The Unlikely Genius: How a Part-Time Calculus Teacher Cracked the Prime Number Puzzle


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Ready for a real story of a beautiful mind?

A 58-year-old temporary calculus teacher solved an unsolvable prime number problem.

He had never published a paper before...

Mathematics is known as a young man's game.

Very few mathematicians make real discoveries after the age of 50.

Most that make it to the history books do their best work in their 20s.

Zhang did nothing of note for 50+ years.

Zhang aka "Tom" was born in Shanghai in 1955.

His mother was a secretary in a government office and his father was a college professor of electrical engineering.

He spent most of his time reading math books that he bought for less than a dollar.

Zhang got his doctorate in mathematics.

After graduating, most of his peers went into either computer science, finance, or academia.

Zhang got a job as a lowly temporary part-time calculus professor at the University of New Hampshire.

Zhang loved the job. It gave him time and space to think.

A school can become very dependent on a good calculus teacher.

They're cheap and reliable, and there’s no reason to fire them.

He could do it on autopilot.

Most peers would have pursued tenure.

But the pursuit of tenure requires publishing frequently, which often means refining one’s work within a field.

This isn't a match for the deep thinking required to solve hard ambitious problems Zhang cared about.

A mathematician at the beginning of a difficult problem is trying to maneuver his way into a maze.

You can almost be totally lost not knowing exactly where you want to go.

You have to try different doors for years.

Not knowing if a door even exists.

When you find your way, it happens in a moment.

Then you live to do it again.

He spends most days walking, thinking, and trying doors.

"I like to walk and think. This is my way"

Concentration is the most important talent for a mathematician.

A prime number is a natural number greater than 1 that is not a product of two smaller natural numbers.

2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, and 47 are the primes below fifty.

No formula predicts the occurrence of primes. They behave as if they appear randomly.

Euclid proved in 300 B.C. that there is an infinite number of primes.

The problem Zhang solved is the “Bounded Gaps Between Primes” which is related to the larger twin-prime conjecture.

As primes get larger, they grow rarer and the distances between them (gaps) grow wider.

Zhang showed that although the gaps between subsequent primes grow larger on average, there are infinitely many pairs that stay within a certain finite distance of each other.

This was earth-shattering for the math world.

They went from the universe being infinite to finding it has an end somewhere.

Zhang chose a ruler of a length of seventy million because the large number made it easier to prove his conjecture.

For the still unproven twin-prime conjecture, the number would have been two.

From Zhang’s discovery, we know there is a number smaller than 70 million which precisely defines a gap separating an infinite number of pairs of primes.

But Zhang isn’t interested in finding the smallest number defining the gap.

It's “ambulance chasing". Just manual labor.

That's how Yitang Zhang, a part-time calc teacher who never published a paper, solved a prime number problem that has stumped mathematicians for over a century.

Now he is back in the news with a new breakthrough around the distribution of prime numbers & the Riemann hypothesis.

Yitang Zhang on tackling big problems:

- Walk & think

- Chase big goals

- Passion & persistence

- Age shouldn't stop you

- Study previous attempts

- Create space for deep work