Maths Banter

Over the years I'm sure you've seen many types of proof, in your next lecture; see if you can spot these lesser-known types:

Proof by cumbersome notation:
Best done with access to at least four alphabets and special symbols.

Proof by reference to inaccessible literature:
The author cites a simple corollary of a theorem to be found in a privately circulated memoir of the Slovenian Philological Society, 1883.

Proof by importance:
A large body of useful consequences all follow from the proposition in question.

Proof by intimidation:
"Trivial."

Proof by metaproof:
A method is given to construct the desired proof. The correctness of the method is proved by any of these techniques.

Proof by vehement assertion:
It is useful to have some kind of authority relation to the audience.

Proof by semantic shift:
Some of the standard but inconvenient definitions are changed for the statement of the result.

Proof by accumulated evidence:
Long and diligent search has not revealed a counterexample.  

Evariste Galois

Unfortunately what is little recognized is that the most worthwhile scientific books are those in which the author clearly indicates what he does not know; for an author most hurts his readers by concealing difficulties.

--Evarist Galois

I blog because I want to:

1)  Introduce some unexpected influences and ideas into my intellectual and academic work. I want to unsettle the overly domesticated, often hermetic thinking that comes with academic specialization. I want to introduce a "mutational vector" into my scholarly and intellectual work.

2)  Publish small writings, odd writings, leftover writings, lazy speculations, half-formed hypotheses. I want a place to publish all the things that I think have some value but not enough to constitute legitimate scholarship. I want a chance to branch into new areas of specialization at a reduced level of intensity and seriousness.


3)  Find out how much of my scholarly work is usefully translatable into a wider public conversation.


Tim Burke, Swarthmore College
weblogs.swarthmore.edu/burke