what is a discovery

Here's my definition: a scientific discovery is the cataloging of a principle about how the universe works. For example, discovering the neutron. Or finding the molecule that causes the scent of pine trees.

A "principle" doesn't necessarily mean some reduction of the complexity of our understanding of the universe. Often it is the opposite: like the early experiments in quantum mechanics created more complexity in our theory of the universe. A principle somehow reduces the number of unexplained or unaccounted physical phenomena we observe though. Like the fundamental forces, natural selection, and a chemical bond all provide better accounting of empirical observations. If you take that viewpoint, it should seem clear that science has some endpoint when we've enumerated all of these principles.

Certainly there may be a long tail. There will be some long list of testable hypotheses that require insane cost (e.g., 100 TeV particle accelerators) or are at the end of some kind of technology chain that requires many engineering breakthroughs. Like getting physical samples from a pulsar. But, that long tail will mean we should expect to see a decrease in scientific productivity. There should be a natural ordering as we identify and catalog easy discoveries, meaning what is left will necessarily take longer.

discovery is getting harder

We see empirical evidence for declining productivity of science from multiple independent sources:

1. The time between Nobel Prize work being completed and awarded is increasing, meaning it's harder to identify ground-breaking work. ¹

2. The cost of research and development of drugs is increasing, meaning there is a continuous decline in productivity of pharmaceutical research. ²

3. There are fewer disruptive papers published per year, even controlling for amount of papers and journal quality. ³

4. The cost of major discoveries is doubling every decade in inflation adjusted dollars, far outpacing the increase in scientific funding. ⁴

5. Papers are requiring more specialized technical expertise, with the average number of co-authors increasing from 1 to almost 5 over the last 50 years. ⁵

This viewpoint has been articulated by John Horgan in general audience book End of Science and recently from a variety of metrics by Bloom et. al. ⁶ It seems like a reasonable hypothesis and there is clear evidence from multiple sources. I would say that, yes, there is a decrease in consensus "major" discoveries.

is discovery really finite?

There is a counterargument to be made though. There are emergent complex systems in the universe that beguile a reduction down to fundamental principles. Like the biology of ants. It may require many more years of fundamental research to understand all components of ant behavior. Like how they collaborate. Why army ants from one colony do not attack other colonies of army ants, but do attack non-army ant colonies. Biology is littered with these complex phenomena that could consume 100 PhD theses. Assuming no pause in life on earth, evolution should continue to produce such systems as well.

Another example is mathematics -- there should be no end to theorems and no end to discoveries. And since most of mathematics is created by humans, rather than the result of physical observation, there may be no end to discoveries in mathematics. There are always new problems in math that come from humans creating new structures that are then explored. Certainly, we can always find more digits of $\pi$!

I used to do physical simulations of particle systems - like Ising models or Potts models. These simulations can be written in a few hundred lines of computer code, and yet there have been thousands of papers published on observations and principles from Ising model simulations. Like performing multiple parallel simulations at different temperatures or complex sampling procedures.

Ants, math, or Ising models may sound trivial to you. Consider human diseases. There are 3 billion base pairs in the human genome and any one human has 3-4 million differences from a hypothetical "reference" genome. 3 billion choose 3 million is an enormous number far beyond the number of atoms in the universe. Every one of those variations contains diseases - at least, currently every human eventually dies of some disorder. Identifying and curing all human diseases is a task with a finite end - once humans no longer die of disease. But a cataloging of all the effects of these mutations may lead to an astronomical number of discoveries. Then, you can repeat the process of all organisms on Earth. Then for hypothetical organisms - either from Eath's past or a simulation of Earths' future. Then for all hypothetical organisms in all hypothetical habitable planets.

There is this category of "labyrinth" tasks like modeling behavior of ants, uncovering the principles of Ising models, and characterizing all human mutations that admit a near endless supply of discoveries. We are also inventing new labyrinths all the time by creating new complex systems for discovery. Like equivariant neural networks, normalizing flows, and Wordle; all topics that were recently defined by humans and have many discoveries left to yield.

This brings me to a hypothesis: scientific discoveries are fundamentally narratives written by humans, for humans. There is an infinite number of discoveries available to us, and the choice of what we elevate to be a "novel scientific discovery" is a human preference decision. Discoveries are story telling exercises. They of course have to be supported by evidence, and even better if they have concise equations and neat explanations.

Some subsets of scientific discoveries helps predict the universe better - like when the sun will rise and what effect fertilizer will have. But, another set only better describes some endless supply of complex systems that humans define: like branches of math, biology of an Orca Whale, or the properties of a novel high-entropy alloy. The line is blurry between these two. I believe what separates an amazing scientific discovery from a trivial restatement of an obvious fact of the universe is human judgement.

information theory

Obviously there is a ton of prior art in defining and accounting for discoveries. Bayesian design of experiments provides tools for assessing hypotheses and experiments.⁷ Solomonoff inductions, which are related to Kolmogorov complexity, provide a nice thought experiment for articulating a discovery as a finite program.⁸ And if you define a discovery as a predictive model, there are many tools like Bayesian hierarchical modelling, to compare models. These are regularly used in specific domains, although usually they are secondary to empirical performance.

These tools have utility when in some kind of constrained setting. Like you either limit yourself to sampling from a specific distribution (e.g., you're observing a single black box function), or there is some finite set of discoveries that you're ranking. They become incomputable, or meaningless, when trying to determine if an accounting of bird populations in California in 1491 is a new discovery or a restatement of known population dynamics. Or, if proving a dominating strategy in a competitive card game is significant enough to be counted as a scientific discovery.

discussion

When I flip through Science magazine's recent research articles, almost all of them are instances of discoveries of unknown utility. But high interest from other scientists. This week (May, 2025, Vol. 388, No. 6746) there are articles on mechanical properties of flowers, North American bird population declines, how RNA binds multivalently according to Cryo-EM, and characterization of a new trimetallic Cerium catalyst that has high selectivity for propylene for dehydrogenation of propane. These are all basic discoveries very much from the well of infinite discovery. They may be part of an ongoing path that leads to better control of RNA, or maybe better design of catalysts, but their utility is unknown and their rise to significance is from judgement of human scientists of interest, not expected utility on humanity.

Let's compare with Vol. 30 (1909) about 100 years ago. There is a letter titled "Determination of the Coefficient of Correlation" by Karl Pearson, who invented the correlation coefficient, an article from Lewis (inventor of modern theory of acids and bases), an update on the campaign against Tuberculosis in the United States, and a description of a simple construction of an interferometer. I truly pulled this issue randomly and all the items here are of shockingly high utility. A simple argument could be that the utility of the articles today - about say Cerium catalysts - will reveal themselves to be significant in 100 years. I guess we cannot prove it today, but the statistics earlier in this essay are compelling measures that this will not be true.

So how do we reconcile these? I believe the pace of discovery is not declining and we will not run out of discoveries, but the utility of an average discovery is declining. Maybe this is only a consequence of trying to fit discoveries still into one research paper at a time. Maybe I'm just cynical and nihilistic, and scientists of all generations believe this to be true.

artificial intelligence

As the process of discovery becomes automated by robotics and AI, the role of a scientist will move towards a "science curator." Our role is to decide what is interesting enough to report as a discovery.

I was intrigued with Akshay Venkatesh's lecture about evolving role of humans in the domain of mathematics.⁹ He has the correct gist of what the future will be for science, in my opinion. We will become the deciders of where to orient research automation -- what questions to ask. So if you want to build an AI Scientist, make sure you have a way to capture good human taste.

scientist-engineer

It does make me wonder if there is a more direct way to measure "utility" of a discovery. I think the concept of an AI scientist-engineer - an AI scientist that makes discoveries oriented around an engineering outcome - is a more tractable and steerable problem. For example, identifying a better catalyst for converting carbon dioxide to aviation fuel is something that requires a number of discoveries that can then be ranked according to their progress towards the desired engineering goal.

A human health AI scientist-engineer could be another example. Rather than any discovery about human biology being desired, an AI scientist-engineer in would be steered towards curing specific diseases via discoveries. We are not judging based on human assessment of the discoveries, but rather on their ability to be links in a technology chain that leads to a therapeutic.

reflection

I think there are two paths forward for automating science.

Down path 1, we do our best to sample intelligently from an infinite well of discovery. It makes sense to build preference models, focus on interesting hypotheses, and judge success of an AI scientist on number of high-impact papers.

Down path 2, we pick a concrete goal. A measurable outcome or change in the universe we want to effect. Curing diseases. Making new materials. Catalyzing new chemistries. Then we judge our discoveries against progress towards the goal. There is not an infinite well of discovery, but instead of set of specific discoveries we need to find.

Footnotes

1. The Nobel Prize delay https://arxiv.org/abs/1405.7136; The Nobel Prize time gap. https://www.nature.com/articles/s41599-022-01418-8 ↩

2. Eroom's law https://en.wikipedia.org/wiki/Eroom%27s_law ↩

3. Park, Michael, Erin Leahey, and Russell J. Funk. "Papers and patents are becoming less disruptive over time." Nature 613.7942 (2023): 138-144. https://www.nature.com/articles/s41586-022-05543-x ↩

4. me, https://diffuse.one/p/d1-003 ↩

5. Analysis of 10.6084/m9.figshare.17064419.v3 ↩

6. Bloom, Nicholas, et al. "Are ideas getting harder to find?." American Economic Review 110.4 (2020): 1104-1144. https://doi.org/10.1257/aer.20180338 ↩

7. Berger, James O. Statistical decision theory and Bayesian analysis. Springer Science & Business Media, 2013. https://link.springer.com/book/10.1007/978-1-4757-4286-2 ↩

8. Rathmanner, Samuel, and Marcus Hutter. "A philosophical treatise of universal induction." Entropy 13.6 (2011): 1076-1136. https://www.mdpi.com/1099-4300/13/6/1076 ↩

9. https://www.youtube.com/watch?v=vYCT7cw0ycw ↩