Results in mathematics come in several flavours — theorems are the big important results, conjectures will be important results one day when they are proved, and lemmas are small results that are just stepping stones on the way to the big stuff. Right? Then why has the Fields medal just been awarded to Ngô Bào Châu for his proof of a lemma?

Eron Lindenstrauss got the Fields Medal for developing tools in the area of dynamical systems and using them to crack hard problems in the seemingly unrelated area of number theory.

To kick off our ICM adventure, Plus attended the International Conference of Women Mathematicians, which started yesterday in Hyderabad. Women from around the world gathered to present their mathematical work to each other, but mostly to network and exchange experiences. It was great talking to women whose experience as professional mathematicians is quite different from what we're used to in Europe.

Over 3000 mathematicians have gathered to sounds of the tabla and bansuri playing traditional Indian music in the Hyderabad International Convention Centre, and they are all baiting their breath. They are all waiting for the announcement of the Fields medals, the highest honour in mathematics, and the prestigious Gauss, Nevanlinna and Chern Prizes. The hall is a colourful scene filled with mathematicians from around the world, including many local participants in beautiful saris and suits. You can hear a pin drop as the entire hall stands for the entrance of Pratibha Patil, the President of India, who will award the medals to the prize winners...

Plus has opened its temporary head office in Hyderabad! We're here for the International Conference of Women Mathematicians, starting today, and the International Congress of Mathematicians starting on Thursday. The highlight (apart from Plus' presentation on public engagement with maths) will be the award of the Fields Medals 2010. Watch our news section or follow us on Twitter to find out all the news first.

Plus is proud to host the 68th edition of the carnival of mathematics, celebrating mathematical blogging!

The carnival invites mathematical bloggers to submit the recent blog posts they're most proud of and the current host then publishes a list of the best ones on the first Friday of the month.

Two computer geeks claim to have calculated the number pi to 5 trillion digits — on a single desktop and in record time. That's 2.3 trillion digits more than the previous world record held by the Frenchman Fabrice Bellard.

Renowned cosmologist and mathematician John D. Barrow has turned his attention to rowing, with intriguing results. As others did before him, Barrow noticed that the force generated by a rower in a boat has two components: one drives the boat forward and one to the side. Since the sideways motion represents wasted effort, rowers should be positioned in the boat so that it is minimised. So what exactly is the ideal positioning of rowers, the ideal rig?

It's not just evil villians who can blow smoke rings, it seems peat moss has been doing it for millennia.