# special functions identities for 5 year olds

So you’re looking at the contents of the <a href=”http://dlmf.nist.gov/”>NIST Digital LIbrary of Mathematical Functions</a>, and there are all these equations, and (well I,) you say to yourself, ‘this is an enormous amount of wallpaper, how am I ever going to get this into my kinesthetic memory? I’ve started copying down bits from the section about q-hypergeometric series, but I think there’s a better way to do this:

So far I’ve made videos demonstrating the Borwein cubic theta functions identity:

And two showing how the j-function is invariant under SL(2,Z):

And you look at papers about the Borwein Cubic theta functions, or libraries of modular forms, and it’s all oily, stringy, two dimensional symbol manipulation. That creates an enormous barrier of entry to the material. Here is what I’m proposing:

We translate the content of the DLMF into realtime interactives http://www.visual.wegert.com/ phase portraits</a> on the complex plane that a five year old could interact with on an ipad or other tablet with suitable fast graphics processor.

Looking at something like this is worthwhile:

https://www-m10.ma.tum.de/bin/view/Lehrstuhl/StefanKranichPickIt#pickit

(insert a I am not a reformer or revolutionary tag here.I’m just your friendly transcendental kuroko 🙂

There is the absurdly barbaric suggestion that mathematics education should start with drilling addition, subtraction, multiplication, and division, or that all mathematics necessarily *starts* there. Imagine that being a Ramanujan could be common if only we got around to making a realtime user interface for all this special functions material.

(the longer term goal is to construct a new user interface for mathematics that doesn’t involve computer simulacra of two dimensional symbol manipulation with a cursor or mouse doing the input. I’d like to use a didgeridoo to drive real time special functions fractal generation and have that be the arena in which I do mathematics in rather than dealing with messy collections of symbol-spaghetti which are prone to error, but hey, I get this nice cultural syncretism between mathematics and a 40,000 year old instrument, and lots of rainbows, so potential win)

additionally, I know people usually kvetch about colored equations, but so many q-hypergeometric identities seem to look like wallpaper without colors: