This is a story of how the impossible became possible. How, for centuries, scientists were absolutely sure that solids (as well as decorative patterns like tiling and quilts) could only have certain symmetries – such as square, hexagonal and triangular – and that most symmetries, including five-fold symmetry in the plane and icosahedral symmetry in three dimensions (the symmetry of a soccer ball), were strictly forbidden. Then, about twenty years ago, a new kind of pattern, known as a “quasicrystal,” was envisaged that shatters the symmetry restrictions and allows for an infinite number of new patterns and structures that had never been seen before, suggesting a whole new class of materials. By chance, solids with five-fold symmetry were discovered in the laboratory at about the same time. Even so, for nearly twenty years, many scientists continued to believe true quasicrystals were impossible because, they argued, such a pattern could only be formed with complex and physically unrealistic inter-atomic forces.
Impossible Crystals is an abstract but ultimately satisfying video lecture by Paul Steinhardt, Albert Einstein Professor of Physics at Princeton University. The presentation is targeted at the layman but realistically, some background in solid state physics/symmetry is necessary to appreciate what Steinhardt is saying. You don’t need a high speed internet connection: you can simply download the PDF and listen to the MP3 of the presentation. There are many other public lectures available for download at Perimeter (see link that follows).
Link to the presentation (look for Impossible Crystals)
Wikipedia entry for Quasicrystal
Wikipedia entry for Aperiodic Tiling
Another teaser image
say to 
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but may have a more complicated large scale structure. The surface of Earth is a simple example: At small distances it looks like the Euclidean 
but from far away it is 
, the two dimensional surface of a sphere. The behaviour at the small scale and large scale can be totally different. For instance, in 
Indian wins big math prize
In March 2007 an Indian won a big award in Mathematics. I had written about it at IIT Madras (for a mailing list). I reproduce the writeup here:
The 2007 Abel Prize has been awarded to S.R. Srinvasa Varadhan (Faculty NYU) (Ph. D. ISI Calcutta 1963) for his contributions to probability theory.
The Abel prize is worth approx USD 997,000 and is presented by the King of Norway. The winner is selected by the Norwegian Academy of Science and Letters. Some people say that the Abel Prize is the Nobel equivalent for Mathematics (Though this can be disputed by those who would give that place to the Fields Medal which has a longer history. Interestingly the fields medal is only awarded to mathematicians under 40. This, I believe makes it
a “flawed” prize. Also, the fields medal would only make you richer by US $13,000).
The Abel prize is named after a Norwegian mathematician Niels Henrik Abel who made many impressive contributions before he died at the age of 26(!).
Perhaps that bodes well for the prize in the public’s imagination.
(When something is commutative i.e. a*b = b*a we also call it Abelian in his honour). What’s interesting to me is that Abel rhymes with Nobel
S.R. Srinivas did his Ph. D. in ISI Calcutta (1963) and then went for his postdoc at the Courant Institute of Mathematical Sciences at NYU. Incidently he is from Chennai and did his B.Sc. from Presidency (1959).
I have found Tamil translations on the website of the prize. Go to
here for a tamil translation.
Lets go for the big prizes!! We Indians can do it (perhaps not in
cricket??) !
For those who are really interested
The authoritative source
http://www.abelprisen.no/en/
More Info:
http://en.wikipedia.org/wiki/Abel_Prize
Some news articles:
International Herald Tribune
The Hindu
Minor Quibble: The Hindu incorrectly lists the amount as US $850,000. Its
about US $975,000