I think this is a nice argument [1] and gets to the crux of some things. One of the most interesting is the tradeoff between time preference and explicitness. Without a doubt, if you and your team possess strong and relevant convention and the problem is simple enough then you can win on time by being implicit. Essentially: why write things everyone already knows.

What comes to mind suddenly is a perhaps-useful relation to the styles of two famous mathematicians. I’ll take a little bit of artistic liberty here, but…

Paul Erdös was an itinerant mathematician who traveled the world, crashing on other mathematicians’ couches and writing beautiful, small papers with them. His particular joy was tackling “small” outstanding “problems” in interesting ways (particularly in combinatorics). In other words, he didn’t build theories as much as he cleverly tackled problems people didn’t realize they could already solve. In the small, his work perhaps feels unimportant but over his entire career his techniques were refined by himself and others and built into practices and theories that got the ball moving in areas people where people were stuck.

Alexander Grothendieck was an profound motivator of 20th century mathematics where he worked at his peak over just a couple years embedded in a cabal of French mathematicians who he inspired to rewrite… everything. He compared his approach to other mathematicians with a metaphor of cracking a nut: some mathematicians would find the biggest hammer they had and whack at it hoping to crack the shell and then wresting it open; he sought instead to raise the level of the sea until the water would surround it and soften the shell making it trivial to open gently. He built master theories of category theory and used it to rewrite algebraic geometry, moving the field to a new era of exploration. His theories permeated other branches of mathematics and were both criticized for being “abstract nonsense” and also adopted as being better foundations for work and inspiring new revolutions in many other branches (logic, topology, probability, algebra, all over).

Both are considered wildly successful and vital forces for mathematical development, but both also approached the different sorts of problems with very different techniques.

Erdös could solve 30 small problems before Grothendieck got out of bed all while illustrating a great space of opportunity that people couldn’t see. His leadership was implicit. Grothendieck would then step in and eliminate the reasons we even believed those 30 problems were problems in the first place and connect Erdös’ implicit vision to every other branch of mathematics as the obvious, if abstract, bedrock. He explicitly sought to improve the tools all mathematicians use. Erdös worked alone and in very small collaborations and is known as prolific in many fields. Grothendieck commanded a following that publicly revolutionized one field and laid the bedrock for 30 other revolutions elsewhere.

So which sounds more like the problem solving you do? Most likely none of us are as influential as either of these examples, but I can sketch out a continuum between their approaches. What kinds of problem solving would work best for the kinds of outcomes you are seeking?

[1] although I caution the reader around some of the discussion of monoids which is slightly but not materially wrong

Finally a sober (i.e. non-ideological) take on the static vs dynamic discussion! Came here to post this because Jean-Louis Giordano (who I’ve never heard of until this article) expresses love for both Haskell and Clojure in a much more technically-sophisticated language than I can :)

I think this is a nice argument [1] and gets to the crux of some things. One of the most interesting is the tradeoff between time preference and explicitness. Without a doubt, if you and your team possess strong and relevant convention and the problem is simple enough then you can win on time by being implicit. Essentially: why write things everyone already knows.

What comes to mind suddenly is a perhaps-useful relation to the styles of two famous mathematicians. I’ll take a little bit of artistic liberty here, but…

Paul Erdös was an itinerant mathematician who traveled the world, crashing on other mathematicians’ couches and writing beautiful, small papers with them. His particular joy was tackling “small” outstanding “problems” in interesting ways (particularly in combinatorics). In other words, he didn’t build theories as much as he cleverly tackled problems people didn’t realize they could already solve. In the small, his work perhaps feels unimportant but over his entire career his techniques were refined by himself and others and built into practices and theories that got the ball moving in areas people where people were stuck.

Alexander Grothendieck was an profound motivator of 20th century mathematics where he worked at his peak over just a couple years embedded in a cabal of French mathematicians who he inspired to rewrite… everything. He compared his approach to other mathematicians with a metaphor of cracking a nut: some mathematicians would find the biggest hammer they had and whack at it hoping to crack the shell and then wresting it open; he sought instead to raise the level of the sea until the water would surround it and soften the shell making it trivial to open gently. He built master theories of category theory and used it to rewrite algebraic geometry, moving the field to a new era of exploration. His theories permeated other branches of mathematics and were both criticized for being “abstract nonsense” and also adopted as being better foundations for work and inspiring new revolutions in many other branches (logic, topology, probability, algebra, all over).

Both are considered wildly successful and vital forces for mathematical development, but both also approached the different sorts of problems with very different techniques.

Erdös could solve 30 small problems before Grothendieck got out of bed all while illustrating a great space of opportunity that people couldn’t see. His leadership was implicit. Grothendieck would then step in and eliminate the reasons we even believed those 30 problems were problems in the first place and connect Erdös’ implicit vision to every other branch of mathematics as the obvious, if abstract, bedrock. He explicitly sought to improve the tools all mathematicians use. Erdös worked alone and in very small collaborations and is known as prolific in many fields. Grothendieck commanded a following that publicly revolutionized one field and laid the bedrock for 30 other revolutions elsewhere.

So which sounds more like the problem solving you do? Most likely none of us are as influential as either of these examples, but I can sketch out a continuum between their approaches. What kinds of problem solving would work best for the kinds of outcomes you are seeking?

[1] although I caution the reader around some of the discussion of monoids which is slightly but not materially wrong

For those who want to learn a bit more about Grothendieck’s rather unusual life and writings: http://www.ams.org/notices/200808/tx080800930p.pdf (I found this after @tel’s comment piqued my curiosity).

Finally a sober (i.e. non-ideological) take on the static vs dynamic discussion! Came here to post this because Jean-Louis Giordano (who I’ve never heard of until this article) expresses love for both Haskell and Clojure in a much more technically-sophisticated language than I can :)