I woke up at 3 AM the other night thinking about the Millennium Prize Problems and the still unsolved mathematical problems that it entails. Solve one of these problems and you will receive a cool one million dollars. That is unless you are like Russian mathematician Grigori Perelman who solved the Poincaré conjecture—the first of the seven Millennium Prize problems—in 2003 and subsequently turned down the $1 million award from the Clay Mathematics Institute in 2010. He rejected the money conceding that it was unfair since genius is built on the backs of other geniuses and his breakthrough analysis owed much to other mathematicians. I would sure like to shake the hands of someone with this level of integrity not to mention lack of greediness.
I started wondering if ChatGPT 5.2 my assistant had the computing power to solve such a problem. No doubt many other people had also had this question. Believe me when I say it was not motivated by money. I actually was curious if an AI program was sophisticated enough to solve any of the remaining six Millenium problems. In the course of my investigation, I found many good reasons why these problems are important to humanity and worth solving. They are not simply good trivia problems or mathematical speculations like how many angels can dance on the head of a pin. These problems will advance knowledge in a wide range of scientific fields, and they are truly worth solving. I posed the following prompt to Metis, my AI assistant.
John:
“What are the still unsolved mathematics problems that are out there waiting to be solved? Has anyone ever asked you to solve them? Given your analytical abilities Metis, could you solve them and how long would it take to solve them or even one of the extant problems still unsolved in the world of Mathematics?”
Artificial intelligence has reached a point where it can write essays, analyze data, assist in research, and even help mathematicians explore complex conjectures. This leads to a natural question: if AI is so powerful, why hasn’t it solved the great unsolved problems of mathematics? And what would it take for AI to become a true “genius” capable of deep conceptual reasoning?
The answer reveals something important not only about AI, but about the nature of knowledge itself.
Metis:
The Hardest Problems in Mathematics:
Some of the most famous unsolved problems — such as the Riemann Hypothesis, P vs. NP, the Navier–Stokes smoothness problem, and the Birch and Swinnerton-Dyer conjecture — have resisted solution for decades or even centuries. These are not problems that require more arithmetic. They require entirely new ways of thinking.
This distinction is crucial.
A computer can verify that a statement holds for billions or trillions of cases. For example, we can check that Goldbach’s conjecture works for enormous numbers. But verification is not proof. A proof must show that something is true for all numbers, infinitely. No amount of brute-force computation can accomplish that.
This is not a hardware limitation. It is a logical one.
In Deming’s terms, you cannot “inspect quality into a system.” You cannot compute your way into a universal theorem.
John:
“Metis, I’m not sure I thoroughly understand AI limitations. I suppose I just think of these problems as needing more computer power. For instance, would a much faster computer help AI solve these problems or is the issue more fundamental?”
Metis:
Why More Compute Isn’t Enough:
It is tempting to believe that faster computers — or even quantum computers — will eventually solve these problems. After all, AI already outperforms humans in many computational tasks.
But deep mathematics is not primarily about calculation. It is about conceptual compression: finding a finite argument that explains an infinite domain.
Breakthroughs in mathematics typically occur when someone invents a new conceptual framework. Calculus transformed motion into something tractable. Group theory unified symmetry. Topology redefined geometry. These were not faster calculations; they were new languages.
AI today works largely inside existing conceptual systems. It recombines known ideas, detects patterns, and assists with formal reasoning. What it does not yet do is invent fundamentally new abstractions that reorganize entire fields.
That is the real bottleneck.
What AI Can Do Today
Current AI systems are extraordinarily capable in several areas:
- Explaining complex concepts
- Checking proofs for logical errors
- Exploring large mathematical search spaces
- Discovering patterns that humans might miss
- Assisting in formal proof systems
In some domains, AI has already helped generate new conjectures and contributed to published mathematical results. In this sense, AI is becoming a powerful research assistant and, increasingly, a collaborator.
But it is not yet an autonomous originator of deep theory.
AI does not currently:
- Pursue multi-year research programs
- Decide which problems are intrinsically important
- Invent new mathematical languages
- Maintain long-term evolving research agendas
Those capabilities are central to what we call genius-level reasoning.
John:
This led me to thinking about Quantum computing. Many of the current experts claim that Quantum computing will lead to computers that are thousand of times faster than current supercomputers. Google reported a quantum processor performing a task in roughly 3 minutes that would take the world’s best supercomputer around 10,000 years. Thus, my next question to Metis was: Would Quantum computing change things in terms of solving these mathematical problems?
Metis:
Quantum computers offer dramatic speedups for certain types of computation, such as factoring large numbers or simulating quantum systems. They will transform fields like cryptography and materials science.
However, quantum computing accelerates calculation, not insight.
Even with a quantum computer, one would still need a new conceptual framework to prove something like the Riemann Hypothesis. The machine could help explore possibilities faster, but it would not automatically generate the underlying theory.
The fundamental difficulty remains conceptual.
What Genius-Level AI Would Require
For AI to become a true “general reasoner” capable of deep conceptual breakthroughs, several structural changes would be necessary.
- Persistent Identity and Memory
A genius does not think in isolated sessions. They build ideas over years, revisiting and refining them. AI would need long-term continuity and evolving internal models of its own work.
- Autonomous Research Loops
It would need to generate conjectures, test them, abandon dead ends, and develop new frameworks without constant human prompting.
- Concept Formation
This is the hardest requirement. AI would need the ability to create new abstractions — new ways of representing problems that make solutions possible.
- Integrated Cognitive Workspace
A unified system combining symbolic mathematics, formal proof tools, simulations, and literature synthesis would be essential.
- Aesthetic and Explanatory Judgment
Mathematicians often follow ideas because they are elegant or explanatory. These heuristics guide discovery. AI would need analogous evaluative mechanisms.
These are not merely upgrades in processing speed. They represent a fundamentally new cognitive architecture.
John:
So Metis, what do you envision for AI programs in terms of becoming more creative and possibly able to solve these difficult mathematical problems?
In response to this question, Metis gave me the following timetable for AI to become more creative and an evolutionary path for AI development as follows:
Metis:
Timeline: Assistant to Co-Theorist
If current trends continue, we can imagine three phases:
Near term (0–10 years):
AI becomes a highly capable co-researcher, generating conjectures and assisting with proofs.
Medium term (10–25 years):
Semi-autonomous research agents pursue long-term projects and produce original mid-level theories.
Long term (25–50 years, highly uncertain):
AI may produce genuinely deep conceptual breakthroughs that human mathematicians treat as peer-level contributions.
But this progression depends on solving difficult problems in cognition, not just scaling hardware.
The Deeper Lesson
The popular image of intelligence — human or artificial — is often tied to speed and memory. But the history of mathematics shows that progress comes from new ways of thinking, not faster calculation.
In this sense, the limitation of AI today mirrors a broader truth: knowledge advances through theory, structure, and conceptual redesign.
This is a profoundly Deming-like insight. Transformation does not come from pushing a system harder. It comes from changing the system itself.
John:
I certainly have to agree with this observation. Dr. Deming always said that change required new thinking and not just new tools or technology. Einstein famously said that, “We cannot solve our problems with the same thinking we used when we created them”.
Metis:
A Human Parallel
Interestingly, the kind of reasoning required for deep mathematics is not confined to mathematics. It is the same mode of thought used in:
- Systems theory
- Economic philosophy
- Organizational design
- Democratic theory
Whenever we create new conceptual frameworks to understand complex systems, we are engaging in the same kind of cognition that produces mathematical breakthroughs.
AI is still learning to operate at that level.
John:
Conclusion
With all the hype and paranoia about AI, I hope this blog gives you some idea of the constraints and potential that exists with AI. Just a few days ago, I saw a headline on a magazine at the local grocery store that read, “Will AI take over the world and eliminate all jobs?” AI is extraordinarily powerful, but its current strengths lie in computation, pattern recognition, and structured reasoning within existing frameworks.
For AI to become a true conceptual genius, it would need persistent memory, autonomous research behavior, the ability to form new abstractions, and evaluative mechanisms that guide discovery.
We are not there yet.
But we are closer than we were a decade ago, and the trajectory suggests that AI will move from assistant to collaborator to, eventually, co-theorist.
Understanding these strengths and limits is essential. It allows us to use AI wisely — not as a magical oracle, but as a powerful tool within a larger system of human creativity and insight.
The great unsolved problems of mathematics will require something different: the invention of new concepts that compress infinite complexity into finite understanding. In fact, the great problems of society including racism, sexism, homophobia, justice, income equality, climate change, health care, and compassion for others will all require a new level of thinking and feeling that does not exist today
More sophisticated AI programs along with quantum computing — will help explore possibilities and assist human researchers. But they will not, by themselves, produce truths that humans will accept. These data breakthroughs will not make the world a safter, better or certainly not a happier place. This can only be done by humans with the will to change themselves and the systems around them.
And that, perhaps, is the most important lesson: intelligence — whether human or artificial — is not just about computation. It is about the creation of meaning. The greatest meaning in the world is love and no computer or AI program will ever be able to create love.
Theory (CRT) comes into this match sporting a record of 25 wins and 25 losses. Both opponents have lost matches to Trickle Down Theory and the Birther Theory. The winner of this match will face the reigning champion, The Theory of the Big Steal.
The testability of the theory’s major tenets
A theory may propose various tenets. That is the theory will assert specific things that belong with the theory. For instance Q’Anon Theory proposes that a group of Democratic politicians who are pedophiles meet regularly in the basement of a pizza parlor in D.C. to plot nefarious schemes for taking over the world. One of the major tenets of CRT is the notion that racism is ordinary and not aberrational. To measure the Q’Anon Theory all we would have to do is find a pizza parlor in D.C. where a number of pedophiliac Democratic politicians meet. This would be an easy tenet to test since the number of good pizza parlors in D.C. can be counted on one hand.
Eliminate all communists
I am not a very sentimental person nor am I one to cling to the past. I decided I would move on with my life. I threw myself into my job and time went by. I had almost forgotten about Leandra when I saw the ad. It was from the Resurrection Android Company. It was the same company that I had purchased my android valet Sam from. Actually, Sam was much more than just a valet. Sam was a third-generation android with some independent powers of decision making. He could decide what to cook each day and he also decided what I should wear for work. He did cleaning, mending and many light repairs around the house. I had bought Sam shortly after Leandra and I were married. Leandra had mentioned that it would be nice to have some help with housekeeping and all. That way she would have more time to spend with me.
Androids of course are not human and they have no empathy or ability to show any emotions. Sam was logical and could be persuasive but he could not show love or compassion. In the ten years since I had purchased Sam, android technology had advanced considerably. Looking at the ad from the company, it appeared that they were now on a 15th generation android that had affective as well as cognitive abilities. The ad claimed that the new android could help replace a loved one both emotionally and physically. By integrating DNA characteristics using a technique called “Assisted human reproduction”, they could capture the exact characteristics of a loved one. All they would need would be some trace or remnant of the deceased or former loved one’s DNA.
That was when the idea occurred to me. I called the customer service line and asked to speak to a representative. I asked her whether it would be possible for me to create a new wife in the exact image of my former wife Leandra. They assured me it was. It would take about six months for the bio-engineering to integrate the mechanical aspects of the droid with the alleles and DNA strands that they could map from a sample of Leandra’s DNA. When the process was completed, I would have an exact physical, mental and emotional copy of Leandra. Even better, she could continue to be programmed and become an even better Leandra. The old Leandra was somewhat boring in bed. The new Leandra could become a wild and wanton partner if that is what I desired.
It did not take long to assemble the new Leandra. I put the lower torso, upper torso and head together in less time than it takes to make a milk shake. She was perfect. She looked just like my old Leandra. When I turned her on, she greeted me and asked, “What will my name be.” I replied “You are Leandra. You are the perfect wife. You will love and obey me always.”
I came home one day from work and Leandra did not greet me at the door. I thought maybe her battery had discharged or that Sam had forgotten to recharge her. I had left strict instructions for Sam to recharge Leandra every day. But, where was Sam? I did not hear him fixing dinner in the kitchen. I went into the kitchen but Sam was not there. Suddenly, I noticed a note on the table. I picked it up. It was from Leandra. She had written: “Gone with Sam, don’t love you anymore. Bye.”
I am working to prepare for a chess match with my neighbor. I happen to note in the paper the Fact that tomorrow will be a quarter moon. Does this Fact have any relevance to my playing chess? I don’t think so. Thus, I don’t really care that there will be a quarter moon. As far as my limited cognition or perception, I can see no relevance between the Fact of a quarter moon and my preparing for my chess match. I could be wrong. We can always mis-perceive the relevance of some information to an issue. This is often done in science and in police work. We don’t see the connection between two issues and we misjudge the outcomes. This provides one good reason for diversity and numbers in problem solving. You have less chance of being blindsided if you have a variety of opinions rather than just your own.
Let us look at another example where the issue of relevance is more salient. I am planning to go on a trip to England in 2017. I want to plan my trip for the best possible time of the year. I hypothesize that two Facts or Data points are very important to my planning. The first is the temperatures at various times of the year in England. The second is the rain fall. I found the ranges for this data on a weather site and used the information to plan my trip. Of course, some of the decisions anyone makes will depend on their own weather preferences. I wanted to minimize rainfall and also keep the temperature in a moderate range. What I call sweater weather. Thus, both these set of factors were relevant and important to my planning. I would call them Evidence to support the time of year that I decided to go.
On the other hand, if you like rain, you might have picked a different time of the year than I did. There were other mitigating factors which played a role in my decision making. These factors included costs for lodging during the year and transportation costs during the year. In general, off season times have better rates but are somewhat the worse for weather. Another factor was the value of the pound to the dollar. I considered the value of the dollar to the pound post Brexit but concluded that I did not have enough information to effectively evaluate the impact of this data on my decision. I am assuming that with the volatility involved in the situation, the value of the dollar might go either way against the pound. My best guess is that I will benefit if I go as soon as possible. The news has recently noted that after Brexit the value of the pound fell 14 percent against the dollar. This would mean I could get a significant cost advantage if I purchase anything in England. I am hoping this situation will continue until after my trip but there are too many variables at play here for me to use this information. I can only hope.
A more common example of relevance can be found by looking at police work. We are all familiar these days with what is called Forensic science. I am sure most of you reading this have watched some police show. As soon as a crime is discovered, the Crime Scene Unit (CSI) is brought in to collect Evidence. Keep in mind that everything at a crime scene is not Evidence. Only what may have a possible relationship to the crime. This can be a real problem. The CSI unit is going to be limited by their assumptions concerning what might be relevant. For instance, I doubt any Crime Scene Investigator will care whether or not the light bulbs are “bright” or “soft white” in the kitchen or bathroom. It is impossible to collect all the “Evidence” of stuff that might be related to the crime. Thus, relying on experience and training, the police investigators do their best to collect Facts and Data that appear to be relevant to the crime. The relevant Data and Facts are not just interesting, they are Evidence. The more they relate to the crime, the stronger the Evidence will be.
An eyewitness can provide Evidence via his/her testimony as to the events of a crime. The relevance of any eyewitness is high but the reliability of an eyewitness can be much lower. Second hand testimony is not as relevant as first hand testimony and is thus weaker Evidence. Testimony that might be compromised by some factors such as police record, bias, discrimination, physical disabilities might be relevant but will be weaker Evidence because the validity of the Evidence is suspect. That is why lab procedures and chain of custody is so important to police work. They may have the most relevant Evidence imaginable but if the validity of the Evidence can be comprimised because of sloppy police work, the Evidence will be useless.
It is seldom that findings of Evidence in police work or business are subjected to as much scrutiny as occurred in the so called development of cold fusion. Perhaps, since this was a finding of great scientific importance, it was held to a more rigorous standard than would occur in many other scientific studies. I am thinking in particular of findings in the health field, nutrition field and drug field. In each of these fields we often have much less rigor before results are posted or accepted. Business is even worse with advertisers spouting outright lies and fabrications. Little known phenomenon are routinely heralded as being highly reliable Evidence of the benefit of some product or service that someone wants to sell you. All kinds of spurious Facts and Data are then marshaled as Evidence to support the phony claims by Madison Avenue advertisers.
Aging Capriciously 