In defense of curiosity driven research

A surprising feature of the recent 2026 NSF budget is that while the total cut amounts to 55%, the funding for research has been cut 61%. The specific cuts for the hard sciences are even more drastic. Thus the division of Mathematical and Physical Sciences, which includes mathematics, physics, chemistry, and astronomy, is cut by 67%. A large part of the cuts reflect the reasonable intention of the Trump administration to cap indirect costs¹ for universities, often exceeding 60- 65% of a grant, to 15%, or to reduce support of activities not directly tied to research. Still, one cannot fail to notice that fundamental research is getting the shorter end of the stick. The expressed goal, to “harness the full power of American innovation by empowering entrepreneurs and fostering private-sector creativity” has little to do with what NSF is uniquely capable to do, that is to support important “curiosity driven” projects that cannot be funded by the private sector.

A possible reason for the pro-technology priorities of the Trump administration was voiced by its current science advisor, Michael Kratsios, who is quoted as claiming that federal science funding is experiencing diminishing returns. “Money spent does not correlate with scientific impact,’’ Kratsios said in a recent address to the National Academy of Sciences. He is not the only one to make such statements. Peter Thiel, who is one of our most thoughtful business leaders and public intellectuals, has often made even stronger and more pointed such remarks.

Kratsios's statement is almost certainly true, for many different reasons, but I doubt that diverting funding from fundamental research to “empowering entrepreneurs” will do anything to change the situation. At a time when scientific competitiveness with China is becoming more and more acute, this is clearly a matter of national importance.

Some of the top reasons for the “diminishing returns” can be traced to ill-advised policies of NSF itself, especially with regard to STEM education, DEI and social sciences. One can argue that funding for STEM education, done through notoriously incompetent schools of education, has not only not helped, but may have even contributed to the present catastrophic state of US math and science education. One can make a similar case about the net negative societal impact of many of the social sciences, dedicated more to the promotion of so-called “social justice” and radical gender ideology than to the pursuit Truth wherever it leads. Social sciences are also most responsible for the ongoing replication crisis.

DEI is another major internal NSF reason for diminishing returns on science funding. According to the 2022-2026 NSF strategic planning document, the top core values based on which NSF makes its decisions are, in order: scientific leadership, diversity and inclusion, and integrity and excellence. Long before the current obsession with DEI, the USA had by far the most diverse STEM scientific community compared to any time in history and anywhere in the world. It just did not have the strict equality of outcomes that the current crop of racial or gender centered bureaucrats are obsessed with. People everywhere in the world, including myself, were attracted by US scientific institutions because of their merit-based policies, excellent working conditions and unique concentration of talent. The recent DEI policies pursued by NSF, up to this 2026 budget, have had the unfortunate impact of diluting considerations of scientific merit with a mishmash of other, irrelevant, ones, mostly based on race and gender, but also on age or the geographic area of the country in which the research is to be done. Some form of misplaced sense of “we need to spread the funding around” is clearly at play.

The reasons for the diminishing returns of science funding are not only those internal to NSF; various other external reasons² also contribute to the perception of a slow-down of scientific progress in the US and the rest of the world. In this essay I want to focus on one specific reason for this perception, one which goes to the heart of what is meant by “curiosity driven” research, that is research which is not driven by specific applications, technological or otherwise, but attempts to deepen our understanding of an important theoretical matter.

The assertion of a slow-down depends on specific expectations of how progress is to be measured. If your expectation is that funding in fundamental research has to translate into the discovery of new basic physical laws of nature, something that has happened only a handful of times throughout the entire history of science, then you are bound to be disappointed. By contrast with the first three quarters of the last century, which saw the birth of two major scientific revolutions (relativity and quantum mechanics) followed by an unending number of dramatic applications to astrophysics, particle physics, and chemistry, the last fifty years may indeed seem uneventful.

This extremely ambitious definition of progress, however, is profoundly unrealistic. It ignores, among other things, the essential role of mathematics, not just in devising new physical laws, but also in the exploration of the deeper, hidden, consequences of the old ones. In her excellent book Lost in math Sabine Hossenfelder provides a broad perspective of the current sense of crisis that exists in theoretical physics. She attributes this to two main factors, the dearth of new data, due to the enormous expense required by new high energy experiments, and the failure of the current mathematical theories to either explain the current experimantal data, or to provide a satisfactory mathematical basis for the merging of general relativity with quantum mechanics, one that does not lead to unpalatable conclusions, such as the existence of infinitely other alternative universes, the Landscape or, to use a more fashionable language, the Multiverse.

But mathematics interacts with physics not just by providing ready-made mathematical structures which theoretical physicists can play with. It also undertakes the task of probing the far-reaching consequences of older, established, physical theories. Euclidean Geometry provides a perfect example of an ancient “physical theory” of empty space, which was developed by mathematicians for centuries after Euclid, as a pure “curiosity driven” mathematical discipline which, through the parallel developments of algebra, Cartesian geometry, calculus and the revolutionary works of Gauss, Riemann, Poincare, Weyl, Cartan and others, grew to the point of having profound consequences for modern theoretical physics; both special and general relativity and the gauge field theories of particle physics. The mathematics of quantum mechanics itself would be inconceivable without complex numbers, discovered in the context of solving algebraic equations of degree 3 and higher, or the works on the foundations of Newtonian mechanics, due Euler, Lagrange, Jacobi, Hamilton, Noether, etc. We owe to their work a fundamental reformulation of the laws of Physics, without which modern research in theoretical physics would be inconceivable.

The mathematician working on a physically inspired problem lifts it to the idealized space of pure mathematical considerations where he is free to make unexpected connections to other problems, to make simplifications or generalizations according to the inner logic of the problem and his or her personal taste³. This unique investigative process⁴, free from the need to be directly relevant to physics, is what led Einstein to state⁵ that “the truly creative principle (in the natural sciences) resides in Mathematics.”

Pure mathematical considerations have not only had profound consequences on our present understanding of the physical laws of nature, they have also had numerous transformative effects on technology. It suffices to point out that behind the ubiquitous, life saving MRI's , data analysis techniques, or the extraordinary achievements of large language models, or any other AI models for that matter, lie sophisticated mathematical algorithms based on mathematical ideas discovered long before they were found useful in these or any other unrelated applications.

One could argue that this free creative spirit of mathematics exists independent of NSF funding, or even that the funding may in some sense hurt it. But it is unquestionable that its existence has helped attract the world's best mathematicians to the US and that their presence here has helped maintain the dominance of the US in science and technology. Cutting NSF funding in its core mission, that is to encourage curiosity-driven research, may not stop progress, but it would almost surely drive the best and the brightest to those places, such as China today, which make aggressive efforts to attract them.

1. Universities have often diverted these unreasonably large indirect costs to bureaucratic initiatives which have little to do with the specific needs of the grants.

2. There are other unfortunate, unintended, consequences of NSF funding even when the evaluation process is fair and based on the recommendations of top experts in the field: 1) It often leads to resistance against new, unproven, research directions. Legitimate biases of an older generation of experts may make it difficult to stop funding a dead-ended research direction or to initiate the funding for a new promising, but not-yet-proven one. 2) Given the enormous influence of NSF funding on the career of a researcher, the evaluation process stimulates extravagant exaggerations of progress or even sheer intellectual dishonesty in some cases. 3) NSF funding has contributed to an exponential increase in the number of published papers in all areas of STEM. It has also led to an extreme fragmentation between various subfields, with less and less communication between them. The large number of papers being published, with the vast majority of them being mediocre or worthless, has produced a severe cluttering effect, a situation which makes it difficult to detect worthwhile directions from the background noise.

3. The great 19th century mathematician Poincare described this “as the feeling of mathematical beauty, of the harmony of number and form, of geometric elegance”.

4. Mathematics continues to make steady progress in that sense. The last century has seen, for example, tremendous progress in the analysis of partial differential equations of various types, in particular those which are at the heart of subjects such as continuum mechanics and general relativity.

5. On the Methods of Theoretical Physics” -Philosophy of Science, Vol. 1, No. 2 (Apr., 1934), pp.163-169.