. However, you wouldn’t say something like ‘PoincarĂ© ansatz’.

2. 2 Marat

I’ve always taken a conjecture to be something that is a “completely formed statement” in some sense, i.e., something with some sort of predictive power. On the other hand an ansatz is merely an assumed form that is taken at the beginning of a formulation without a basis in underlying theory that is them shown to meet some necessary condition. My typical analogy would be “guessing” the solution of a differential equation.

In that sense I guess I tend to think of the two as having different causal relationships: “ansatz -> theory” vs. “theory -> conjecture”. An ansatz is later justified by agreement with your theory, whereas a theory motivates a conjecture.

That was probably a bit too pedantic, but then again I did almost become a linguist.

3. Good points, both of you!

4. 4 robert

i find it hard to believe that, as a frenchman, poincare would ever have had an ansatz. Linguistic imperialism, in scholastic as well as in other fields, is a bad thing. In two hundred years’ time, will we all be speaking Chinese? Or rather confused amoebiforms, wondering where all the clever people went?