Disciplinary Boundary Erosion

Definition

A field's boundary erodes when enough of its neighboring disciplines start doing work that is indistinguishable from the field itself — not by redefinition from the center, but by accretion at the edges. The report argues this has happened to the mathematical sciences: the old distinctions between "core" and "applied" math, and between math and fields like theoretical physics, bioinformatics, or theoretical computer science, have become "increasingly artificial" because so much of the interesting work now happens in the overlap.

In the Book

Chapter 3 replaces the traditional picture of mathematics as a bounded discipline with "interfaces" (Figure 3-1, updated as Figure 3-2 to show how much further the boundary has spread since 1998) with a model of "mutual entwining and meshing" — regions where fields blend rather than a clean dividing line. The book names the mechanism concretely: statisticians embedded in geosciences and bioinformatics, number theorists doing cryptography, real analysts contributing to machine learning, physicists and biologists relying on sophisticated mathematical methods as a matter of course. It coins the term "dual citizens" for people professionally aligned with two or more disciplines at once, evidenced by which conferences they attend and which departments they belong to — and argues the field's health depends on welcoming them rather than policing who counts as a "real" mathematician. The book backs this with data: NSF grants outside its own Division of Mathematical Sciences were found to be publishing in journals with clearly mathematical content, showing the discipline's true footprint is broader than its funding structure recognizes.

Why It Matters

This is a general diagnostic for when a field's institutional map (departments, journals, funding lines, job titles) has stopped matching its actual footprint. Wherever that gap opens, two failure modes appear: people doing the field's real work go uncounted and unsupported (because they're not "labeled" correctly), and the field's own institutions become slower to recognize where the frontier has actually moved. Recognizing boundary erosion early — rather than defending the old boundary — lets an institution redesign around where the work now lives instead of where it used to live.