Theorists as connectors: from Poincaré to mathematical medicine

November 4, 2012 by Artem Kaznatcheev

Henri Poincaré (29 April 1854 – 17 July 1912) is often considered to be the last universalist of mathematicians. He excelled in all parts of theoretical physics, applied, and pure mathematics that existed during his time. Since him, top mathematicians have become increasingly more specialized, as have scientists. Poincaré was part pure mathematician, part engineer; he advocated the importance of intuition over formality in mathematics. This put him at odds with the likes of Frege, Hilbert, and Russell — men that are typically considered the grandfathers of theoretical computer science. As an aspiring CSTheorist, I think we are misplaced in tracing our intellectual roots to the surgical and sterile philosophies of logicism and formalism.

A computer scientist, at least one that embraces the algorithmic lens, is part scientist/engineer and part logician/mathematician. Although there is great technical merit to be had in proving that recently defined complexity class is equal (or not) to a not-so-recently defined complexity class , my hope is that this is a means to a deeper understanding of something other than arbitrarily defined complexity classes. The mark of a great theorist is looking at a problem in science (or some other field) and figuring out how to properly frame it in such a way that the formal tools of mathematics at her disposal become applicable to the formulation. I think Scott Aaronson said it clearly (his emphasis):

A huge part of our job description as theoretical computer scientists is finding formal ways to model informally-specified notions! (What is it that Turing did when he defined Turing machines in the first place?) For that reason, I don’t think it’s possible to define “modeling questions” as outside the scope of TCS, without more-or-less eviscerating the subject.

As experimental science becomes more and more specialized, I believe it is increasingly important to have universal theorists or connectors. People with the mission of finding connections between disparate fields, and framing different theories in common languages. That is my goal, and the only unifying theme I can detect between my often random-seeming interests. Of course, CSTheorists are not the only ones well prepared to do take on the job of connectors. Jacob G. Scott (@CancerConnector on twitter; where I borrow ‘connector’ from) suggests that MD trained scientists are also perfect as connectors:

I completely agree with Jacob’s emphasis on creativity, and seeing complex problems as a whole. Usually, I would be reluctant to accept the suggestion of connectors without formal mathematical training, but I am starting to see that it is not essential for a universalist. My only experience with MD trained scientists was stimulating conversations with Gary An, a surgeon at University of Chicago Medical Center and organizer of the Swarmfest2012 conference on complex adaptive systems. He brought a pragmatic view to computational modeling, and (more importantly) the purpose of models, that I would have never found on my own. For me, computational models had been an exercise in formalism and a tool to build intuition on questions I could not tackle analytically. Gary stressed the importance of models as a means of communication, as a bridge between disciplines. He showed me that modelers are connectors.

As most scientists becomes more and more specialized, I think it is essential to have generalists and connectors to keep science unified. We cannot hope for a modern Poincaré, but we can aspire for theorists that specialize in drawing connections between fields, and driving a cross-fertilization of tools. For me, following Turing’s footsteps on the intuitive road of theoretical computer science and algorithmic lens is the most satisfying, but it is not the only way. Jacob shows that translating between distant disciplines like math/physics and biology/medicine and engaging their researchers can drive progress. Gary shows that pragmatism and viewing modeling as a means of communication is equally important. In some way, they (and many like them) act as a 21st century Poincaré by bringing the intuition of mathematics and computer modeling to bare on the engineering of modern medicine.