Life is full of temptation, with various addictive substances and habits lurking all around us. From the infamous sex, drugs and rock and roll to the rather more everyday (but no less addictive) coffee, chocolate and the like, there’s no lack of hazardous potholes in the road of life.
I’m pretty sure, however, that mathematics would not be at the top of most people’s lists of most dangerous addictions. So let this serve as a warning – maths ain’t as innocent as it may appear!
Just ask today’s birthday star, Hungarian mathematician Farkas Bolyai (9 Feb 1775 – 20 Nov 1856) who spent much of his 81 years in the grip of a horrible maths addiction.
Bolyai, who was a friend and contemporary of the German mathematician Carl Gauss, spent a lifetime trying in vain to prove Euclid’s famous Fifth Postulate. (Euclid’s Fifth Postulate, often called the ‘parallel postulate’, states that only one line can be drawn through a given point so that the line is parallel to a given line that does not contain the point. Or, stated very simplistically, that two parallel lines do not meet.) So bad did it get, that he ended up fervently discouraging his son János, who also had a strong interest in mathematics and became interested in Euclid’s parallel postulate, from pursuing the study of this topic. In a letter to his son, Bolyai wrote: “For God’s sake, please give it up. Fear it no less than the sensual passion, because it, too, may take up all your time and deprive you of your health, peace of mind and happiness in life.”
As so often is the case with parents warning their children against the dangers and temptations in life, Balyoi’s warning to his son only served to encourage young János to venture deeper into the dark arts. Following in his father’s footsteps, János Balyoi continued working away at Euclid’s parallel postulate, eventually coming to the radical and unexpected conclusion that consistent geometries exist that are independent of the parallel postulate. Known as non-Euclidian geometries, these are curved spaces where parallel lines aren’t necessarily parallel (in hyperbolic space parallel lines actually diverge from each other) and where the inside angles of a triangle do not add up to 180°. This lead young János, in a letter to his father, to enthuse: “Out of nothing I have created a strange new universe”.
I’m sure Balyoi the elder must have initially thought his son had given in to one of the other addictive substances!
While János Balyoi’s work was truly groundbreaking in the new field of non-Euclidian geometry, he was discouraged by Carl Gauss to pursue it (Gauss claimed to have discovered the same results some years earlier, even though no proof exist to support this claim). Worse, a Russian mathematician, Nikolai Lobachevsky, independently published essentially the same results two years before Balyoi, and so János never received recognition for his work. He became reclusive and eventually went insane, dying in obscurity in 1860.
Let this tale of woe serve as a warning of the very real danger lurking in a life in mathematics. Don’t blame me when you’re old and alone, throwing page after page filled with Greek symbols and insane scribblings on the fire to keep you warm. You have been warned!