从 NFL 到麻省理工，他解开一个三十年的数学问题

October 5, 2026, Monday.

A paper appeared online.

The paper's name is On the Growth Factor of Random Matrices.

The person who wrote the paper is named John Urschel.

He is 35 years old this year.

He is a mathematics professor at MIT.

Previously, he was an NFL football player.

This paper discusses a very old mathematical method.

This method is called Gaussian elimination.

Gaussian elimination is used to solve equations.

An equation is a problem that contains a number you don't know.

You need to find this number.

Banks use it to calculate money.

Computers use it to compute things.

In electrical circuits, it is also present.

A circuit is something inside computers and machines.

Many people use it every day.

But many people don't know why it is good.

This paper asks a question:

When the problem is very large, will this method make mistakes?

People have thought about this question for thirty years.

In 1995, a mathematician named Nick Trefethen stated a conjecture.

A conjecture is a question.

Many people think it is correct, but no one can prove it.

In 1997, he and David Bau wrote a book.

On page 169 of the book, this conjecture is also stated.

For thirty years, no one proved this conjecture.

On October 5, 2026, John Urschel's paper says: this conjecture is correct.

In the paper there is a theorem.

The theorem says: when the problem is very large, this method rarely makes mistakes.

Rarely is it much higher than the square root of n.

n is the size of the problem.

The larger the problem, the larger n is.

Some problems have a very large number of numbers.

About 100% of the time, this method is correct.

Not 100%, but about 100%.

This result is about random matrices.

A matrix is many numbers put together.

A random matrix means these numbers have no pattern.

This result makes many people who study mathematics happy.

But mathematical results need many people to look at them.

Right now, this paper is still a preprint.

A preprint is an article that has not yet been formally published.

It has not yet undergone peer review.

Peer review is other mathematicians reading this article.

They need to verify this proof.

They need to see: is this proof correct?

This stage is very important.

If the proof is not correct, this result is meaningless.

So, this result still has to wait for them to look at it.

But this question, people have already thought about for thirty years.

Why is this method important?

Because many places use it.

Banks, finance, computers, circuits all use it.

Finance is the business of banks and money.

When the problem is very large, there is a lot of data.

When there is a lot of data, calculations need to be very fast.

This method is very efficient.

So, many people use it.

But where is its risk?

Risk is whether it will make mistakes.

If it makes a mistake, the result is wrong.

So, mathematicians want to know: how big is the probability that it makes a mistake?

Probability is the size of the possibility.

His paper answers exactly this question.

It says: the probability of making a mistake is very small.

This method is almost always correct.

Many people read this paper because of the person who wrote it.

Many people know John Urschel because of football.

In the United States, football is very famous.

The NFL is the largest football league in the United States.

Playing football, there is a lot of money, and many people know you.

In 2014, the NFL chose him.

He was selected in the fifth round.

He studied mathematics at Penn State University.

His mathematics was always very good.

He played football while taking classes at MIT.

He was also writing mathematics papers.

His team did not know he was taking classes at MIT.

A team is the people who play football together.

In August 2015, his brain was injured.

That injury was very serious.

After the injury, he continued to play football.

But he was very worried.

He worried that his brain would get worse in the future.

He feared he would no longer be able to think about mathematics.

Many people worry that after a brain injury, memory and thinking will be worse.

In 2017, he decided to retire.

Many people did not understand this.

Playing football, there is a lot of money, and many people know you.

He gave all of this up.

Why retire?

One reason is his brain.

Another reason is that he loves mathematics.

He went back to study mathematics.

Later, he obtained a mathematics PhD.

In 2019, he published a book.

In the book, he talks about football and also about mathematics.

Now, he teaches mathematics and also supervises doctoral students in research.

He sometimes goes to conferences and talks about his mathematics.

He also gives interviews.

In an interview, he said: I really enjoy no one knowing me.

He likes going to places where no one knows him.

On MIT's website, his introduction does not mention football.

His CV only mentions football on page eight.

Once, during an exam, a student wore his football jersey.

He said: if football can make students come to study mathematics, that is great.

He said, he wants to know why, and also wants to know how.

Now, many media outlets write about him.

Media are newspapers, television, and websites.

Many people say this is a breakthrough.

A breakthrough is a very big achievement.

But a mathematical breakthrough takes time.

This result still has to wait for peers to look at it.

This is also the way of mathematics.

A result must be verified by many people before it is true.

Verification is a very important thing in mathematics.

So, this result still has to wait.

But this question, people have already thought about for thirty years.

Many people say this is a very big question.

John Urschel also wants to know the answer.

Think about it.

A question that many people have thought about for thirty years, and no one can prove.

If it were you, would you also want to give it a try?