Albert Einstein loved to think about physics, especially about light and about gravity. But he really hated school, and particularly math classes. So a classmate would take notes in math classes for Albert, and then Albert would use them to cram for exams, and that way he could devote the time otherwise "wasted" in math class to thinking about what the world would look like while riding on a beam of light or what it would feel like falling down an elevator shaft (I'm not kidding....). Many years later, Einstein was already famous for his Theory of Special Relativity which explains why light behaves the way it does, when he decided to take on gravity.

Although Newton's theory of gravity explained many questions, such as why the planets move the way they do and why things fall, and made very accurate predictions for experimental observations, there were a few things that were amiss. For some strange reason, the planet Mercury's orbit was a little off from what Newton's gravity predicted for its motion, and a few other little things here and there didn't add up perfectly. But for all practical purposes, Newton's theory of gravity worked very well and was a huge leap forward in our understanding of Nature. Einstein, however, wondered about the little odds and ends that weren't explained by Newton's theory.

For eight years, Einstein did nothing but tinker with Newton's theory of gravity. He had many brilliant insights, but the structure of what he put together was very messy mathematically. There was no tidy way to put down in equations the essential meaning of his new ideas. Then he talked to an old classmate who had taken notes for him in math classes. Einstein explained his new hypothesis about gravity and asked the fellow if he had any ideas about how to structure gravity more clearly mathematically. His friend told him about a discipline of mathematics that had been discovered while they had both been in school — tensor calculus and matrix mechanics in linear algebra. When he heard this, Einstein spent a lot of time slapping himself in the head. This mathematics was not only elegant and beautiful, but it took the untidy equations Einstein had formulated and put them in a structure that was compact, showed relationships easily, and brought elegance and ease of understanding to what later became known as Einstein's General Theory of Relativity. Einstein's General Theory of Relativity boils down to this one equation in the language of tensor calculus:

The second example is about How Imaginary Numbers gave us computers!