like we know now how to get certain answers through different processes and all that fun stuff. but when they were first coming up with it, how did they know they were doing it right?
In: Mathematics
I’ll disagree with some of the others and say mathematics was invented. What they’re describing is *counting*. If I take 2 apples and put them on a rock (tables haven’t been invented yet), then put 2 more apples on the rock, I can count 4 apples.
Mathematics, on the other hand, was invented to be able to write that down in the abstract. 2+2=4 is divorced from whether or not I have 2 or 4 apples in front of me, or no apples anywhere in sight. I can go back to the apples and check my math, but once proven, I’m confident that 2+2=4.
Mathematics was invented to solve not just how many apple there are, but those all-important questions like:. If a man owns a farm, 5 pigs, and 6 fig trees, how much tax does he owe? If each of my graineries holds X bushels of grain, and I have 6 graineries, how much grain did I take from the farmers? We should probably tax the farms more fairly (emphasis on the more). So we invent the concept of area.
Or even more complex: If I have Y bushels of grain stored, and 2,000 townspeople, 20 priests, and the 8 royal family to feed, how many standard bowls of grain do I give out a day to last until harvest? Given that the priests get more, and the royals get even more.
So far math is pretty grounded in the real world. But by the Classical period, we start thinking about more abstract things, like the area and volume of geometric shapes. We see mathematical *proofs*, where we build on already proven concepts to *prove* a higher concept. One of these the *method of exhaustion*, where we divide a shape into smaller and smaller shapes of known area/volume and sum those. They got pretty close to calculus, but that had to wait for Leibniz and Newton, who again used proofs of earlier known concepts to build a new field of mathematics.
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