Mathematics deals with perfection, with absolute truths. Scientific theories on the other hand always have a sense of approximation. Whereas a mathematical statement like the theorem of Pythagoras holds true for all right angled triangles (and hence may be used to define a right angled triangle), scientific theories like the theory of gravitation are subject to constant revision and updating. In science, people come up with hypotheses to explain phenomena. If experiments then corroborate the predictions made by these hypotheses, then they gain credibility and are elevated to the status of a theory and become part of our everyday understanding of the world around us.
Here’s a question which serves to illustrate the difference. You have a chessboard in which two squares from opposite corners are removed. So instead of 64 squares, you now have 62. And you are given 31 dominoes that cover 2 squares each. Is it possible to cover the board with the dominoes? (source : Simon Singh, Fermat’s Last Theorem)
The scientific way to answer this question would be to try filling the board in different ways and see for yourself whether the question permits a solution. After a few dozen attempts you may come to the conclusion that it is not possible to fill the squares with dominoes but still an element of doubt prevails. This is now a theory based on experiment and is readily overturned if even a single counter-example can be produced.
Another way is to argue using logic. You notice that the squares on opposite corners of a chessboard are always of the same colour (say, black). Hence, if you remove those squares you’ll be left with 32 white squares and 30 black squares. Also any two adjacent squares in a chessboard (which we wish to cover using dominoes) must necessarily be of opposite colours. Hence after 30 dominoes, we’ll be left with two white squares and a single domino. But since the two white squares cannot be adjacent, we can conclude with absolute certainty that it is impossible to fill the squares with the dominoes. It is this absolute nature that gives mathematics its beauty.
Prof. V. Balakrishnan once told us in class that although we (physicists) know that the photon has zero rest mass, the state-of-the-art experiments can only confirm that its mass is less than 10-54 kg. So if the photon has a mass, it must be less than 10-54 kg. This blatant acceptance of its limitations, I believe, may be why we would never be able to convince a creationist (or a climate-change denier) of the truth and explanatory power of some of the theories in science. They just don’t understand the way science works1, that there is such a thing called the relativity of wrong. As Asimov nicely puts it:
When people thought the earth was flat, they were wrong. When people thought the earth was spherical, they were wrong. But if you think that thinking the earth is spherical is just as wrong as thinking the earth is flat, then your view is wronger than both of them put together.
The shape of the Earth is not oblate spheroidal either though it is a better approximation still. Now the shape of the Earth has a special name – geoid – which in Greek means “shaped like the Earth” (The mathematics now gets more complicated though.) So our Earth is a geoid (no surprises there). To me, it is this sense of adventure and exploration, deepening our knowledge while at the same time remaining humble of its limitations that gives science its beauty.
1. There is this funny little story about the philosopher Ludwig Wittgenstein (1889-1951). Once he asked one of his friends why people always say that it was natural for men to assume that the sun went around the earth rather than the earth was rotating. His friend said: “Well, obviously, because it just looks as if the sun is going around the earth.” To which the philosopher replied: “Well, what would it look like if it had looked as if the earth were rotating?”