The idea had its roots in the “dream of cows” that Einstein experienced much earlier before working on his theory. The dream involved: the cows, their Master, and their reaction to electric shock. Observers saw differently and that difference in perception was not coherent with the current notion of time and space, thus the Bigger Ideas were hiding from the winds, allowing faster growth in mind, finally flourshing so vividly one could not foresee their fruitfulness.
My brother was more intelligent than I am – once Tesla said (his brother fell from a horse and died). But this wasn’t about intelligence, but -as mr Ravi Vakil from MIT has it – its about learning to ask the right questions. Mr. Einstein’s transformations weren’t ingenius. But, his revolutionary vision was. It was not because there was tremendous visionary intelligence (Einstein said he’d change his life completely- for more, please, learn more about him and his Eduard), but “standing on the titans’ arms. All the ideas were collapsing until the speed of light was considered constant.
But, do we really understand it? Did he? I would not take a chance at guessing.
Nevertheless, Einstein in “Transformation of the Maxwell-Hertz Equations” and “Transformation of the Energy of the Rays of the Light. Theory of the Radiation-pressure on a perfect mirror” clearly explained his ideas (in human, based on only elementary mathematics, way) . It is about relativity of perception of what happens for various observers. This is, therefore, about the shape of the universe and the way it behaves. It is that we can’t move faster than the speed of light.
But the nearest star is far away and i’d take some time to get there? We know Michelson’s experiment but can we find a mathematical idea behind all this to make faster travel possible, ie. explain differently what we could possibly incorrectly perceive.
This is somewhat the place when (and why) quantum effects have been introduced (to make irregular jumping over sets of numbers possible). Lets now look at the NPT: we have the decimal system, where each next number grows by 1. There are also rational and irrational numbers we learnt about. The primes create all the integers forming our decimal system and seem tangible. But are all the integers tangible?