Attention is all we have

Some people are smarter than others—and some are fabulously smart. We may disagree on many things, but can we at least agree on that?The origin of cognitive inequality is a hot, divisive topic. The existence of cognitive inequality is hardly controversial. We do struggle to come up with a satisfactory definition of intelligence, especially in its most creative and socially valuable forms, but most agree that people like Leonardo da Vinci, William Shakespeare, Nikola Tesla, or John von Neumann were extraordinarily intelligent.This aligns well with my experience in pure math academia, where careers and even personal identities are shaped by the shared perception of a mesmerizingly wide cognitive gap between mathematicians. This is a central theme in their discussions and a source of both fear and admiration.Yet for all the culture wars on the origins of cognitive inequality, there is little debate on its very nature.When someone is unusually smart, what is going on in their brain? This is a different question from “where does cognitive inequality come from?”, and also from “can we really measure it?” (another controversial topic).It is a basic, foundational question that stems from two widely accepted facts—that some people are smarter than others, and that intelligence is a manifestation of brain activity—and asks for the natural follow-up: what is really going on? What are the physical differences between the brain of a super smart person and the brain of a normal person?Despite its adjacency to some of the most contentious issues in science, this topic has remained relatively quiet. It might be because of this very proximity.Or maybe the question is too simple and natural. Five-year olds love to ask brutal questions like this one, but grown-ups are usually more hesitant, as they don’t want to come across as unsophisticated.Or perhaps this is because there were historical precedents where people went looking for answers and came back empty-handed. The brain of Carl Friedrich Gauss sits in a jar on a storage shelf somewhere at the University of Göttingen, and is so unremarkable that it remained mislabeled for over a century without anyone noticing. After Albert Einstein died in 1955, the pathologist removed his brain without the permission of the family, preserved it in formaldehyde, and dissected it into hundreds of slices—some researchers claimed to have observed peculiarities in the samples, but these findings are generally regarded as unconvincing.If we stick to solid science, there is remarkably little we know on the subject.But here’s the catch. While the simplest and most natural question remains unaddressed, people continue to rely on the same flawed brain metaphors and the same dubious biological assumptions. This only adds to the confusion around IQ and the heritability of intelligence.For example, people marvel at the “speed” and “working memory” of von Neumann’s brain, as if it were a CPU with a unique clock speed and L1 cache. But from a biochemical perspective, what could this even mean?Genes code for proteins, which assemble into cells, which assemble into tissues. Within-species genetic variability isn’t about new genes coding for new proteins with new functional roles that open the possibility for radically new architectures—it is about minute variations in the quantity and conformation of the same proteins, which retain the same overall structures and functional roles.It is true that these minute variations compound over embryogenesis and life, resulting in sizable physical and physiological differences between individuals. Yet it is also true that all human beings are built with the same architecture and the same functional blueprint. It’s not like some people have normal hearts while others have 500 horsepower turbopumps. And it’s not like some have Snapdragon 8 smartphone processors in their brains while others have NVIDIA H200 Tensor Core GPUs.To stick with this terrible CPU metaphor, it’s more like some people have a Snapdragon 7 while others have a Snapdragon 8—the performance gap is noticeable, but everybody runs the same apps.There is one caveat to that. Genetic anomalies can derail brain development and hamper its normal functioning. A Snapdragon 8 with a defunct thermal management probe will not operate properly. Phenylketonuria, also known as PKU, is an example of a recessive genetic condition that, if untreated, can lead to microcephaly and severe learning disabilities.By contrast, there is no accidental change to a Snapdragon 8 that magically turns it into an NVIDIA H200. This probably explains why we have never found any specific mutation that causes a drastic increase in cognitive ability.Yet, still, there MUST be a physical difference between the brain of a super smart person and that of a normal person. If not, where would the cognitive difference come from?Throughout my journey as a pure mathematician, it often struck me that progress wasn’t only about mathematics itself, but also metacognition and emotion control.Like many math students, I started out with a strong hereditarian prior, because I couldn’t think of an alternate model for the shocking inequality pattern around me—which, clearly, couldn’t be explained by social determinism.Then, over time, I realized that genetic determinism was equally problematic, not least because it couldn’t account for my own progress trajectory.Later on, I found out that many prominent mathematicians had tried to articulate the idea that their talent was first and foremost a cognitive attitude. A famous example is that of Descartes who, in the opening lines of his Discourse on Method, insisted that he wasn’t particularly gifted:For myself, I have never presumed my mind to be any way more accomplished than that of the common man.Instead, he attributed his successes to his chance discovery of a miraculous “method” that, for all practical matters, is an assortment of metacognitive techniques aimed at improving the clarity and reliability of one’s intuition. If you were to generate a tag cloud of his favorite words, intuition, clear and distinct would stand out with massive fonts. The same themes can be found over and over again in the writings of Poincaré, Hadamard, Thurston, Grothendieck, and many others.This is part of a broader pattern where some of the biggest names in science have rejected the notion that they were born with unique abilities, insisting instead on their curiosity and stubbornness:Isaac Newton: “But if I have done the public any service this way it is due to nothing but industry & a patient thought.”Albert Einstein: “I have no special talent. I am only passionately curious.”Richard Feynman: “I was an ordinary person who studied hard. There are no miracle people. It just happens they got interested in this thing, and they learnt all this stuff.”Alexander Grothendieck: “This power is in no way some extraordinary gift—like an uncommon cerebral strength, (shall we say). . . . Such gifts are certainly precious, worthy of the envy of people (like me) who haven’t been blessed with them at birth, ‘beyond measure.’”Needless to say, these bold declarations have barely made a dent in the hereditarian carapace of the general public.To be clear, I completely get why most people find these statements absurd and hypocritical. I remember hearing Einstein’s “no special talent” quote when I was fifteen, and instantly hating it. Seriously, who wants to hear supermodels lecturing us on the importance of inner beauty? Then I became a professional mathematician and Einstein’s quote gradually felt less and less irritating. And, after I crossed a certain threshold in my career, it even appeared profound.If all these brilliant people failed to communicate their point, it might have been because they weren’t explicit enough about what they meant by industry, patient thought, or curiosity.This is a central theme of my book Mathematica, a Secret World of Intuition and Curiosity, which opens with Einstein’s “no special talent” quote and tries to fill in the missing details—what it means to do math, the unseen actions that we perform in our heads, the slow and gradual build-up of our intuition.We have no good words to discuss these things. No one ever explained to us what it means to think, meditate, imagine, reason, or dream.What is the neurological basis of these activities? What do they have in common? What differentiates them? What are their long-term effects on our brains? Could it be that some people practice them the wrong way, while others have stumbled upon remarkably effective techniques that radically transformed their capabilities?I am a mathematician, not a neuroscientist, and I didn’t get to these questions through theoretical considerations. Rather, I took the practical path of trying to become better at math, experimenting with myself, tinkering with my mental imagery, and doubling down on what worked best.On the surface, this is just a story about mathematics—and this part is fairly consensual.Most mathematicians agree on the phenomenology of “doing math”, and they often feel that traditional discourses about mathematics miss or misrepresent something fundamental about their inner experience.The consensus breaks down when discussing the consequences. Surprisingly, some agree that math talent develops through a specific mental practice that school never really explains, yet stick to the idea that it is primarily innate.This is where the relatively niche story of extreme mathematical talent collides with the much broader cultural and scientific issue of cognitive inequality.Mathematics is widely considered to be the purest and most “g-loaded” form of intelligence—the dispute about the actual thought processes of one-in-a-million outlier mathematicians reveals, at its core, a dispute about the fundamentals of human cognition.John von Neumann, the poster child of the math genius mythThis puts us mathematicians in an awkward spot, as our