math

  • Elite technical culture has produced a peculiar kind of intellect. It excels on examinations, dazzles in standard problem sets, and performs confidently in environments that look like clean textbook exercises. Yet it falters, sometimes catastrophically, when confronted with even slight deviations from the familiar. The same person who can solve a thousand routine engineering problems

    Read more →

  • Edifice and Craft

    Mathematics often advances by a prior about compressibility. Some investigators trust that with the right abstractions the world can be funneled into an additive and exact environment where one can add and subtract, take kernels and cokernels, and push information through functors without losing control. Others trust that essential difficulty lives in nonlinear and metric

    Read more →

  • There are two ways mathematics moves. One way is workshop craft. You build a device that bites a concrete problem, you show the estimate that turns the lock, you expose the counterexample that pins the exponent, and you leave the constants visible so anyone can audit the work. The other way is platform industry. You

    Read more →