How a Rubik’s Cube Inspired a Mathematician’s Eureka Moment

New Scientist
Stories from New Scientist.
Aug. 17 2014 7:12 AM

Rubik’s Quadratic Forms

How a toy inspired an award-winning mathematician’s Eureka moment.

Rubiks.
Rubik’s cubes can be life changing.

Photo courtesy of Rubik’s

This article originally appeared in New Scientist.

Manjul Bhargava has just won a Fields medal, the most coveted prize in mathematics. Now 40, he was one of the youngest people to be made a full professor at Princeton University, at age 28. He explains the link between Rubik's cube and his groundbreaking work in number theory.

Does the Fields medal mean more to you than any other award you have won?

Advertisement

Any award is a milestone, which encourages one to go further. I don’t know that I think of any award as meaning more to me personally than any other. The mathematics that led to the medal was far more exciting to me than the medal itself.

The award citation says that you were inspired to extend Carl Friedrich Gauss’ law of composition in an unusual way. Can you explain what that is, and what you did?

Gauss’ law says that you can compose two quadratic forms, which you can think of as a square of numbers, to get a third square. I was in California in the summer of 1998, and I had a 2-by-2-by-2 mini Rubik’s cube. I was just visualizing putting numbers on each of the corners, and I saw these binary quadratic forms coming out, three of them. I just sat down and wrote out the relations between them. It was a great day!

Have any of your other discoveries had unusual origins?

I do tend to think about things very visually, and the Rubik’s cube is a concrete example of that visual approach. But that one is probably the most unusual and unexpected origin of all.

You have proved several theorems. Do you have a favorite?

Mathematicians often say that choosing a favorite theorem is like choosing one’s favorite child. Although I don’t yet have any children, I understand the sentiment. I enjoyed working on all the theorems I have proved.

Are there any mathematicians, living or dead, that you have particularly looked up to?

My mother [Mira Bhargava, a mathematician at Hofstra University in Hempstead, New York] has been a source of inspiration to me from the very beginning. She was always there to answer my questions, to encourage and support me, and she taught me how much the human mind is capable of.

This year a woman, Maryam Mirzakhani at Stanford University, has finally won one of the Fields medals, after 52 consecutive male winners. How do you view this achievement?

This is long overdue! Hopefully in a few years we will not even need to discuss this, as more and more females receive the award. I am honored to be a recipient in the same year as Maryam. It has been a pleasure to know her—we overlapped for a year early in our careers at Harvard, and later at Princeton. Her work is absolutely fantastic. I hope the media will not speak of her only as a top-rate female mathematician, but also as a top-rate mathematician who is doing truly groundbreaking work.

Dana Mackenzie is a freelance mathematics and science writer based in Santa Cruz, Calif. He is the author of The Universe in Zero Words and The Big Splat, or How Our Moon Came to Be. He also writes a popular chess blog.

TODAY IN SLATE

Politics

The Irritating Confidante

John Dickerson on Ben Bradlee’s fascinating relationship with John F. Kennedy.

My Father Invented Social Networking at a Girls’ Reform School in the 1930s

Renée Zellweger’s New Face Is Too Real

Sleater-Kinney Was Once America’s Best Rock Band

Can it be again?

The All The President’s Men Scene That Captured Ben Bradlee

Medical Examiner

Is It Better to Be a Hero Like Batman?

Or an altruist like Bruce Wayne?

Technology

Driving in Circles

The autonomous Google car may never actually happen.

The World’s Human Rights Violators Are Signatories on the World’s Human Rights Treaties

How Punctual Are Germans?

  News & Politics
Politics
Oct. 22 2014 12:44 AM We Need More Ben Bradlees His relationship with John F. Kennedy shows what’s missing from today’s Washington journalism.
  Business
Moneybox
Oct. 21 2014 5:57 PM Soda and Fries Have Lost Their Charm for Both Consumers and Investors
  Life
The Vault
Oct. 21 2014 2:23 PM A Data-Packed Map of American Immigration in 1903
  Double X
The XX Factor
Oct. 21 2014 3:03 PM Renée Zellweger’s New Face Is Too Real
  Slate Plus
Behind the Scenes
Oct. 21 2014 1:02 PM Where Are Slate Plus Members From? This Weird Cartogram Explains. A weird-looking cartogram of Slate Plus memberships by state.
  Arts
Brow Beat
Oct. 21 2014 9:42 PM The All The President’s Men Scene That Perfectly Captured Ben Bradlee’s Genius
  Technology
Technology
Oct. 21 2014 11:44 PM Driving in Circles The autonomous Google car may never actually happen.
  Health & Science
Climate Desk
Oct. 21 2014 11:53 AM Taking Research for Granted Texas Republican Lamar Smith continues his crusade against independence in science.
  Sports
Sports Nut
Oct. 20 2014 5:09 PM Keepaway, on Three. Ready—Break! On his record-breaking touchdown pass, Peyton Manning couldn’t even leave the celebration to chance.