It is often remarked that the greatest geniuses that have ever lived were Archimedes, Newton and Einstein. This is a myth that mixes the greatness of a discovery with that of the discoverer. It is like deifying Neil Armstrong for being the first man on the moon, and neglecting to see that he was one cog among the hundreds of NASA workers who made the whole venture possible. As Newton himself remarked, he saw far because “he stood on the shoulders of giants” before him.
One of these giants is certainly Johannes Kepler. This year marks the 400th anniversary of his publications of the third law of planetary motion, which states that the cubes of the planets’ distances from the sun are proportional to the squares of their period. It is part of his book Harmony of the World, which contains a wealth of mathematical innovations.
The climax of the book is his less known explanation as to why the planets have the distances they do.
He found that the minimum and maximum angular speeds of the planets have simple ratios: For the five planets from Venus to Saturn, they are 24:25, 15:16, 2:3, 5:6 and 4:5, all well-known musical ratios or ‘intervals’, hence the title of the book. Such unscientific musings may seem bizarre today.
Newton himself wrote more on alchemy and religion than on all of maths and physics combined; from his studies of the Biblical Book of Daniel, he predicted the “end of the world” in 2060.
Like most people, geniuses get some things right, and others wrong. Many results were discovered independently by different people, and were simply ‘ripe’ for the picking.
Without in any way lessening their achievements, geniuses are often at the right place at the right time, albeit with the intelligence, experience, and skill to take the step to the next level.