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In the December 2010 issue of Scientific American, an article "A Geometric Theory of Everything" by A. G. Lisi and J. O. Weatherall states "... what is arguably the most intricate structure known to mathematics, the exceptional Lie group E8." Elsewhere in the article it says "... what is perhaps the most beautiful structure in all of mathematics, the largest simple exceptional Lie group. E8." Are these sensible statements? What are some other candidates for the most intricate structure and for the most beautiful structure in all of mathematics? I think the discussion should be confined to "single objects," and not such general "structures" as modern algebraic geometry.

Question asked by Richard Stanley

Here are the top candidates so far:

1) The absolute Galois group of the rationals

2) The natural numbers (and variations)

4) Homotopy groups of spheres

5) The Mandelbrot set

6) The Littlewood Richardson coeefficients coefficients (representations of $S_n$ etc.)

7) The class of ordinals

8) The monster vertex algebra

9) Classical Hopf fibration

10) Exotic Lie groups

11) The Cantor set

12) The 24 dimensional packing of unit spheres with kissing number 196560 (related to 8).

13) The simplicial symmetric sphere spectrum

14) F_un (whatever it is)

15) The Grothendiek-Teichmuller tower.

16) Riemann's zeta function

17) Schwartz space of functions

And there are a few more...

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In the December 2010 issue of Scientific American, an article "A Geometric Theory of Everything" by A. G. Lisi and J. O. Weatherall states "... what is arguably the most intricate structure known to mathematics, the exceptional Lie group E8." Elsewhere in the article it says "... what is perhaps the most beautiful structure in all of mathematics, the largest simple exceptional Lie group. E8." Are these sensible statements? What are some other candidates for the most intricate structure and for the most beautiful structure in all of mathematics? I think the discussion should be confined to "single objects," and not such general "structures" as modern algebraic geometry.

Question asked by Richard Stanley

Here are the top candidates so far:

1) The absolute Galois group of the rationals

2) The natural numbers (and variations)

4) Homotopy groups of spheres

5) The Mandelbrot set

6) The Littlewood Richardson coeefficients (representations of $S_n$ etc.)

7) The class of ordinals

8) The monster vertex algebra

9) Classical Hopf fibration

10) Exotic Lie groups

11) The Cantor set

12) The 24 dimensional packing of unit spheres with kissing number 196560 (related to 8).

13) The simplicial symmetric sphere spectrum

14) F_un (whatever it is)

15) The Grothendiek-Teichmuller tower.

16) Riemann's zeta function

17) Schwartz space of functions

And there are a few more...

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In the December 2010 issue of Scientific American, an article "A Geometric Theory of Everything" by A. G. Lisi and J. O. Weatherall states "... what is arguably the most intricate structure known to mathematics, the exceptional Lie group E8." Elsewhere in the article it says "... what is perhaps the most beautiful structure in all of mathematics, the largest simple exceptional Lie group. E8." Are these sensible statements? What are some other candidates for the most intricate structure and for the most beautiful structure in all of mathematics? I think the discussion should be confined to "single objects," and not such general "structures" as modern algebraic geometry.

Question asked by Richard Stanley

Here are the top candidates so far:

1) The natural numbers (and variations)

2) The absolute Galois group of the rationals

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2) The monster vertex algebranatural numbers (and variations)

4) The class Homotopy groups of ordinalsspheres

5) The Cantor Mandelbrot set

6) The homotopy groups Littlewood Richardson coeefficients (representations of spheres$S_n$ etc.)

7) The Mandelbrot setclass of ordinals

8) The monster vertex algebra

9) Classical Hopf fibration

10) Exotic Lie groups

9

11) The Cantor set

12) The 24 dimensional packing of unit spheres with kissing number 196560 (related to 8).

13) The simplicial symmetric sphere spectrum

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14) Stone Cech compactification F_un (perhaps of the natural numberswhatever it is)

11

15) Schwartz space of functionsThe Grothendiek-Teichmuller tower.

And there are a few more...

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Post Reopened by Gil Kalai, Fedor Petrov, Richard Borcherds, Chandan Singh Dalawat, Deane Yang
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Post Closed as "subjective and argumentative" by Pete L. Clark, Ryan Budney, Franz Lemmermeyer, Andrew Stacey, José Figueroa-O'Farrill
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