Joshua Gans: Position Statement

The Digital Heritage Library of Mathematics needs to "think big" and also to "think different."

Thinking Big:

As I see it, the problem facing mathematical knowledge (and indeed all knowledge) are several fold:

(i) how do we ensure that knowledge is codified and captured for the very long-term (millennia)?

(ii) how do we ensure that, given the vast amount of knowledge, it can be drawn upon in an efficient manner?

(iii) how do we ensure that the form to solve (i) and (ii) above is 'technology independent'?

While a set of pdfs can solve (i), the way knowledge is coded in articles fails (ii). While paper can solve (iii), it cannot hope to do (i) or (ii). While developments such as Mathematica and also textbooks and other translations of knowledge can solve (ii), it is unclear they resolve (i) and especially (iii).

It seems to me that the goal should be something akin to the Oxford English Dictionary. It should be a way of codifying mathematical knowledge in a useful way that can be drawn upon for the very, very long-term. In other words, we are not limited by current copyright durations in how we think about this and we should ignore it completely. In addition, the content from copyrighted materials needs to be drawn out and reconstituted. Put simply, the system of how we store knowledge has to be re-designed. Anything short of that is a limited and probably uninteresting exercise.

Thinking Different:

The hard part will be how to achieve this. Drawing knowledge from existing sources will no doubt rely on algorithmic or machine methods alongside considerable human input. Moreover, it is unlikely a fully commercial system can achieve these outcomes although there may be commercial complements (a la the Human Genome Project and the Oxford English Dictionary).

This meeting needs to consider the various tasks that would have to be undertaken, the infrastructure needed and the set of experiments on design and contribution to ensure the task is actually completed. My guess is that this project could take at least a decade once it has begun.