Computation and Data as Twin Drivers

Definition

Two distinct but deeply intertwined forces expand a mathematical discipline's reach into other fields: (1) the widespread availability of computing power, which makes simulation of complex systems routine, and (2) an explosion in the amount of data being collected, at a scale that "can only be evaluated through mathematical and statistical techniques." The report treats these as the two engines behind the mathematical sciences' growing footprint — not applications of math, but structural pressures that make math unavoidable.

In the Book

Chapter 3 states plainly that "computational modeling is inherently mathematical" — so any sector that leans on simulation automatically deepens its dependence on the mathematical sciences, whether or not it recognizes this dependence. The book grounds this with concrete cases: Terrence Sejnowski's computational simulation of biochemical activity at the Salk Institute, described as infeasible until recently and now enabling novel biological investigation; and the progression of ultrasound imaging from static images to a dynamically beating heart to a full fetus in the womb, which required solving inverse problems drawing on wave-propagation theory and fast numerical methods. The book is explicit that computation and data are not separate stories — "it is becoming increasingly standard for major research efforts to require expertise in both simulation and large-scale data analysis" — and that over the past 10-15 years, computational capacity crossed a threshold that made methods like Markov chain Monte Carlo and large-scale data mining newly feasible.

Why It Matters

This gives a causal account, not just a correlation, for why "everything is becoming quantitative." It separates two distinct mechanisms that are often lumped together as "digitization": the ability to simulate (computation) and the ability to measure at scale (data), each of which independently forces a field toward formal methods, and which compound when combined. That separation is useful diagnostically — a field swamped by data but with weak models needs different investment (statistics, dimensionality reduction) than a field with strong models but limited compute (numerical methods, algorithms) — and helps explain why "learn to code" and "learn statistics" became parallel, not identical, imperatives across so many disciplines at once.