obsessive listologist David Hilbert

The end of this month sees the end of my current grant BioPreDyn. Or, to give it its full title, “From Data to Models: New Bioinformatics Methods and Tools for Data-Driven, Predictive Dynamic Modelling in Biotechnological Applications”.

It’s a time for reflection. Not only on what was achieved (my travelling round Europe by boat and train), but on what wasn’t achieved. Those ideas, both revolutionary and rubbish, that remain unfinished and unstarted, because you were too busy delivering deliverables, or answering emails.

Rather than leave these ideas to gather dust in my mental filing cabinet, I’ll spend this final week setting them out, for you to rubbish, or to run off with and claim as your own.

The first idea is by far the most frivolous. Little boys like to collect stamps. Big boys like to make Bucket Lists. German mathematician David Hilbert was no exception, and in 1900 compiled his list of 23 unsolved problems that were to shape the course of mathematics for the next century. One hundred years later, the Clay Institute set out seven unsolved maths problems, each carrying a $1,000,000 prize for their solution.

Which led me to ponder: can we follow Hilbert’s lead, and compile a list of the most important open problems in Mathematical Biology? Such a list could focus the field towards a common goal, just as it did back then. In 2008, Darpa announced 23 mathematical challenges, some of which had a biological flavour. The difficulty we face in constructing our list is highlighted by comparing Hilbert’s first problem:

Is there a set whose cardinality is strictly between that of the integers and the real numbers?

with Darpa’s first challenge:

Develop a mathematical theory to build a functional model of the brain.

Hilbert’s question is very well-defined (though, it turns out, is impossible to answer). By contrast, Mathematical Biology problems are, and should be, application-driven, and are hence necessarily fluffier. Darpa’s challenge, for example, is vague, and we could never tell if an answer amounted to a solution.

Our task then is to set out not only the big open problems in Mathematical Biology, but those concrete enough to be answered.

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