maybe computational notebooks will only take root if they’re backed by a single super-language, or by a company with deep pockets and a vested interest in making them work. But it seems just as likely that the opposite is true. A federated effort, while more chaotic, might also be more robust—and the only way to win the trust of the scientific community.

“I think what they have is acceptance from the scientific community as a tool that is considered to be universal,” Theodore Gray says of Pérez’s group. “And that’s the thing that Mathematica never really so far has achieved.” There are now 1.3 million of these notebooks hosted publicly on Github. They’re in use at Google, Bloomberg, and NASA; by musicians, teachers, and AI researchers; and in “almost every country on Earth.”

Out of the box, Python is a much less powerful language than the Wolfram Language that powers Mathematica. But where Mathematica gets its powers from an army of Wolfram Research programmers, Python’s bare-bones core is supplemented by a massive library of extra features—for processing images, making music, building AIs, analyzing language, graphing data sets—built by a community of open-source contributors working for free. Python became a de facto standard for scientific computing because open-source developers like Pérez happened to build useful tools for it; and open-source developers have flocked to Python because it happens to be the de facto standard for scientific computing. Programming-language communities, like any social network, thrive—or die—on the strength of these feedback loops.

Gray brought the same basic concept to Mathematica, with help refining the design from none other than Steve Jobs. The notebook is designed to turn scientific programming into an interactive exercise, where individual commands were tweaked and rerun, perhaps dozens or hundreds of times, as the author learned from the results of their little computational experiments, and came to a more intimate understanding of their data.

The notebook interface was the brainchild of Theodore Gray, who was inspired while working with an old Apple code editor.

Progress is inhibited by the exceedingly crude way in which mathematicians express their relationships.

“The number of moving parts is so vast, and several of them are under the control of different groups. There’s no way you could ever pull it together into an integrated system in the same way as you can in a single commercial product with, you know, a single maniac in the middle.”

His Senior year at CCNY, Arrow took the advanced course on relational logic taught by Alfred Tarski, where the eminent philosopher took pains to reintroduce the ideas of Charles Sanders Peirce, the greatest yet most neglected American philosopher.