How it started

A few days ago I had a conversation with Professor Ivo Sbalzarini. One thought has stayed with me since. The conversation did not start there , it started as a technical one , I spent the past few days on profiling a GPU kernel and we spent the first half of the conversation in that world entirely before shifting from memory bottlenecks,warp divergence to the physics underneath.

Somewhere in there ,almost offhand , I asked Professor Sbalzarini "Where are we actually heading?" referring to the news that Navier-Stokes had been solved or at least that is what the mass public was talking about. Like everyone else I heard the headline too, and thought that the famous unsolved problem in fluid dynamics, one of the seven Millennium Prize Problems apparently cracked. It felt like news. It felt like the walls are closing.

Professor Sbalzarini corrected me gently saying “It hasn’t” at least not in the way you mean.

That was more of a correction than dismissal and he explained why.

What actually happened

What had actually happened was closer to the opposite of closure. On September the 8th 2026 , OpenAI announced that their systems have produced the proof including a formal version checked in the Lean proof assistant that the Navier-Stokes solutions can develop a singularity in finite time. A fluid that starts out perfectly smooth can under the equations own dynamics , spin up to unbounded speed. Thats not a proof that fluid motion always behaves.It is a proposed proof that it does not have to , that the equations can break their own continuum model from inside with nothing infinite fed in by hand.

But the headlines that we read on social media and articles oversell how settled things really are. The proof hasn’t gone through independent peer review. The people who produced the result were more careful with the claim than the headlines about it were.

It’s one very hard and specific question about the equations answered , provisionally by a result its own authors have not asked to be crowned for. The equations are still unpredictable,in the sense most people mean the word as they were before.

Headlines instead of literature

But here’s the part that actually bothered me, I reacted to that headline in the same way most people did. A kind of quiet panic , the feeling that something fundamental had closed and I hadn’t opened it to check. I hadn’t read the paper. I hadn’t looked what the claim was about ,singularity or otherwise. I saw “Navier-Stokes ….solved” and decided to frame my own conclusion. I felt the same thing alot of people feel when a hard problem gets a headline, relief or maybe unease depending on whether you thought the mystery was worth protecting.

Theres a pattern that I recognized somewhere along the timeline many of us shifted from wanting to understand how a problem is solved to just wanting to know that it’s solved or just looking at the solution and assuming we already know it. I still remember what studying used to feel like before AI tools existed , sitting with a physics or math exam coming up, actually working through the papers and lecture notes. I remember the days when I had a science exam for my sophomore year in high school , it was a preparatory holiday. I woke up worried about the exam. It felt like all of the questions that I solved yesterday were getting solved in my mind while I was asleep. The morning wore a coat of gentle winter gold. I took out a daybed and in a few minutes found myself surrounded with books , question papers and notebooks. Now I remember how we used to solve questions , sometimes slowly sometimes at double speed out of panic but working through them , reading the method knowing fully known theres nothing except one's mind and understanding that will help us prove and derive the laws of motion or laws of electrostatics.

Mathematics is practice

The same thing came into my mind right before our call, on the same day of our conversation,in a discrete mathematics class , a friend of mine asked the professor something right before the test, do we need to learn how to find a multiplicative inverse?

The professor ignored him at first. Then he came back with a gentle smile and an answer thats stuck with me since:

“You can get the full marks , there's nothing stopping you from answering any question in anyway. But mathematics is practice it is not just a written answer that rewards you with grades.”

That line and our conversation are the only two dots that made sense after getting connected and that is what this whole written piece is about honestly. Everything else is just me explaining why it hit so hard.

From one bell to two

Later while conversing on the same topic , Professor Sbalzarini took the thought somewhere I hadn’t. The fear he said isn’t just ours as students, Institutions feel that too. The feeling of the institutions cannot be described as fear neither it can be neglected. Some students have started to do assignments in seconds what took them hours.

Then he described something that stopped me, because I had heard the same version of that years before. One of my former physics professors used to draw the class as a bell curve. Marks along one axis and students along the other. Most of us bunched in the middle with 2 thin tails on either sides representing number of failures in the exam and number of top scorers on the other. It was the most ordinary picture in education but at the same time it was in a strange way comforting, it told you roughly where you would land.

Professor Sbalzarini's version has two bells.

One sits at the lowest marks: students who use AI to do the work for them, hand it the assignment and hand back whatever it returns. The other sits at the highest: students who use AI as a teacher, to learn how to do the work, setting their own pace and going back to the fundamentals until they actually understand it. The middle, where the old curve used to keep most of us, is thinning out.

What gets me is what that does to the average. It doesn't move, it sits exactly where it always did. But it stops describing anyone. It is no longer the centre of the crowd but the empty space between two.

“Which bell am I drifting towards?”

Not in general. This semester, this assignment, this week.

And the drifting is the dangerous part. We do not decide to end up in the first bell. It happens one assignment at a time when we say :"I am tired today, I will do it tomorrow" and every time it feels like an exception until the exceptions quietly become the habit. When I sent him this piece, Professor Sbalzarini put it plainly: students need to take conscious control of their own development. The point isn't to stop using AI. It's to not hand it your agency along with the assignment.

The same panic, at a bigger scale

Coming back to the panic , I think the fear around “AI will solve math and physics” comes from the same place where our panic over headlines and losing grades comes from. Reacting to headlines instead of literature , reacting to conclusions without looking at the methods. And the fear of losing grades and trying to mug up the syllabus one night before the exam.

I thought this meant marks had stopped meaning anything. Professor Sbalzarini pointed out it's the other way round. The two bells come from marks in the first place. Students who let AI do their homework without understanding it do end up with worse grades, so a grade does tell you which bell you're in. What it can't tell you is how to get to the other one. No exam is going to hand you that part.

Still if agents and the other tools do get better at solving these problems , and the latest researches done by major AI firms suggests they might. I don't think it threatens the fields the way people fear. It changes what gets automated. It does not change why anyone was doing it in the first place.

The people who have pushed maths and physics forward as we see it today were rarely the ones chasing grades or prize money. They were the ones who found it fun. The curiosity of the human mind that is driven by genuine interest does not disappear because a tool gets faster at producing the answers.

If anything an AI getting better at known problems should free up room for the part that was always the point , asking better and deep questions. I first wrote that the people who ask them come from the bell at the top. Professor Sbalzarini corrected me here too: there's no detectable correlation between school or university grades and later success as a scientist. That's reassuring if you're not a top scorer, and at the same time a wake-up call for the whole education system. The bell you're in says something about how you're learning right now. It says nothing about the questions you'll end up asking.

What I took from it

I dont think any one of us can settle this debate. But I felt more awake that evening than I’d been in weeks, finally answering “Why do I even need to study all this?”

We moved from GPU kernels to a physics question, which led to a headline I’d gotten backwards, which led to questions I had been carrying for months. One question kept opening the next, crossing the boundaries of the subject we started in, until it answered something in a completely different domain.

Somewhere in that chain I understood that being solved was never really the point.

A thank you

None of this would exist without Professor Ivo Sbalzarini.

He had every reason to keep that call about GPU kernel and that too being our first conversation. Instead when a student said something wrong with confidence he stopped and corrected it gently and took time to explain why it mattered and then kept going to the questions that had nothing to do with the work we had scheduled.

So if anyone asks where these ideas came from, my honest answer is :

A professor took the time to answer a student’s questions properly. He did not hand me a conclusion. He showed me the method. That is the same lesson this entire page was about and he taught it by example before either of us named it.

Professor Sbalzarini , I thank you with the deepest respect for your time, your patience and your generosity with a student’s questions. I hope this piece does some justice to what you gave me in one Wednesday Afternoon.

Sources

• On the Navier–Stokes Millennium Prize Problem — OpenAI, September 8, 2026

• Navier–Stokes existence and smoothness — Wikipedia, for the Millennium Prize Problem background and peer-review status