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Mathematician and science communicator Marcus du Sautoy began his talk with the story of Evariste Galois, a Paris revolutionary who died in his brother’s arms. The night before, **Galois had stayed up all night trying to explain his mathematical ideas before his duel the next day. He was trying to explain symmetry.
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But … what is symmetry? **Galois asked whether by knowing one symmetry, we know all of them.** One characteristic of symmetry is that by fixing an object at a point and rotating it in some way, that rotation can happen without it seeming that the object has rotated.

A “twisted, six-pointed starfish,” for example, can be rotated by thirds or fifths of a turn, and still look the same. But after the rotations you can do something besides rotation. **You can “pick it up and put it down again.” Galois called this the “zero” symmetry.** A triangle has the same property. **It can be rotated — and also “reflected.”**

Math is not a spectator sport, says du Sautoy. You have to actually do it to understand it, to enjoy it.

**The interaction of the symmetries is different from the symmetry itself. In other words: “Are the symmetries themselves symmetrical?”** He uses a grid of rows and columns representing the points of a symmetrical figure to illustrate whether it matters what order of rotations you can perform on a given figure. This allows us to explore how the symmetries between different objects are fundamentally different. **This allows us to determine whether two different symmetrical objects have the same underlying abstract symmetry.**

For example, there are only two objects with six symmetries: the twisted six-pointed starfish and the equilateral triangle from the original example.

**But Galois’ language for symmetry allows us to understand the symmetry of objects that we cannot actually see.** Du Sautoy works on symmetrical objects in high-dimensional spaces.

**Du Sautoy presented TED with a new symmetrical object he was working on the previous night**, and offered any TEDster a chance to have their name as the name of the symmetrical object. To win, they had to say how many digits are in the number of symmetries a Rubik’s cube has.** Speaker Andrea Ghez won the contest.**

*Photo: Marcus du Sautoy at TEDGlobal 2009, Session 6: “Curious and curiouser,” July 22, 2009, in Oxford, UK. Credit: TED / James Duncan Davidson *

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You know you’re at #TED **when mathematicians get cheers on stage. :)** — *christinelu*

Marcus du Sautoy talks about symmetry and likes the Alhambra (**which happens to be my view right now** :-) — * TEDxCambridge*

Thinking about symmetries giving me **a slight headache** :-) — *liaonet*

**Sorry, has to be for me –>** “mathematics is not a spectator sport” says Marcus du Sautoy — *Thandelike*

“Leaving something incomplete makes it interesting” quotes Mathematician Marcus du Sautoy. **Next article from me will be half written**. — *WiredUK*

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