Theorem of everything: The secret that links numbers and shapes
For millennia mathematicians have struggled to unify arithmetic and geometry. Now one young genius could have brought them in sight of the ultimate prize
By Gilead Amit
IF JOEY was Chloe’s age when he was twice as old as Zoe was, how many times older will Zoe be when Chloe is twice as old as Joey is now?
Or try this one for size. Two farmers inherit a square field containing a crop planted in a circle. Without knowing the exact size of the field or crop, or the crop’s position within the field, how can they draw a single line to divide both the crop and field equally?
You’ve either fallen into a cold sweat or you’re sharpening your pencil (if you can’t wait for the answer, you can check the bottom of this page). Either way, although both problems count as “maths” – or “math” if you insist – they are clearly very different. One is arithmetic, which deals with the properties of whole numbers: 1, 2, 3 and so on as far as you can count. It cares about how many separate things there are, but not what they look like or how they behave. The other is geometry, a discipline built on ideas of continuity: of lines, shapes and other objects that can be measured, and the spatial relationships between them.
Mathematicians have long sought to build bridges between these two ancient subjects, and construct something like a “grand unified theory” of their discipline. Just recently, one brilliant young researcher might have brought them decisively closer. His radical new geometrical insights might not only unite mathematics, but also help solve one of the deepest number problems of them all: the riddle of the primes.