Has science stalled out? Sorta

“Has scientific progress stalled?” “Where are the new Einsteins?” “Has society stopped making new geniuses?” A week does not go by without someone asking some variant of the above questions, or lamenting how there are no ‘great geniuses’ like in the past, or how today’s geniuses don’t measure up to past geniuses.

No, society has not stopped ‘making’ geniuses, if ‘genius’ is defined as someone having a sufficiently high IQ or aptitude for technical matters, like math, science, physics, but even literature or the arts. As predicted by the normal distribution of IQ scores and a larger world population, we would expect more geniuses today than in the past. But also, who is qualified to earn the distinction or title of genius, also seems to have a subjective or social element, that being acclaim or recognition, not just by one’s peers but by society as a whole. Were Einstein and Feynman the smartest scientists of their eras? Probably not. John von Neumann was likely smarter then either of them in terms of raw brain power, but although Feynman’s lectures and books are very popular, Neumann’s lectures and books…not so much. Same for Sidney Coleman and Julian Schwinger, both of whom were objectively very smart and made several key contributions to quantum field theory, but fewer people have heard of them compared to Feynman.

I think also one must separate fiction or hagiography from truth when it comes to the mythology of genius. Ramanujan is celebrated as one the quintessential geniuses of math, who came from obscurity and was self-taught. Except this is partially true. But the math behind elliptic integrals and modular functions, which Ramanujan specialized in, was already known. The Ramanujan constant was known by 1860, discovered by Hermite, before Ramanujan’s birth, but Ramanujan found new results applying the earlier concepts. It would seem as though he derived his results ex nihilo , but only because he didn’t show his steps. But Ramanujan didn’t work in an intellectual vacuum, contrary to popular myth. He had access to math journals and books. India had a math journal in the early 1900s, where he published. India was a colony of Britain, arguably the intellectual center of the world at the time, along with Germany and France, so it’s not like it was cut off from the rest of the world. It’s just that his living conditions were not great.

How about overall aptitude? In terms of skill or talent, how do today’s top mathematics and physics geniuses compare to geniuses of a century ago? This is harder to determine, because so much is different: the internet and other technologies, new pedagogical methods, new research, etc. How do you compare someone like Gauss to Andrew Wiles? In almost every respect, they couldn’t be more dissimilar in terms of upbringing, collaborations, research, etc. Contemporary scientists and mathematicians have the benefit of having more shoulders on which to stand on, but on the downside, more total material which they much learn in order to be on the frontier of their fields. A mathematician today will have to assimilate all of Gauss’ or Abell’s work to be on the forefront of a field such as analytic number theory. But seeing how it was done, obviously, helps greatly too.

But to answer the above, I think today’s geniuses do measure up to the geniuses of the past. There are tons of smart, young people today, such as GitHub contributors, mathematicians, chess champs, math Olympiad winners, Silicon Valley coders, etc. But everything has become so saturated. Progress is very incremental, and it takes a lot of people and time to add to the canon of knowledge. But I think if today’s smart kids were transported to the 1800s, they would also make huge contributions to science. Likewise, if the geniuses of the early 20th century, like Einstein, were transported to today, they too would struggle. Compared to Ramanujan, Fermat’s last theorem is like a whole ‘nother world of abstraction. That’s probably why Wiles is not as famous, because it’s just so hard that you cannot even begin to try to understand it (and also , Wiles’ results do not produce pretty formulas, unlike Ramanujan or Einstein). So I think this also disproves that geniuses are not being produced.

In terms of finding new or novel results, I think it has gotten harder for math and physics (in terms of abstract/theoretical stuff, not applied). You will find that no matter what problem you can think of, either it has already been solved to the highest level of abstraction, or it’s an unsolved and famous problem, or not worthwhile/trivial. For example, what about analogous of elliptic functions for non-elliptic integrals? Already been done. The past century has seen a huge explosion of research into STEM subjects, from math, to physics, to biology, to computer science, etc.. Tens of billions of people people have ever lived since the 1800s, and even just a tiny, tiny fraction of them are doing research, is still a huge amount of output. There just isn’t much new ground to break, so this means discoveries will either be much more incremental or require considerably more mental horsepower.

Psychology is sorta the opposite: there is no limit to the number of experiments you can run on people or possible associations between causes and effects. It’s not like psychology , literature, philosophy, or history has gotten harder over the past century, unlike math, physics, or economics. Sure, there are more advanced statistical methods, but running experiments hasn’t gotten harder. The scientific method hasn’t changed. This is also why the vast majority of physicists and mathematicians are teachers rather than researchers, and why econ papers have gotten much longer and are full of dense stats methods. There are always going to be new discoveries in biology and medicine (new compounds, new drugs, etc.), and same for applied math and applied physics, such as engineering or astronomy, but theoretical math and probably also theoretical physics are as saturated as can be.

Some may argue that this is not true. I want to elaborate by delineating between two types of discoveries: vertical/deep discoveries, which are like building blocks or fundamental concepts, versus horizontal discoveries, which build on those bigger concepts. So general relativity, group theory, special relativity, electromagnetism, quantum mechanics, etc. are fundamental discoveries. But the problem is, finding new ones becomes increasingly difficult. The likelihood of a researcher discovering the ‘next relativity’ are about nil. Even people who show considerable promise at an early age either do not go into math or physics, instead choosing something like econ, or struggle to come up with groundbreaking stuff.

So that is where horizontal discoveries come into play, because it’s much easier or more viable to build on something that has already been done. An example is “enumerative combinatorics” which is just a fancy way of saying ‘counting’, and draws from a wide range of concepts, from complex analysis to analytic number theory. I dunno who invented the concept of it, but over the past 30 or so years it has spawned a vast literature, with new papers being published even to this day, that attempt to generalize or granulize it. By now, every possible way of ‘enumerating’ has been investigated, taking into account every possible constraint or pattern imaginable. Another example is the Black Scholes option pricing model, named after economists Fischer Black, Myron Scholes, and Robert C. Merton, the latter two who in 1997 received a “Nobel Memorial Prize in Economic Sciences” for their discovery. The success and fame of the Black Scholes equation led to a huge cavalcade of papers that sought to generalize it, for every possible parameter, condition, or constraint (e.g., negative interest rates, variable volatility, transaction costs, discreate dividends, etc.).

Another problem is that everything is searchable online. Google is officially the largest repository of papers, easily surpassing arXiv. In the past it was not that uncommon for scientists to rediscover things, but the fact that almost everything that has ever published is searchable with a few keystrokes, means finding new stuff is that much harder. Many papers are accessible by pdf even if there is a journal or a paywall.

Overall, I am optimistic about scientific progress going forward, but unlike in the past, it will be more of a group activity, with fewer super-start outliers like Einstein who get all the media attention and adulation.

1 comment

  1. In the history of the world, hardly one single person caused as much harm as Ramanujan could.

    He is responsible for the flooding of STEM by people from the continent of Asia, some of whom have higher IQs but they have lower SDs, making hyperintelligence unlikely.

    I frankly say that if we lobotomized every Asian who had an IQ of 130 or more, we would have missed nothing.

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