For example, a sapient doesn’t need integers to build a hearth with a cooking fire nor to make a stone-tipped spear. That is an example of science and technology without numbers.
I guess the question here is what we are calling ‘math’? Arithmetic perhaps obviously arises as something in a situation where things need to be counted or kept track of for practical purposes.
But a generalization from that to a formal system is an interesting question. The Greeks like Archimedes and Eristophanes started down that road. But if you follow it to its logical end, this leads to irrational numbers… powers and logarithms. And then to concepts like calculus and imaginary numbers…
True, but other species on Earth have been observed to use tools in some form. Of course this doesn’t imply that they developed them from any theoretical basis?
I guess you need math when you run out of fingers and toes. How useful is math for a species that can count on their individual cells?
Ha Ha! The genius amoba? Right out at the 20th standard distribution.. but not logically impossible.
You should write an SF story about that. The loneliness of being so far ahead of your kind! James Blish almost had something like that with his protos in ‘Surface Tension’…