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
Another angle most people don’t consider is that the very basis of mathematics is that if you have A) a new idea, and B) a body of already-accepted ideas, then what you need to do is 1) assume your new idea is correct and then 2) find where it either contradicts itself or contradicts what you already know to be true. That is how you might say somebody “invents” new math (sorry, not British). If your new idea violates what you already know, then that is generally a good sign that it *might* be incorrect. But if you can invent a theory of Calculus, and 1 + 1 still equals to 2, then you might be on to something.
For example, something most people don’t know is that the reason that division by zero is considered an invalid mathematical operation is because, you can get the result that any number equals any other number. The easiest place to see this is the graph of 1/x, where when x=0, y seems to be = ∞ AND -∞. Thus ∞=-∞. Clearly, this is infinitely incorrect. In fact, you can algebraically manipulate a division by zero to say anything you want, like 1=2. 1=2 doesn’t line up with what we already know to be true, so clearly there is something wrong with our new idea (lest there be something wrong with the old ideas– though the cumulative effect of this whole process is that we tend to suss out the right ones)
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