I have a confession that probably won’t
surprise anyone who knows me well: I love reading books about mathematicians.
Not because I understand the dense mathematics. I struggled through four
semesters of calculus before scrapping paper and pencil in favor of letting a
computer do that heavy lifting. What fascinates me are the people themselves
and the stories behind their discoveries.
Mathematics produces some of history’s most
interesting characters. Eccentric geniuses, relentless problem solvers, and
obsessive thinkers who devote decades, sometimes entire lifetimes, to questions
that can be explained in a single sentence but defy solution for generations.
One that I’ve not yet read about in detail,
but has just jumped to the top of my list is the Hungarian mathematician Paul
Erdős. Erdős lived a life that almost sounds fictional. He owned little,
traveled constantly, collaborated with hundreds of mathematicians around the
world and published more than 1,500 papers. More importantly, he left behind a
remarkable collection of problems and conjectures that challenged future
generations to push the boundaries of human knowledge.
Many of those questions were deceptively
simple. Anyone could understand them. Solving them was another matter entirely.
One such puzzle, first posed in 1946, became
known as the unit distance problem. Imagine placing points on a flat plane.
We’ll call the number of points, n. Given n points in the plane, what is the
maximum number of pairs of points that are exactly one unit apart?
With 4 points arranged as a square of side
length 1, there are 4 unit-distance pairs (the edges). With 6 points arranged
as a regular hexagon of side length 1, there are 6 unit-distance pairs around
the perimeter, plus additional unit-distance pairs across certain diagonals. As
n grows larger, mathematicians ask: how quickly can the number of unit-distance
pairs grow? The challenge is finding the optimal arrangement of the n points.
It is the sort of question that sounds almost
trivial when stated aloud. Yet some of the brightest mathematical minds of the
twentieth and twenty-first centuries spent decades wrestling with its
implications. For eighty years, no one could fully resolve one of Erdős’s
central conjectures related to the problem.
Last month, unexpectedly, an artificial
intelligence system did.
I would encourage you to read this article in Ars Technica penned by Kai Williams,
who reports that researchers at OpenAI developed a reasoning model that
produced a proof disproving Erdős’ long-standing conjecture about the unit
distance problem. The result was reviewed by leading mathematicians, including
some of the most accomplished researchers in the field, and ultimately
validated as a genuine mathematical breakthrough.
The achievement is remarkable on its face. Yet
the more I thought about it, the less interested I became in the mathematics
itself. Because this story is not really about math. In fact, it is arguably
about the exact opposite.
For most of the public’s experience with
artificial intelligence, mathematics has been one of its weakest areas. Large
language models were never designed to be calculators. Prediction engines
leverage probabilities. Mathematic proof is deterministic, not probabilistic.
LLM’s were built to predict words and patterns
in language. Even a year or two ago, many of these systems still struggled with
math problems that competent high school students could solve. They
hallucinated answers, skipped logical steps, and often displayed far more
confidence than accuracy.
To be sure, LLM’s have improved at a
breathtaking pace. Modern reasoning models are dramatically more capable than
their predecessors. But mathematics has remained one of the clearest examples
of a domain where human expertise appeared secure.
What makes this breakthrough so fascinating is
not that AI became exceptionally good at geometry. It didn’t. Instead, it
approached the problem from an unexpected direction. The proof reportedly
emerged by applying concepts from algebraic number theory to a problem in
discrete geometry. To non-mathematicians, that distinction may sound
insignificant. To mathematicians, it is extraordinary. These are fields that
typically occupy different corners of the discipline. Researchers often spend
entire careers becoming experts in one area without deeply engaging the other.
The breakthrough emerged not from greater
specialization but from making an unusual connection. In many ways, the AI
behaved less like a specialist and more like what I would coin a Synthesist.
A Synthesist is someone capable of drawing connections between disciplines that
rarely interact.
For centuries, human progress has largely been
driven by specialists. As knowledge expanded, we divided it into disciplines
and sub-disciplines. Scientists became physicists, chemists, biologists, and
engineers. Physicians specialized in organs and systems. Economists focused on
markets while sociologists studied societies. Specialization made sense. There
was simply too much information for any individual to master.
The modern world was built by experts. Yet
history’s most transformative breakthroughs often occurred when ideas crossed
boundaries.
● The transistor emerged from the
intersection of physics and engineering.
● Biotechnology arose from the
convergence of biology and computing.
● Modern logistics combines
mathematics, economics and operations research.
● GPS fused theoretical physics
(Einstein’s relativity) with engineering.
● The Internet represents the
collision of telecommunications, computer science, military research, and human
behavior.
Innovation frequently happens not within a
discipline but between disciplines. Humans have always possessed this
capability. We often call it creativity, but another word may be more precise.
Synthesis. The ability to connect ideas that appear unrelated and discover
something new in the intersection.
Creativity is often portrayed as something
mystical, but in many cases it is simply the ability to connect ideas that
previously appeared unrelated. A scientist notices a pattern from another
field. An entrepreneur applies a solution from one industry to another. An
inventor combines existing technologies into something entirely new. The
individuals most adept at this process are Synthesists.
The challenge is that human beings have
limits. No matter how intelligent or educated a person may be, there are only
so many fields they can deeply understand. Every year spent becoming an expert
in one area is a year not spent mastering another. The very process of
specialization that creates expertise also narrows perspective.
Artificial intelligence operates under
different constraints. An AI model can absorb literature from mathematics,
medicine, economics, philosophy, engineering, history, and countless other
fields simultaneously. It does not spend 20years building a career inside
a single discipline. It does not join conferences attended only by members of a
particular specialty. It does not inherit the institutional assumptions that
naturally develop within professional communities. (Well, not too much – there
may still be data bias to overcome).
As a result, AI may be uniquely positioned to
discover connections that humans overlook. That possibility raises questions
far larger than mathematics. What if the next breakthrough in medicine comes
from an unexpected relationship between oncology and network theory? What if
advances in energy storage emerge from patterns discovered in biology? What if
solutions to environmental challenges arise from concepts borrowed from
financial markets or evolutionary systems?
History shows that valuable insights often do
not come from digging deeper into a field but rather from connecting multiple
fields together.
Consider the Renaissance. It wasn’t driven by
specialists. It emerged from the fusion of art, science, philosophy,
engineering, religion, and commerce. Leonardo da Vinci is the embodiment of a
Synthesist. Da Vinci wasn’t the world’s greatest painter, engineer, anatomist,
or inventor. He was uniquely valuable because he built first-principles
knowledge in many fields and then moved between all of them.
History’s greatest Synthesists all moved
freely between subjects. Aristotle synthesized ethics, politics, biology, and
logic. Ibn Sina was a physician, philosopher, astronomer, mathematician,
theologian, and political advisor. Alexander von Humboldt, connected
“everything to everything else” via his work as a naturalist, geographer,
explorer, ecologist, and philosopher. Benjamin Franklin synthesized science,
diplomacy, philosophy, and public policy.
Even modern AI systems of today originated
from cross-discipline thinking. Herbert Simon worked in economics, psychology,
political science, cognitive science, and artificial intelligence. He won a
Nobel Prize in Economics but helped create some of the earliest AI systems. His
work focused on how humans make decisions, bridging the gap between machine
reasoning and human cognition.
What is common between these examples is that
these individuals were not constrained by academic boundaries because those
boundaries barely existed.
In more recent times we have siloed and
specialized. The great innovators of the last two centuries have predominantly
been specialists. The scientific revolution, the industrial revolution, and the
information age rewarded deep expertise. Society needed chemists who understood
chemistry better than anyone else. Physicists who understood physics better
than anyone else. Engineers who could solve increasingly complex technical
challenges.
We educate people based on their major, highly
limiting their ability to take “elective” courses outside of their
specialization. We hire based on narrow expertise. We organize companies around
skill set groups. Specialization has become the norm.
But if AI becomes increasingly capable of
mastering individual domains, the value of human contribution may begin to
shift. The great discoverers of the future may look less like specialists and
more like philosophers. More like Synthesists.
That possibility carries profound implications
for education. For generations, parents and educators have encouraged students
to choose a field, develop expertise, and build careers around specialized
knowledge. It has been excellent advice.
I would argue that today, expert knowledge is
abundant. AI has created that abundance nearly overnight. There is little
reason to spend excess resources on developing deep domain expertise. Imagine
if every student carries an AI companion with access to more technical
knowledge than any human could accumulate in a lifetime?
In such a world, knowledge itself may no
longer be the scarce resource. Armed with a solid foundation of first
principles across many disciplines, that student can now focus on where AI is
not particularly adept. While expertise is abundant, judgment remains scarce.
Curiosity is scarce. Imagination is scarce. The ability to ask meaningful
questions may become more valuable than the ability to recite established
answers.
The educational challenge of the AI era may not be producing students who know more facts. AI already knows more facts. The challenge may be producing students who can recognize which facts matter, which assumptions deserve scrutiny, and which questions have not yet been asked. In other words, the goal shifts from information acquisition toward intellectual navigation.
Should our children focus primarily on
becoming experts, or should they spend more time learning how to think broadly
across disciplines, challenge assumptions, and identify connections others fail
to see? In other words, to become the next generation of Synthesists. This
could mean more focus on fields that are traditionally outside STEM.
Philosophy teaches first principles reasoning.
It forces us to examine assumptions and question accepted truths. Religion
wrestles with purpose, morality, and meaning. History provides a laboratory of
human behavior stretching across centuries. Literature explores motivation,
conflict, and the complexity of human decision making.
These fields rarely produce patents or
engineering specifications.
Yet they may become increasingly valuable if
AI assumes more responsibility for technical execution while humans focus on
determining which problems are worth solving in the first place.
The future may not belong exclusively to
engineers or scientists. Nor will it belong exclusively to machines. It may
belong to Synthesists. Individuals capable of combining human judgment, broad
first-principles knowledge, and AI-powered exploration. Those who can combine
human wisdom with machine intelligence. To individuals capable of asking
questions that span disciplines and then partnering with AI to explore answers
at a scale no previous generation could imagine.
If the Industrial Age rewarded labor and the
Information Age rewarded expertise, I believe the AI Age will reward synthesis.
Paul Erdős famously spoke of “The
Book,” a mythical volume in which God kept the most elegant proof of every
mathematical theorem. Mathematicians, in his telling, spent their lives
searching for glimpses of its pages. For generations, those pages remained
hidden from view. The unsettling possibility before us today is that artificial
intelligence may not simply help us read the Book.
It may begin opening chapters we never knew
existed. The question for humanity is whether we will still be the authors of
the questions worth asking.