So this is the first ingredient of the approach. So let me do now the second ingredient.”

Screenshot 2015-11-24 16.08.11

That first little quote, from a talk on Min-Max Theory and its Applications by Andre Neves, points to a quite interesting parallel: mathematics discourse and recipes.

Here’s something that my supervisor wrote about recipes. I’m just picking and choosing a few snacks from it.

David Farkas, an information designer with a background in linguistics[8], points out that a piece of procedural discourse typically has two aims: first, to sell itself as a procedure – the recipe must try to be convincing and credible and implicitly assure the reader that it comes from a reliable source; and second, to convince the reader that any effort put into following it will be rewarded.

I will explain how to find an infinite number of minimal hypersurface in a manifold, OK, or that’s the idea”

So the aim of mathematical writing might be to convince the hearer that the maths is correct, and that following the speaker’s footsteps to create the mathematical meaning in their own mind will be rewarding. It depends on and expects a shared prior knowledge.

Rotman’s written about maths papers in terms of procedural discourse. It’s really nice that Neves makes that explicit.

Philosopher Steven Schiffer calls this condition “mutual knowledge.” Consider the exchange in (16):
(16) A: Is he a good chef?
        B: Well, he worked at The French Laundry for three years.
A’s successful understanding of the implied meaning, or implicature, conveyed by B’s utterance—that he probably is a good chef—depends not just on prior discourse but on a mutually known, shared background knowledge of the American culinary scene.

If m3 is hyperbolic then this is true by Khan-Markovic this was in 2012 or Rubinstein in 2005”

Names become objects. These references assume a shared prior knowledge, expects hearers to be experts (not this one, sorry!). The year and name points to the right bit of work and the assumption is that the audience knows enough to know what the content is. However, the extreme specialism in mathematics and quantity of papers in the world means that some audience members will indeed have read that particular paper, but many others won’t. So rather than knowing what content they mean, i.e. being convinced of the truth, perhaps they’re instead just convinced that the speaker knows what content they mean – and is using it correctly.

Some audience members won’t have read the paper, but may know the author and the result by reputation. Many people know that Andrew Wiles has written a proof of Fermat’s last theorem, but very few have read and understood it. Making this reference to Wiles’ proof expects that the hearer shares an acceptance of the verification offered by the structures and institutions of mathematics and so will be convinced.

Wharton goes on to talk about the evocative side of recipes, that leads them to be published in big, shiny books, pored over comfortably on the sofa, read as well as used. They suggest a lifestyle as well as a meal.

Sperber and Wilson’s theory of communication and cognition builds on Grice’s work. They argue that what a communicator intends to convey is better characterized as an intention to modify not the hearer’s thoughts directly but his “cognitive environment.”
What cognitive environment, then, is this, when we’re talking about imaginary content? Or – well, what is mathematics? We could say that it’s about platonic objects and we’re perceiving some new aspect of them. Or we could say that it’s about perceiving new aspects of existing mental constructions.
Something interesting happens in the referencing mentioned above – there are whole bits of the structure of a proof, of the mathematical facts, that can be skipped. If a person had to understand every step to be convinced, they would have to understand every reference, and I’ve heard anecdotal evidence that that isn’t what happens (I need some interviews or something to back that up). People talk about perceiving the structure of a proof, grasping the gist of the mathematics (see: Luke’s user’s guides). That gist therefore must be made up in some part by a trust in the institutions of maths – reinforcing them.

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