STScI Webcast

The Equation that Couldn't be Solved: How Mathematical Genius Discovered the Language of Symmetry

Presented by: Mario Livio (Space Telescope Science Institute) |

Category: Special Interest Duration: 1 hour and 30 minutes Broadcast date: September 22, 2005 |

For thousands of years mathematicians solved progressively more difficult algebraic equations, from the simple quadratic to the more complex quartic equation, yielding important insights along the way. Then they were stumped by the quintic equation, which resisted solutions for three centuries until two great prodigies independently proved that quintic equations cannot be solved by simple formula. These geniuses, a young Norwegian named Niels Henrik Abel and an even younger Frenchman named Evariste Galois, both died tragically. Galois, in fact, spent the last night before his fatal duel (at the age of twenty) scribbling a brief summary of his proof, occasionally writing in the margin of his notebook “I have no time.” Galois’ work gave rise to group theory, the “language” that describes symmetry. Group theory explains much about the esthetics of our world, from the choosing of mates to Rubik’s cube, Bach’s musical compositions, the physics of subatomic particles and the popularity of Anna Kournikova.