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Did abstract mathematics, such as Pythagoras鈥檚 theorem, exist before the big bang? (continued)

Richard Swifte
Darmstadt, Germany

I would lump mathematics in a similar category to language, art, music, etc. 鈥� inventions of the human mind that are highly relevant and meaningful to our species, but have no reality otherwise. It is amazing that the evolving human brain happened to gain the ability to think up abstract mathematics (going beyond the simple practical ability to count objects), since this has no obvious survival value to our species.

However, what a useful invention mathematics has been, essential to developing scientific theories and in technical calculations. Without it, we would never have acquired our knowledge of the structure of the solar system and our subsequent ability to accurately send spacecraft to investigate it.

There is simply no circumstance in which 2 + 2 doesn't equal 4, not even in a universe containing fewer than four particles

But while geometrical examples such as Pythagoras鈥檚 theorem are precise, we should regard mathematical equations in science as good approximations to truth rather than 100 per cent precise. Consider, for example, that Isaac Newton鈥檚 beautifully simple equation describing gravity became accepted as perfectly accurate until slight observed anomalies in planetary orbits showed its imprecision, corrected by Albert Einstein鈥檚 more complicated general theory of relativity. Time will tell whether the latter is yet another approximation to the truth.

Mathematics is a highly useful tool invented by the human mind 鈥� and probably by other intelligent alien species 鈥� that has been essential for developing our modern society and knowledge. But if it weren鈥檛 around, the rest of the universe (pre or post-big bang) would simply keep on existing and evolving in the same way.

Luce Gilmore
Cambridge, UK

Maths is eternal, that is to say, its rules are unaffected by time. They don鈥檛 wear out and they can鈥檛 be overloaded by excess use. There is simply no circumstance in which 2 + 2 doesn鈥檛 equal 4, not even in a universe containing fewer than four particles. Maths isn鈥檛 invented; it is discovered. This is the Platonic stance, popular among mathematicians. Pythagoras鈥檚 theorem is easily proven by simple arithmetic, so it is eternally true.

If anything at all existed 鈥渂efore鈥� the big bang, it would be maths. The absence of mathematicians would be entirely irrelevant.

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