Innovators are arriving at the frontier later and knowing less of it

Robert Gordon's layer is historical. The century from 1870 to 1970 delivered electrification, the internal combustion engine, running water, chemicals and antibiotics, each of which arrives once in a household and cannot arrive again, and the US productivity record across that period reads as a single wave rather than a trend. Bloom, Jones, Van Reenen and Webb's layer is an accounting exercise: write growth as the number of researchers multiplied by their productivity, measure both, and aggregate US research effort from the 1930s to the 2000s rose by a factor of 23 while measured research productivity fell by a factor of 41. Park, Leahey and Funk's layer is bibliometric, covering six decades and every field, and finds papers and patents becoming steadily less likely to displace the work they build on.

The middle layer supplies most of the figures in circulation. Sustaining Moore's Law took roughly eighteen times as many researchers in 2014 as in the early 1970s. The transistor density it bought grew at the same 35 percent a year throughout. In cancer research, the years of life saved per 100,000 people per clinical trial publication fell from more than eight in 1985 to just over one by 2006.

The bibliometric layer reached the newspapers and has held up worst. The disruption index it rests on responds mechanically to how many references a paper carries, to where the citation database is truncated, and to records carrying no references at all. Correcting for pre-1976 patent citation truncation removes 88 percent of the measured decline in patents. In an August 2026 Nature exchange the critics narrowed their claim from hidden drivers to partial drivers. The original authors replied that the corpus the critics had assembled contained 456 For Dummies guides, 50 Dr. Seuss and Curious George books, and the Captain Underpants series.

The accounting layer has a sampling problem rather than an arithmetic one. Fort, Goldschlag, Liang, Schott and Zolas assembled a 45-year panel covering the universe of US patenting firms from Census microdata. Patents per real R&D dollar rise from 1977 to 2017, and the within-firm elasticity of patents to R&D almost doubles from 0.26 to 0.48. They find statistically significant secular declines in only 2 of 18 specifications. Over the same period Compustat's coverage of US patents fell from 63 to 55 percent, and manufacturing's share of breakthrough patents fell from 73 percent to 12 percent. The firm-level evidence for a slowdown was drawn from a shrinking part of where the patenting was happening.

Total factor productivity, the quantity supposed to carry technology through all of this, is computed as whatever growth remains once capital and labour have been accounted for. Solow wrote on the first page of the 1957 paper that he was using technical change as shorthand for any shift in the production function whatsoever, including slowdowns. It cannot separate innovation from reallocation, it omits intangible investment, and it responded to the personal computer on a lag of roughly a decade. Ideas may also have become harder to find between 1970 and 2020 and easier since. Most of the empirical work on both sides is compatible with that, so part of the disagreement is about tense.

Jones collected the ages of 55,000 US inventors and built their individual patent histories from the Hall, Jaffe and Trajtenberg data. Age at first invention trends upward at 0.6 to 0.66 years per decade, robust to controls for technological field and team size. Team size on US patents rises 17 percent per decade. The probability that a solo inventor's next patent falls in a different technological category declines in 34 of 36 categories, implying roughly 6 percent greater specialisation per decade.

The companion paper looks at great inventors and Nobel laureates. The mean age at which they produced the work they are known for rose by about six years across the twentieth century, or about eight once controls are added. Productivity does not rise later in life to compensate for the delay.

The prediction that separates this from the obvious alternative explanations is the least dramatic result in the paper. Because innovators arbitrage income across fields, total educational attainment should show no variation across technological fields. Specialisation and team size should still be larger where the underlying knowledge is deeper, and the cross-section shows both. Longer doctorates, corporate hiring practice, credentialism and authorship inflation all raise age at first patent and team size. None of them produces a flat education profile alongside a varying team size.

Patents per US R&D worker fell roughly 50 percent after 1975, close in magnitude to the rise in team size over the same period. That gives an account of where the additional researchers went.

Knowledge is modelled as a circle of specialisms with a frontier at some distance from the ground. An innovator climbs from zero to the frontier in whichever slice of the circle she picks, and only from there can she push it outward. As the stock accumulates the climb lengthens, so she begins producing later and has fewer productive years remaining. She also narrows the arc she climbs, because narrowing is the only way to keep a lengthening climb finite.

Narrowing carries the consequence the rest of the argument rests on. An idea whose execution requires knowledge from an adjacent arc can no longer be carried out by one person, and requires a teammate who has climbed that arc. Team formation in this account is a forced substitution for breadth that individuals used to hold internally, rather than a preference or a fashion. Jones sets the mechanism against the fishing-out theories of Kortum and Segerstrom. Fishing-out has the orchard emptier, while the burden of knowledge has the orchard as full as it was and the ladder to reach it longer. The second is a claim about the fixed cost of getting into position rather than about the supply of ideas.

The connection between a mechanism in one field and a problem in another was historically made inside one head that had climbed two arcs of the circle. A rising burden of knowledge means fewer heads contain two arcs, so the connection has to be made across a team boundary. Crossing that boundary requires that someone already knows the other arc exists and bears on the problem.

Field-bounded literature search works against that, because the vocabulary of the other arc is different. The same mechanism is named differently, indexed under different terms and published in venues the searcher does not read. The constraint is the ability of the person holding the problem to recognise the result when it is written in a vocabulary he was never trained in. The years of training that would fix that are the cost Jones measured. A representation that is neutral with respect to field vocabulary acts on that cost rather than on the supply of results.

The two figures on our front page are measurements of people who did hold two arcs. Krauss (2024) reports 54 percent of Nobel Prize-winning discoveries coming from researchers who already held degrees in two or more fields. For major discoveries that did not win the figure is 42 percent. Root-Bernstein (2022) reports 84 percent of physiology and medicine laureates having combined two or more developed interests inside their own field, with peace laureates lowest at 54 percent.

Jones's evidence is US patents and US inventors, read in a 2009 paper from data that mostly ends in the 1990s. Age at first patent can rise from labour-market structure rather than from the length of the curriculum. The cross-sectional education result is a strong defence against that reading rather than a proof against it.

A corollary ties part of the theory to evidence the second section spent some time discounting. Wu, Wang and Evans analysed more than 50 million papers, patents and software products from 1954 to 2014. They found that large teams develop existing directions while small teams disrupt. If the burden of knowledge forces larger teams, and larger teams are less disruptive, then the mechanism predicts declining disruptiveness. It predicts it on the same CD index whose sensitivity to reference-list length is described two sections above.

Whether a retrieval or representation system measurably reduces the burden of knowledge is directly testable. As far as we have been able to establish it is untested, by us included. The experiment gives researchers structurally matched work from outside their field and measures their rate of cross-field citation, cross-field collaboration and output against a control group receiving ordinary field-bounded search results.