Monday, November 3, 2014

Who let the algebraists write the Wikipedia geometry definitions???

It must take a certain type of personality to slave for hours over a hot keyboard to give Wikipedia and the world a clear definition of some mathematical term - hard to format and complicated. But apparently this personality type tends towards the "French" formalism of - what was it? ...yes! - the Erlanger program[OOPS! THAT NOT IT - try - Bourbaki]. I see little effort made in Wikipedia to make simple math ideas accessible, simply.

I am reading Wikipedia for their definition of "fiber bundle" and it seems to me it used to be a bit more comprehensible. Then I look up "double fibration" and hit a bunch of stuff about Twistor space, like:


and I think - geez! what happened to the geometry? I mean pictures. In general, Wikipedia mathematical definitions are abundantly formal, often failing to give the common sense meaning. For example do they show the picture for Lagrange multipliers? Actually they do, but not the right picture.

Lagrange multipliers find where the optimum valued isotherm touches the constraint for the last time. The key idea being that you can look for where the red and green vectors coincide: