To me though this seems like just the start. I typed ‘dissemination of mathematics’ into Google about six months ago and I’ve just typed it in again. Much the same has happened this time, although there are several new sites of interest. Basically, you get resources and initiatives concerned with mathematics education, some of which like http://iccams-maths.org/ seems like great stuff at a glance. Another site I found the other day in a similar vein was https://undergroundmathematics.org/, although I came to this a different way.

This kind of thing isn’t about the dissemination of mathematics amongst professional mathematicians themselves, however. Dissemination sideways if you like. Rather it’s about dissemination from the top down, if that’s the right way of putting it. It’s worth mentioning that this is a very laudable goal and anyone who’s ever taught mathematics at any level should appreciate these initiatives.

But what about dissemination sideways? To me to be able to fully disseminate mathematics sideways means that it must be formalised, however unfashionable amongst the majority of mathematicians this continues to be. The reason is that with formalised mathematics you have a corpus that is discoverable and usable, although I’m searching for the words here. I don’t think that formalisation is an end in itself and nor do I think that a formalised proof is necessarily any more worthy just because it has been verified by a computer. It just seems that it’s the only true place to start.

I think that mathematics that has been formalised has a structure and nature that somehow makes it much more amenable to being discoverable, reusable, searchable, etc. I got very excited when I watched a talk https://www.youtube.com/watch?v=Is_lycvOkTA by Thomas Hales again recently, since he seemed to be striking similar chords in places.

The arxiv, open-source web-based journals and an increasing number of on-line mathematics databases are fantastic but to me they still seem, because of their interfaces, to some degree like mathematics at a distance, again I’m searching for the words. They’re like Wikipedia on steroids. The content is more refined and detailed, so much so that it’s hardly a comparison, but the means for interactivity and collaboration are still limited. These sites might serve as resources for a mathematician taking part in a Polymath project, for example, but they do not serve as its context or arena. They afford the learning of mathematics amongst mathematicians, which is great obviously, but I think they are limited in affording the *doing* of mathematics. Both of these are needed for discovery of new mathematics or improvement of existing mathematics, I think.

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