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> Even humans do not fully agree on mathematics. There is no “one” mathematics because mathematics is the human exploration of idealized objects using a variety

> Even humans do not fully agree on mathematics. There is no “one” mathematics because mathematics is the human exploration of idealized objects using a variety of human logical systems. Maybe not in its entirety, but I find it hard to imagine that any civilization as advanced as ours (let's say a civilization that manages to harness nuclear fission, just to set a baseline) will not come up with concepts such as prime numbers, real number, complex numbers, calculus, etc. If they do that, they will inevitably find the same structures we found using function theory. They will know about differential equations and prove similar theorems about them as we did. And the Pythagorean theorem is a universal truth that holds everywhere.

lostmsu 4y ago
In that list prime numbers might not be a thing.
lmkg 4y ago
> real number, complex numbers, calculus, etc Some humans believe that the prominence of real numbers is a historical accident. It seems quite plausible to me that a human society, much less an alien one, would go down a mathematical evolutionary path based on the constructable numbers and the computable numbers. Regardless of whether we eventually find the same structures, there are things that we might consider basic which they find esoteric and vice-versa. Heaven forbid we encounter an alien civilization that discovered an O(log n) algorithm for integer factorization before they invented steam power.
- bmitc 4y ago
  > Some humans believe that the prominence of real numbers is a historical accident. That is a great point. The continuum is contentious and pretty highly debated philosophically. I also encourage people interested in that to also learn about smooth infinitesimal analysis. Just a small tweak in the underlying logic and model yields unique mathematics and questions established assumptions.
illogical_spock 4y ago
> And the Pythagorean theorem is a universal truth that holds everywhere. Or at least in every world where there exist straight lines, yes? For instance: > The Pythagorean theorem is derived from the axioms of Euclidean geometry, and in fact, were the Pythagorean theorem to fail for some right triangle, then the plane in which this triangle is contained cannot be Euclidean. More precisely, the Pythagorean theorem implies, and is implied by, Euclid's Parallel (Fifth) Postulate.[59][60] Thus, right triangles in a non-Euclidean geometry[61] do not satisfy the Pythagorean theorem. For example, in spherical geometry, all three sides of the right triangle (say a, b, and c) bounding an octant of the unit sphere have length equal to π/2, and all its angles are right angles, which violates the Pythagorean theorem because {\displaystyle a^{2}+b^{2}=2c^{2}>c^{2}}. https://en.wikipedia.org/wiki/Pythagorean_theorem#Non-Euclidean_geometry https://en.wikipedia.org/wiki/Pythagorean_theorem#Non-Euclid...

lostmsu 4y ago

In that list prime numbers might not be a thing.

lmkg 4y ago

> real number, complex numbers, calculus, etc Some humans believe that the prominence of real numbers is a historical accident. It seems quite plausible to me that a human society, much less an alien one, would go down a mathematical evolutionary path based on the constructable numbers and the computable numbers. Regardless of whether we eventually find the same structures, there are things that we might consider basic which they find esoteric and vice-versa. Heaven forbid we encounter an alien civilization that discovered an O(log n) algorithm for integer factorization before they invented steam power.

bmitc 4y ago
> Some humans believe that the prominence of real numbers is a historical accident. That is a great point. The continuum is contentious and pretty highly debated philosophically. I also encourage people interested in that to also learn about smooth infinitesimal analysis. Just a small tweak in the underlying logic and model yields unique mathematics and questions established assumptions.

illogical_spock 4y ago

> And the Pythagorean theorem is a universal truth that holds everywhere. Or at least in every world where there exist straight lines, yes? For instance: > The Pythagorean theorem is derived from the axioms of Euclidean geometry, and in fact, were the Pythagorean theorem to fail for some right triangle, then the plane in which this triangle is contained cannot be Euclidean. More precisely, the Pythagorean theorem implies, and is implied by, Euclid's Parallel (Fifth) Postulate.[59][60] Thus, right triangles in a non-Euclidean geometry[61] do not satisfy the Pythagorean theorem. For example, in spherical geometry, all three sides of the right triangle (say a, b, and c) bounding an octant of the unit sphere have length equal to π/2, and all its angles are right angles, which violates the Pythagorean theorem because {\displaystyle a^{2}+b^{2}=2c^{2}>c^{2}}. https://en.wikipedia.org/wiki/Pythagorean_theorem#Non-Euclidean_geometry https://en.wikipedia.org/wiki/Pythagorean_theorem#Non-Euclid...