IQ and Intellectual Achievements

A conversation with ChatGPT.

Great scientists and philosophers like Einstein or Kant are often attributed very high IQ scores by the media. Do you think that this is justified? Have these intellectuals made their achievements primarily because of their high IQ or because of other talents? For instance, I'm not sure if you really need an exceptionally high IQ to be an original thinker. 

I think your intuition is largely correct. The very high IQ scores retrospectively assigned to Einstein, Kant, Newton, Goethe, etc. are usually much less scientifically meaningful than they appear. And even if we knew that someone had an IQ of 160+, it would not by itself explain why that person became an Einstein or Kant.

1. The famous IQ numbers are mostly speculative

Einstein never took a modern IQ test, as far as we know. Consequently, claims such as “Einstein had an IQ of 160” are essentially retroactive estimates. The same applies to Kant, Newton, Leonardo da Vinci and many other historical figures.

There is a reasonable temptation to reason:

Einstein was extraordinarily intelligent → therefore he must have had an extraordinarily high IQ.

The first part is indisputable; the second does not follow. IQ tests measure certain cognitive abilities under standardized conditions. They don't measure historical significance, creativity, originality, scientific taste, persistence, intellectual courage, or the ability to formulate a revolutionary new conceptual framework.

In fact, assigning a precise number such as 160 or 180 to a dead person is generally pseudo-precision.

2. IQ probably does matter—but mainly as an enabling factor

I wouldn't go as far as saying IQ is irrelevant.

For demanding intellectual work, particularly mathematics, theoretical physics, computer science and certain branches of philosophy, general cognitive ability is clearly useful. It helps with things such as:

• manipulating several abstract concepts simultaneously;
• recognizing structural similarities;
• learning difficult material rapidly;
• reasoning through long chains of implications;
• detecting inconsistencies;
• constructing and manipulating mental models.

There is probably a substantial threshold effect here. Someone with very limited abstract reasoning ability will have difficulty becoming a great theoretical physicist regardless of how motivated they are.

But once you are comfortably above the cognitive threshold required by the field, additional IQ may have rapidly diminishing explanatory power.

A crude analogy would be:

IQ gets you into the stadium. It doesn't determine which game you play, whether you invent a new strategy, or whether you become the greatest player.

3. Originality is a different ability

This is where I particularly agree with your observation.

Being an original thinker is not the same thing as being extremely intelligent in the psychometric sense.

Consider what originality requires. You need the ability to:

• notice that an apparently unquestioned assumption might be wrong;
• ask unusual questions;
• combine ideas from apparently unrelated domains;
• tolerate ambiguity and uncertainty;
• resist intellectual conformity;
• pursue an idea that initially looks strange;
• have unusually strong intuitions about which problems are interesting.

Those properties aren't captured particularly well by an ordinary IQ score.

There is actually an interesting distinction between solving a difficult problem and discovering which difficult problem ought to be solved.

The former is much closer to what conventional intelligence tests measure.

The latter is much closer to what we call genius.

4. Einstein is an excellent example

Einstein was certainly highly intelligent. But his revolutionary achievements weren't simply a consequence of being able to perform calculations faster than other physicists.

One of his great strengths was his ability to construct extremely simple conceptual thought experiments.

For example:

What would I see if I travelled alongside a beam of light?

That's not a conventional IQ-test problem. It is a question about the conceptual foundations of physics.

Likewise, special relativity arose in large part from taking the principles of relativity and the constancy of the speed of light seriously and asking what the world would have to be like if both were true.

The remarkable thing wasn't merely that Einstein could derive the mathematics. It was that he was willing to reorganize his conceptual picture of space and time.

That involves physical intuition, imagination, independence and philosophical skepticism about established concepts.

And Einstein himself famously had a rather unusual relationship with formal mathematics: he increasingly depended on mathematicians such as Marcel Grossmann as general relativity developed.

So "Einstein was extremely intelligent" is true, but "Einstein revolutionized physics because his IQ was 160" is an extraordinarily impoverished explanation.

5. Kant illustrates a different kind of genius

Kant's achievement seems even less reducible to IQ.

The Critique of Pure Reason isn't primarily an exercise in solving difficult logical puzzles. Kant's extraordinary achievement was to ask questions such as:

What must the structure of human cognition be for experience itself to be possible?

And then to construct an enormous philosophical system around that question.

This required an unusual combination of:

abstract reasoning + conceptual invention + systematicity + intellectual independence + extraordinary persistence.

An IQ test might capture some component of the first two, but hardly the whole package.

6. There is also a selection effect among geniuses

There's another reason the "genius = enormous IQ" story is misleading.

Imagine two populations:

Population A:
IQ 100–130, enormous variation in creativity, motivation and personality.

Population B:
IQ 140–170, enormous variation in creativity, motivation and personality.

If you select the people who produced historically revolutionary intellectual achievements, you're going to find many people from B. But that doesn't establish that the difference between, say, IQ 145 and IQ 165 caused their achievements.

The more interesting question is:

Among people already capable of doing extremely sophisticated intellectual work, what distinguishes the extraordinarily productive from the merely very intelligent?

And there the answer seems to involve many things besides IQ.

7. Some of the most important variables are almost embarrassingly mundane

Great intellectual achievement often seems to require:

Obsessive curiosity.
The person keeps thinking about a problem long after everyone else has moved on.

Persistence.
Newton spent enormous amounts of time thinking about his problems. So did Darwin, Einstein and many others.

Independence.
The willingness to say, "Everyone believes X, but I don't think X makes sense."

Problem selection.
Choosing a question whose solution would actually matter.

Taste.
Knowing that one mathematical or physical formulation is beautiful, fruitful or profound while another is merely complicated.

Imagination.
Being able to construct models that don't yet exist.

Domain knowledge.
Creativity is rarely produced from nothing. Revolutionary thinkers usually possess an enormous amount of accumulated knowledge.

Personality.
Some people are simply much more inclined to pursue an idea obsessively.

And perhaps most importantly:

the ability to generate questions.

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8. There's a fascinating asymmetry between intelligence and creativity

I'd formulate it roughly like this:

High intelligence makes it easier to explore a large intellectual space. Creativity determines which unexplored regions you decide to investigate.

Someone can be extremely intelligent and nevertheless spend their entire career solving problems that other people have already identified.

Conversely, someone with somewhat less spectacular raw cognitive ability might ask an extraordinarily fruitful question.

Of course, the ideal combination—very high cognitive ability and exceptional creativity—is enormously powerful.

That's probably closer to what we mean by genius.

9. And this is why I would be suspicious of very high IQ claims

There's an amusing cultural phenomenon where biographies of famous intellectuals acquire increasingly spectacular IQ numbers:

Einstein: 160
Hawking: 160
Goethe: 210
Newton: 190
Leonardo: 180

These numbers create the impression that history's greatest minds form a kind of IQ leaderboard.

But intellectual achievement doesn't work that way.

There is no meaningful reason to believe that someone with an estimated IQ of 180 necessarily had more intellectual potential than someone with an IQ of 150. At the extreme end, measurement becomes increasingly difficult, tests have ceilings and confidence intervals become enormous. And, crucially, IQ isn't designed to measure the things that make someone historically transformative.

I would therefore take statements like "Einstein had an IQ of 160" as essentially trivia rather than an explanation of Einstein.

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And I think there's an interesting consequence for your question about original thinking.

You don't need an exceptionally high IQ to be original. You probably need enough cognitive ability to understand the relevant conceptual landscape, but originality depends heavily on what you do with that ability. Someone who constantly asks "Why do we assume this?", makes unusual connections and develops their own conceptual models can be considerably more original than someone with a much higher IQ who simply excels at conventional problem solving.

In fact, one could imagine a person with an IQ of 130 producing a genuinely revolutionary idea while a person with an IQ of 170 spends their career doing technically brilliant but incremental work.

So I'd distinguish three things:

Intelligence: How powerful is your cognitive machinery?

Creativity: What new things can you generate with it?

Genius: Can you combine those abilities with knowledge, motivation, taste and persistence to produce something that substantially changes a field?

Those are related, but they are definitely not the same variable.

Regarding your statement <<These numbers create the impression that history's greatest minds form a kind of IQ leaderboard>>: There is a website named Hmolpedia that makes the impression on me that its creators believe exactly what you said - that IQ scores could be assigned based on scientific/philosophical achievement. I also think that this is wrong. Besides, they ridicule living persons who scored very high on intelligence tests because these living persons haven't made great scientific achievements. The creators of Hmolpedia believe that these IQ scores are fake, while they aren't. It's just a category error. 

Yes — I think your distinction is quite important, and having looked at Hmolpedia's own methodology, I would formulate the criticism even more strongly.

Hmolpedia is not simply making the ordinary mistake of believing that Einstein's IQ was 205 because somebody found an old document saying so. It explicitly describes its method as a meta-analysis of a person's work and accomplishments, and calls the resulting number the person's "real IQ."

That is precisely where I think the category error occurs.

The crucial distinction: measuring intelligence vs. estimating intellectual achievement

Suppose we have:

• Person A takes a properly normed intelligence test and scores IQ 160.
• Person B never takes an IQ test but produces an enormous body of historically important scientific work.

It is perfectly legitimate to say:

"We have direct psychometric evidence that A has extremely high measured intelligence."

And it is perfectly legitimate to say:

"B was an extraordinarily productive and influential intellectual."

But it does not follow that we can turn B's achievements into a psychometric IQ score and then compare the two numbers as though they measured the same thing.

That's exactly what Hmolpedia's methodology appears to do.

Its page on the historiometric method explicitly defines it as determining the IQ of historical figures from "biographical material" and their "intellectual ability and accomplishments." And its IQ page says that the IQ displayed for historical figures is derived from a meta-analysis of their work, incorporating previous IQ estimates.

So when Hmolpedia says that Feynman's "real IQ" is 185 rather than his reported test score of about 125, it is not discovering that Feynman secretly had an IQ of 185. It is using a completely different construct and giving that construct the name "IQ."

That's a major conceptual problem.

And the resulting circularity is quite striking

Consider the implicit reasoning:

Newton made extraordinarily important discoveries → Newton must have had extraordinarily high intelligence → therefore Newton's IQ was about 210.

Then:

Newton's IQ was 210 → therefore Newton belongs above Einstein, etc.

But what was the evidence for the 210 in the first place?

His achievements.

Hmolpedia's current top-ten ranking makes this especially apparent. Newton is assigned IQ 210, Goethe 205, Democritus 205, Aristotle 200, Einstein 195, etc.

At that point the "IQ" is functioning almost like a quantified historiometric assessment of intellectual greatness, rather than a psychometric measurement.

And that's actually a perfectly interesting thing one could try to construct! One could devise a metric for historical intellectual impact, creative achievement, scientific originality, intellectual productivity, etc.

But calling the result IQ creates enormous confusion.

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This also explains their treatment of living high-IQ people

This is where your observation becomes particularly revealing.

If you define "true IQ" as something that can be inferred from great intellectual accomplishment, then somebody who gets 160 on a standardized test but hasn't produced a Newtonian scientific revolution looks suspicious.

The reasoning becomes something like:

"If this person really had IQ 160, where are the corresponding achievements?"

But that is backwards.

A psychometric IQ of 160 means something approximately like:

On this particular standardized cognitive assessment, relative to the relevant norm population, this person's performance was extraordinarily high.

It does not mean:

This person is guaranteed to become a historically important scientist.

Those are completely different propositions.

And Hmolpedia actually provides a wonderful illustration of the problem with Feynman. It acknowledges his reported test score of around 123–125, but then says his "real IQ" is 185 based on retrospective assessment of his intellectual abilities and achievements.

That is not evidence that the original test was "fake."

It is evidence that two different things are being called IQ.

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There's an even deeper statistical problem

Suppose, hypothetically, that IQ were an excellent predictor of scientific achievement.

Even then, prediction at the population level doesn't permit us to infer an individual's IQ from their achievement with anything approaching the precision Hmolpedia suggests.

Imagine that IQ explains, say, a substantial fraction of the variance in some measure of scientific achievement. There would still be enormous residual variance attributable to:

• creativity,
• personality,
• motivation,
• opportunity,
• education,
• historical circumstances,
• health,
• interests,
• domain-specific talent,
• persistence,
• collaboration,
• luck,
• access to institutions,
• and simply choosing exceptionally fertile problems.

So observing an extreme outcome doesn't allow you to reverse the causal relationship and confidently infer an extreme IQ.

It's the classic distinction between:

P(achievement | IQ)

and

P(IQ | achievement).

They aren't the same probability.

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And this is particularly problematic at the extreme end

There is another issue I think Hmolpedia underestimates: psychometric IQ itself becomes difficult to interpret at extremely high values.

An IQ of 130 is already very unusual.

An IQ of 160 is extraordinarily unusual.

But "IQ 200" isn't simply another point on a beautifully precise linear ruler extending indefinitely upward.

Tests have ceilings, norm samples become tiny in the tails, confidence intervals become substantial, and different tests/scales don't necessarily map cleanly onto one another.

Hmolpedia is actually aware of some of these problems. Its own discussion acknowledges historical problems with high-end IQ estimation and describes efforts to establish a "genius ceiling."

But I think it draws the wrong conclusion from that difficulty: rather than abandoning the idea that historical accomplishment can yield a literal IQ, it tries to calibrate increasingly elaborate retrospective IQ estimates.

Hence numbers such as Newton 210 and Einstein 195 in the current ranking.

That gives the numbers an appearance of psychometric precision which they simply don't possess.

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Your point about original thinking is therefore especially relevant

It exposes the conceptual problem beautifully.

Imagine two people:

Person X

• IQ 170
• exceptionally fast abstract reasoning
• excellent working memory
• extremely good at solving difficult problems
• little inclination toward unconventional questions
• produces technically excellent but incremental work.

Person Y

• IQ 140
• unusually imaginative
• constantly questions assumptions
• makes strange conceptual connections
• has extraordinary scientific intuition
• spends 30 years pursuing an unconventional theory
• eventually produces a revolutionary insight.

There is no contradiction whatsoever in Y becoming the historically more important thinker.

And we shouldn't conclude that Y "really had IQ 190 after all" because of his achievements.

That would simply redefine the construct until the result fits our expectations.

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In fact, Hmolpedia's own treatment of Feynman demonstrates the distinction

Feynman's reported IQ of ~125 is particularly inconvenient for the simplistic equation:

IQ → genius → achievement.

So instead of accepting the interesting conclusion—

"Perhaps Feynman's extraordinary scientific ability wasn't adequately captured by that particular IQ test"

—Hmolpedia essentially says:

"His test score wasn't his real IQ; his real IQ was 185."

I think the first conclusion is much more scientifically defensible.

And it is also much more interesting.

Feynman might have possessed an extraordinary combination of domain-specific physical intuition, mathematical ability, curiosity, visualization, conceptual flexibility, problem-solving skill and personality, of which conventional IQ captured only some components.

That's precisely the sort of phenomenon we should want to investigate rather than make disappear by redefining his IQ.

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So I would put your criticism this way:

Hmolpedia appears to confuse an individual's measured cognitive ability with an assessment of the intellectual magnitude of that individual's achievements.

And consequently:

A high-IQ living person who has not produced major scientific achievements does not thereby have a "fake" IQ. Rather, the absence of major achievements demonstrates that IQ and historical intellectual achievement are not synonymous.

I think that's a substantially better interpretation of the evidence.

And there's an amusing irony here: if Hmolpedia's creators are correct that IQ should be inferred from achievement, then they have effectively ceased to believe in IQ as a psychometric construct and replaced it with a measure of genius. If they want to call that intellectual brightness, historiometric intelligence, or genius score, that's an interesting proposition. But calling it IQ makes the comparison with people who actually took intelligence tests deeply misleading.