What are Mathematics and Science?

Mathematics is not science. In fact, his approach is exactly the opposite compared to, for example, physics. Mathematics is an elaborate game, in which it is decided from the beginning to play according to the given rules. Then we proceed by proving theorems; truths already implicitly hidden in these rules. In that way, you could say that mathematics is the easiest thing in the world, since everything is given from the beginning, but of course it requires an incredibly sharp brain to attract and understand what is already built into the rules: the assumptions. initials ("postulates") that can neither be proved nor disproved and all the information you can get from good mathematics journals.

In physics, the situation is quite the opposite. We are observing the world and trying to understand how it works, that is, trying to find the rules that nature follows. At least we assume that nature follows rules. But strategy is difficult because we never have perfect knowledge of anything. It's a bit like covering large parts of a chessboard and then trying to get someone (who is ignorant of chess subtleties) to figure out the rules, only gaining access to some of the 64 squares on the chessboard. For example, let's say you can only see three of the squares; it will be almost impossible to obtain the complete set of chess rules. No matter how long you look at the three squares (during a real game of chess at all 64), you will hardly be able to draw any conclusions about what the pieces are doing, and why! - when you are not seeing them. They appear seemingly random, leaving your three squares just as erratically. We could hardly gain knowledge of the complete rules of the game.

But it works more or less the same way with the fundamental laws of nature, with the difference that the number of "squares" that we must observe is probably considerably greater than 64. Although some physicists believe that we will soon be able to see the equivalent of all "squares", others think that we still see only three or even less.

What is the similarity between mathematics and physics?

Newton developed a large part of modern mathematics in the seventeenth century because he needed it to analyze his laws of motion: mechanics. However, more modern mathematics, such as group theory and differential geometry, developed "by themselves" but were soon borrowed and used in quantum physics and general relativity.

This led the renowned physicist Eugene Wigner, in 1960, to write an article entitled "The Unreasonable Effectiveness of Mathematics in Natural Sciences." Why, Wigner wondered, is mathematics, often designed just for its own sake (fun!), So successful at describing the phenomena of nature. Perhaps nature itself is mathematical in essence?

I think it is much simpler than that. Mathematics is a language developed by the human brain. Although it is the most accurate language we know today, it is still basically a language. Mathematics is a kind of map of how our brain works, with logic as a compass. In the future it may well be that we will find (invent) a language even more precise than mathematics, which will then be used to describe all kinds of phenomena. Since both math and science are the fruits of the human brain, it is also perfectly natural for them to fit like a glove. Saying that mathematics is "unreasonably effective" for use in physics and other sciences is more like saying that our glove making tools are "unreasonably successful" at glove making. The nature book does not necessarily need to be written in mathematics, nor does a computer manual need to be written in English.