Synthesis over invention

I recently finished a great book called Hilbert [1], an eponymous biography of the mathematician David Hilbert. It’s a fun read and conveys an important message for anyone who strives to be creative in a technical field. In contrast to the stereotype of the inventive genius who advances a field by creating fundamentally new concepts, many of the innovations to which Hilbert’s name is attributed are instead examples of synthesis, or the process of combining different existing theories into a single system.

This is a critical distinction which I don’t feel is emphasized enough in the contemporary software development and computer science community.

Nerd nostalgia

Beyond capturing the life of an intellectually preeminent man, author Constance Reid does a fabulous job of snapshotting the energy and unprecedented output of the mathematical society centered around Göttingen, Germany at the turn of the twentieth century.

If you were to trace the lineage of virtually any subfield of modern mathemathics or physics, Göttingen would stand out as an inexorable nexus of theory and innovation. Any subset of the list of folks who passed through would be an intellectual hall of fame: Gauss, Riemann, Dirichlet, Born, Oppenheimer, Teller, Dirac, Planck, Einstein, Noether, Klein, Schopenhauer, Fermi, von Neumann, Heisenberg.

Up there with the Manhattan Project and Bell Labs in the 70s, Göttingen is one of the storied valhallas of nerd nostalgia. Every few decades since the industrial revolution (and before, but with far lesser frequency), some cloistered organization attracts a critical mass of productive brain power and is canonized in history books as a hotbed of R&D. The Georg August University of Göttingen was one such place from its heyday in the mid-19th century up until the German braindrain of the 1930s. Add to this the era of geopolitical turbulence overlapping Hilbert’s lifetime, and you’re left with a fascinating slice of history.

A synthetic character

In the wake of this book, I’m left ruminating over certain characterizations of Hilbert’s work and the historical setting in which he lived. One particularly compelling specialty that Hilbert possessed was an ability to synthesize disparate concepts into cohesive theories that at once fundamentally broke ground and unified different fields.

Hilbert’s student and fellow mathematician, Otto Blumenthal:

“For the analysis of a great mathematical talent, one has to differentiate between the ability to create new concepts and the gift of sensing the depth of connections and simplifying fundamentals. Hilbert's greatness consists of his overpowering, deep-penetrating insight. All of his works contain examples from far-flung fields, the inner relatedness of which and the connection with the problem at hand only he had been able to discern; from all these the synthesis — and his work of art — was ultimately created.”

C. Reid, Hilbert, 1st ed. New York: Copernicus, 1996, ch. 24, pp. 208.

To paraphrase, Hilbert is best known not for inventing lots of fundamentally new science, but for finding and leveraging commonalities between the many good things that his contemporaries came up with. Rather than endlessly adding to an intractable pile of mathematical novelty, Hilbert excelled at synthesis, or the process of combining different theories into a single cohesive system.

In an ambitious age of unbounded possibility and imagination, what better strategy than to seek depth of connections and simplifying fundamentals.

Wherein software eats my book report

This notion has important and obvious lessons for software developers. The existential balance between novelty and synthesis in theoretical mathematics is equivalent to maintaining a balanced diet of abstraction in a computational system.

For example, I would go so far as to say that there is a trend in certain niche programming language communities to culturally appropriate as much from the fields of modern mathematics as possible. This has several adverse consequences, most immediate of which is the imposition of an immense educational burden on newcomers. Longer term, when projects are built around arcane abstractions that few people truly understand, they are inevitably used “improperly” because consumers don’t know any better.

I think that the degree to which a project exposes overly-conceptual abstraction is directly related to the rate at which technical debt accumulates in consuming code. Such cases do all of us a disservice and lead to the eventual marginalization of the abstraction-laden technology.

To me, it’s interesting to think about where the pendulum of creation vs synthesis currently lies in the world of software development. We are awash in heady topics that we collectively feel remiss for not understanding well enough. From elliptic curve cryptography to block chains to consensus protocols to region-based memory management to whatever the hell a monad actually is, there are an increasing number of gaps in our domain expertise and few unifying systems through which to understand them.

I get the feeling that lately we as an industry put too much emphasis on novelty and not enough on unification. We are easily titilated by the newest programming language or the latest gizmo that can fork a process on a far away computer and less interested in ideas that fundamentally simplify how we reason about and work with computers.

Towards synthesis

I’m humbled by Hilbert’s definitive ability to consolidate and simplify. Read by a software developer, the book is a call to action pitting the goal of synthesis against our tendency to run as fast as we can in a million directions at once.

By emulating David Hilbert and studying disparate fields with an eye towards unification, we can produce powerful tools without requiring that our users read 40 whitepapers before understanding anything.

Thanks to Rishi Ishairzay, Marcel Molina, and Arya Asemanfar for reading and providing feedback on drafts of this essay.


  1. C. Reid, Hilbert, 1st ed. New York: Copernicus, 1996.