Difficult mathematics

The largest proof in mathematics, aka the Enormous Theorem, took more than 100 people over 33 years to complete. Michael Aschbacker, an innovator in the abstract field of group theory, finally filled the gaps in the proof’s 15,000 pages of calculations in 2004. He was awarded the Rolf Schock prize in mathematics for his work on the “diabolically difficult” proof.

The theorem is also known as the Classification Theorem of Finite Groups. In maths, groups can refer to a collection of symmetries, such as the rotation of a square that produces the original shape. Some groups can be built from others but, rather like prime numbers, “finite simple” groups are elemental. There is an infinite number of finite simple groups, but a finite number of families to which they belong. The theorem was proposed in 1971 when mathematician Daniel Gorenstein devised a plan to identify all the finite simple groups, divide them into families and prove that no others could exist.

While the Enormous Theorem may be the largest proof ever, it is not the most difficult. That accolade goes to Fermat’s Last Theorem. Proposed by Pierre de Fermat in 1637, no successful proof was published until 1995, despite the efforts of countless mathematicians over the years.

If you have an interest in maths and some time on your hands, you may want to have a go at tackling the Riemann hypothesis, considered the most important unresolved problem in pure mathematics. This is one of the six remaining Clay Mathematics Institute Millennium Prize problems, so find the answer and you can win a $1m prize.