[FoRK] 2004 Abel Prize Awarded to Atiyah and Singer (Science)

[Contempt for Meatheads]

Via K5 this morning.  Chock full o' links, click through for more.

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	http://www.kuro5hin.org/print/2004/3/30/16221/4383

2004 Abel Prize Awarded to Atiyah and Singer (Science)

By flo
Wed Mar 31st, 2004 at 11:06:31 AM EST
News

The 2004 Abel Prize has been awarded jointly to Sir Michael F. Atiyah 
of the University of Edinburgh, and Isadore M. Singer of the 
Massachusetts Institute of Technology,
``for their discovery and proof of the index theorem, bringing together 
topology, geometry and analysis, and their outstanding role in building 
new bridges between mathematics and theoretical physics.''

The Index Theorem

The Atiyah-Singer Index Theorem is considered one of the greatest 
achievements of 20th century mathematics. Unfortunately, the exact 
result is impossible to state in layman's terms, but very roughly it 
provides a link between differential equations and topology. (See this 
paper for a professional introduction, and this comment for a lighter 
treatment). This result is the culmination of a long chain of ideas, 
starting with Stokes Theorem, which some readers may have encountered 
in undergraduate math courses, and passing through Hodge theory and the 
Hirzebruch-Riemann-Roch Theorem. Surprisingly, the Index Theorem has 
numerous applications, not just in pure mathematics, but also in 
theoretical physics. Indeed, this result, as well the tireless efforts 
of Atiyah and Singer in general, have lead to a highly fruitful 
cross-fertilization between mathematics and theoretical physics, which 
has left a profound impact on both disciplines.

The Abel Prize

The Abel Prize was created on the occasion the of the 200th birthday of 
Niels Henrik Abel, a brilliant Norwegian mathematician who tragically 
died at a young age just as his achievements were starting to receive 
due recognition. The prize, worth NOK 6,000,000 (USD 875,000, EUR 
710,000), is awarded once per year by the Norwegian Academy of Science 
and Letters to acknowledge outstanding accomplishments in the field of 
mathematics. It was awarded for the first time last year, when it went 
to Jean-Pierre Serre.

As is well known, there is no Nobel Prize in Mathematics. Instead, most 
people have looked to the Fields Medal as the most prestigious award 
for mathematical achievement. The Fields Medal, however, differs 
significantly from the Nobel Prize in that it is only awarded every 
four years (at each meeting of the International Congress of 
Mathematicians), to two, three or four recipients. Moreover, it is only 
awarded to mathematicians not older than 40, in order to encourage 
further achievements. This also has the pleasant side effect of 
rewarding recent work, rather than work done half a century earlier, as 
is too often the case with Nobel Prizes. Tellingly, both Atiyah (1966) 
and Serre (1954) have also won Fields Medals.

The Abel Prize, by contrast, seems to resemble the Nobel Prize more 
closely. It is awarded annually by a Scandinavian learned society (the 
Nobel Prize is awarded by the Swedish Academy of Sciences), it is worth 
a considerable amount of money, and so far all three recipients are 
over seventy years old. Happily, this allows rewarding those 
(relatively few) mathematicians who missed the Fields Medals due to 
their age. In particular, by 1966 Singer was already over the age limit 
(he was born in 1924), and only Atiyah was awarded the Fields medal for 
the Atiyah-Singer Index Theorem.

Full discussion: http://www.kuro5hin.org/story/2004/3/30/16221/4383