Great Rule Breakers of the Past
Sometimes we think of the rule breakers as people who are living on-the-edge and perhaps just a little bit on the “dark side”. After all, rules have been created to provide order and to help us live together in harmony. But, what if the rules aren’t really the rules? What if the written rules are trumped by the unwritten rules? The unwritten rules that everybody knows are true even though they might not be?
Many of the great innovations in history have been made by people willing to go against the flow and break the rules that define “this is the way we’ve always done it”. Here are two of the best:
Around 300 BC the Greek mathematician, Euclid, published his famous treatise on geometry entitled “Elements”. One of his postulates that all 10th-grade Math students are familiar with is called his 5th postulate. In a nutshell, the 5th postulate states, though it can’t prove it, that 2 parallel lines will never intersect. Everybody knows that to be true. It’s an unwritten rule.
21 centuries later, 2 men looked at the postulate and asked the most dangerous question of all: “What if that is not true? What if 2 paralell lines can intersect?” Around 1830, the Hungarian mathematician János Bolyai and the Russian mathematician Nikolai Ivanovich Lobachevsky separately published treatises on Hyperbolic Geometry (1) and a whole new branch of mathematics (non-euclidean or spherical geometry) was born. By the way, if you doubt the possibility of this happening, just take a look at a sphere. Two lines that are parallel at the equator will indeed intersect at the north and south pole. They were willing to break an unwritten rule and in so doing change the course of mathematical history.
1. Wikipedia:Euclid history