In Computer Science: automated theorem proving. Manchester has Vampire, which is the worlds best resolution based prover, and Cambridge has Isabelle, the worlds best inductive prover. Edinburgh is one of the biggest (and possibly best) research centres for this area in the world.
In the US, only the University of Texas at Austin can compete, with ACL2 (Boyer and Moore, the guys behind this prover both started it at Edinburgh), and Argonne National Labs with Otter (although this seems to be defunct, now).
At the 2006 Conker World Championships Britain almost swept the board. Every winner was British or British born except for the Ladies Team Title which went, disappointingly, to France.
Yes. It’s an area of central importance in AI for a number of reasons (you can synthesise programs from a specification with constructive logics, you can prove programs correct and autonomous agents need (or, more accurately, can use) theorem provers for their reasoning ability). It’s also an area of importance for the semiconductor industry, ever since the Pentium bug.
One of the highlights of the field was a variant of Otter proving that all Robbins algebras are Boolean.
I believe we are still the world leaders in the manufacture of Stiff Upper Lips. I use mine as a makeshift mantelpiece - it can hold a number of ornaments, and a carriage clock.
Not only that, GB has just retained the World Croquet Team Championhips, The MacRobertson Shield, thrashing Australia 19-2 (in Australia) to complete a clean sweep of the series. The world number one and the majority of top players are British, and although the reigning world champion is South African, he has since been defeated by our best player.
Also, GorillaMan beat me to it, but I agree with him that we are the world leaders for most forms of motorsport, particularly design and engines.
The Great Britain team of John Nunn, Colin McNab and Jonathan Mestel, sponsored by Winton Capital Management, retained the World Chess Solving Championship held in Wageningen, Netherlands on 1st-2nd August, after one of the toughest fought contests for years.
Authority on the English language:
Having a member of the Government speak the truth before the Iraq war:
I have chosen to address the House first on why I cannot support a war without international agreement or domestic support.
…
I intend to join those tomorrow night who will vote against military action now. It is for that reason, and for that reason alone, and with a heavy heart, that I resign from the government.