Conjectures, Hypothesis, and Fields Medal

In maths, the list of items that are taken-to-be-true are called axioms (e.g. “A straight line may be drawn between any two points.”). What has been proven is called a theorem (e.g. Pythagoras theorem). And then are aspects a mathematician suspects may be true, but nobody has proven yet. This last set (unproven items) can have different names. Some of them are called conjectures, while others are called hypothesis.

 

In Music of the Primes, Marcus du Sautoy explains the basis for the two terms. Anything new that is proposed as possibly being true but not yet proven starts by being called a conjecture e.g. Goldbach’s conjecture (“Every even number can be expressed as the sum of two primes”). Sometimes, as mathematicians work on other things, they find something they are trying to prove depends on a conjecture being true. If more and more things that mathematicians try and prove end up depending on the same conjecture to be true, then that conjecture is upgraded to the status of a hypothesis. Like the Riemann hypothesis.

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The ultimate prize in the field of maths is called the Fields Medal – it’s like the Nobel Prize for Maths. But it has a strange constraint – it can only be awarded to mathematicians under the age of 40. Why the age limit?

“This is not because of the generally held belief that mathematicians burn out at an early age.”

Instead:

“(John Fields) wanted the award to spur on the most promising mathematicians to even greater achievement.”