How Richard Feynman beat an abacus champion, and what it reveals about AI

Richard Feynman once beat an abacus champion at cube roots using nothing but mental approximation. His trick reveals why today's AI can breeze through calculations yet still struggle with real mathematical reasoning.

In Short

• Feynman beat an abacus master using intuition, not brute calculation
• He spotted 1728 inside 1729.03, then approximated the cube root
• Modern AI aces calculations but still fumbles genuine mathematical reasoning

In the early 1950s, in a quiet Rio de Janeiro restaurant, a Japanese salesman was showing off a soroban, the Japanese abacus, hoping to win new customers.

The waiters, certain the American in the corner could hold his own, pushed him forward to compete.

That customer was Richard Feynman, a young physicist who would go on to win a Nobel Prize.

WHO WON THE FEYNMAN VS ABACUS DUEL IN BRAZIL?

In addition, the salesman thrashed him, fingers flying across the beads while Feynman was still writing the figures down.

On multiplication, the gap narrowed, because Feynman was quick in his head.

Then, cornered and competitive, the salesman reached for the hardest weapon he had.

Cube roots, he demanded, and scribbled down a number almost at random: 1729.03.

HOW DID FEYNMAN CALCULATE A CUBE ROOT IN HIS HEAD?

While the salesman sweated over his beads, Feynman simply sat and thought. He knew that 12 multiplied by itself three times is 1,728, the number of cubic inches in a cubic foot, because one foot is equal to 12 inches. So 1729.03 was a mere whisker above a number whose cube root he already knew: 12.

The rest was a trick from calculus called linear approximation, which just means estimating a hard answer by nudging an easy one you already have. The excess above 1,728 was tiny, so the cube root crept up by roughly a third of that fraction.

Feynman called out 12.002 while the salesman was still grunting. The man could rattle beads, Feynman realised, but he did not know numbers. The very idea of an approximation was foreign to him.

I have loved this story since I was 15, when a copy of Surely You're Joking, Mr. Feynman! arrived as a birthday gift from my father. It found a willing reader. I had won my first abacus contest before the age of 8, mental arithmetic became a habit I could never quite switch off, and I later trained as an engineer. Feynman remains my favourite physicist, precisely because he prized understanding over showing off.

CAN AI ACTUALLY DO MATHS OR JUST PATTERN MATCH?

Seventy years on, the same divide haunts artificial intelligence. Today's AI models are the new soroban: blindingly fast and tireless.

In July 2025, systems from Google DeepMind and OpenAI scored at gold medal level in the International Mathematical Olympiad, the world's toughest school maths contest.

And yet. In 2024, Apple researchers found that changing only the numbers in a sum, or slipping in one irrelevant sentence, could crash a model's accuracy by up to 65 per cent.

Pushed past a certain difficulty, its reasoning can collapse altogether. When Epoch AI first tested leading models on brand new research problems, they solved fewer than two per cent.

WHY DOES HUMAN MATHEMATICAL INTUITION STILL MATTER?

That is Feynman's salesman, reborn in silicon. Speed is not the same as understanding. The hardest part of mathematics is often knowing which sums never need doing, spotting the 1,728 hidden inside the problem.

AI is closing the gap at a startling pace. But for now, the deepest mathematical act stays stubbornly human: not computing the answer, but seeing it.

- Ends