How does one “invent new maths”? Like Isaac Newton inventing Calculus, or John Napier logs. How does one answer a mathematical question that’s never been answered?
In: Mathematics
It’s a philosophical debate on whether mathematics exists in reality or whether it is a human creation.
Most mathematical systems (algebra, geometry, calculus, group theory) and such are sets of rules. You can really create any set of rules that you want. These systems are obviously more useful and studied if they have practical use in the real world. I can make up a system where 1 = 2. That can be a “legitimate” system, but it has little practical use.
Mathematics, such as calculus and logarithms, are “invented” in that Newton and Euler came up with new sets of rules. Those rules were consistent and actually helped calculate things in the real world.
Another example was non-Euclidean geometry. Everyone “knew” what geometry was and how it modeled the real world. It wasn’t until 2,000 years after Euclid “invented” geometry that a couple of mathematicians dropped one of his five rules and came up with a whole new, consistent, geometry.
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