The first thing I should teach the world is what science is, and what science is not. Science is the study of nature (in the general sense of the functioning of the natural universe), leading to consistent results that are verifiable by observation and experiment, and to an understanding and explanation of at least some features of how nature works - ultimately, the laws that govern the functioning of nature.

Anything that falls short of this is not science. Concern with nature, short of study leading to its understanding, is not science. Concern with purely mental constructs, having little or no relation to the actual functioning of nature, is not science. Study of nature, without any success in understanding and explaining how it works, is not science. Views or ideas about the functioning of nature, which are not based upon verifiable observations, are not science.

I also wish everyone understood that nature seems to be governed by laws - it is not random or incomprehensible. What motivates scientists to study science is a great curiosity about how nature actually works, and wonder at the fact that nature can be understood at all.

I do have my own favourites, among specific scientific principles, concepts and discoveries. A toss-up for top place would be the quantum principle, and the relativity principle - that is, the basic principle (quantisation) underlying quantum mechanics, and the basic principle (relativity) underlying the special and general theory of relativity. These were probably the two greatest scientific discoveries of the twentieth century, perhaps the two greatest scientific discoveries of all time (to date). Someone who wants to participate in, or at least understand, the most important intellectual achievements of the times in which we have lived, must at the very least try to comprehend these two great discoveries.

Albert Einstein had a fundamental, pioneering role in both of these discoveries. But quantum theory would certainly have nevertheless developed, even if not for Einstein's pioneering contributions, since others would eventually have made the discoveries that he made and had the insights that he had. The special theory of relativity would also likely have developed, although perhaps under another name, even without Einstein's guidance and clarity of vision.

It is open to doubt, however, whether general relativity and its particular outlook would have developed in other hands, without the geometrically guided vision of physical laws and the inspiration that Einstein had. The contributions of Einstein's contemporaries were all made at his stern - drawn along, by the wake of his propulsion, towards a full understanding of the fundamental laws of physics on a geometrical basis.

See John Harnad's website.