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?
Agreeing to pay £50,000 for something worth £2 wouldn't win you any haggling competitions. In mathematics, however, a similar result can bring you international acclaim. This is the case with recent progress towards the famous twin prime conjecture.
An "electric atomosphere" is not what you expect at a maths lecture. But it is what prevailed when Andrew Wiles announced his proof of a 350-year-old-old problem, Fermat's last theorem, exactly 20 years ago.
This year's Abel Prize has been awarded to the Belgian mathematician Pierre Deligne for "seminal contributions to algebraic geometry and for their transformative impact on number theory, representation theory, and related fields".
One of the most surprising things about mathematics is its many unsolved mysteries. Mathematics is far from "done and dusted", and Steve Humble shows us how we can come up with some mathematical mysteries of our own.