I just came across one of the most fascinating stories in mathematics and human intuition. It’s about Marilyn vos Savant and her famous Monty Hall problem.

It all started in 1990, when Marilyn vos Savant— a woman listed in the Guinness Book of World Records for having the highest IQ in history— published her answer to a puzzle that caused a storm. The problem was simple: a participant chooses one of three doors. Behind one door is a car, behind the other two are goats. The host, knowing where the car is, opens one of the remaining doors to reveal a goat. Now the question: should the participant switch their choice or stick with the original?

Marilyn vos Savant answered clearly: always switch doors. Her reasoning was that switching increases the chances from one-third to two-thirds. Sounds strange, right? People thought she was wrong.

She received over ten thousand letters— nearly a thousand from PhD holders— and ninety percent claimed she made a mistake. Scientists, mathematicians, everyone criticized her answer. She heard: “This is the biggest blunder I’ve ever seen” or “Maybe women don’t understand math the way men do.” It was really harsh.

But here’s the catch—Marilyn vos Savant was right. Completely right.

Here’s why: when you initially choose a door, you have a one-third chance of the car and a two-thirds chance of a goat. Now, the host opens a door with a goat. If you initially picked a goat (which had a two-thirds chance), switching guarantees you win the car. If you initially picked the car (one-third), switching will make you lose. So statistically, by switching, you win two out of three times.

People don’t find this intuitive. We think that since one door is opened, the chances for the remaining two are equal— fifty-fifty. We ignore the initial probabilities. That’s a reset error—treating the second choice as a new, unrelated event, when in fact it’s a continuation of the original probabilities.

A few years later, MIT and other institutions ran thousands of computer simulations. It always came out the same: switching doors gives a two-thirds chance. A popular game show dedicated to debunking myths also verified this. Many scientists who initially attacked Marilyn vos Savant later admitted their mistake.

What strikes me about this story isn’t just the math. It’s the fact that a woman with extraordinary intelligence—who read all volumes of the Britannica Encyclopedia as a child—had to face thousands of letters full of doubts and ridicule. Yet she stood by her answer. It’s a testament to the power of logic and the courage to question what everyone believes.

Marilyn vos Savant’s story and the Monty Hall problem are lessons about the gap between what’s intuitive and what’s mathematically true. Sometimes we have to trust the numbers, even when everyone tells us we’re wrong.