experimental-design
Climb the yield surface
It is 1951 at an ICI chemical works in England, and a reaction's yield depends on temperature and pressure in a way no one can write down — but the plant manager wants the settings that maximize it, and every experimental run costs product and time. Rather than test a blind grid, design a sequence of small experiments that estimate the local slope of the yield surface, step toward the optimum, and then map the curvature near the peak to locate it precisely. Get it wrong and you either burn the budget wandering a grid that never finds the top, or chase noise uphill to a false summit — the art is letting a handful of well-placed runs both learn the surface and move you up it.
Who this problem belongs to
The two figures whose methods fit it best, out of 49 in contention.
This is Box's own career. Working at ICI in England starting in 1951, he and K.B. Wilson developed response surface methodology specifically to answer this question: how do you find the operating conditions that maximize a chemical reaction's yield when every experimental run costs real product and time. Their method fits a local linear model to estimate the steepest-ascent direction, takes a small sequence of runs climbing that direction, then switches to a quadratic model near the apparent peak to characterize the curvature and locate the true optimum precisely. This is not adjacent expertise — it is the specific industrial problem that produced the specific method, from the specific person. The only reason it is not 100 is that Wilson co-developed it and pure history should note the pair.
Boyd's work systematizing convex optimization, culminating in his widely used textbook and the solvers built around it, gives the modern mathematical machinery for exactly the second half of this problem: once a local model of the yield surface is estimated, finding the optimum efficiently and characterizing curvature near it is a convex or locally-convex optimization problem his framework handles rigorously. His treatment of gradient and Newton-type methods generalizes the steepest-ascent step Box used by hand in 1951 into a much broader and more rigorous toolkit. He did not develop response surface methodology itself or work under its original expensive-experiment constraint, which keeps him strong but secondary to Box. That closeness to the method's historical origin is what keeps Stephen Boyd among the stronger carriers in this particular batch.
In the mind map
The same ideas, as concepts rather than history — in John's ML knowledge map.
49 figures are scored on this problem. Draw it in a battle to see where you land.