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After looking at the periodic table of elements this question came to me one day.
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The periodic table is fascinating. Theoretically, it's infinitely possible to come up with a bigger nucleus and create a new element. Or create a new unstable organochemical compound that would NOT under any circumstance (well, there's a probability, but that's a whole other thing) naturally occur anywhere.
But that's chemistry, not math.
Math is different, but at the same time the same.
Math is a web. It already has some threads connecting some "laws" of the universe but another one may be "discovered". But math in the real world is sometimes discovered by accident (Madness? No.) or finally discovered by repeatedly hammering your head against a wall that has a thread on the other side of it. Everything there is to be found in math already exists, but a lot of it is still on atleast somewhat uncovered ground. Math isn't invention or discovery, it logic. Widening and spreading of logic.
Jam it back in, in the dark.