Mayan mathematics included a sort-of-positional notation (with base 20) and a zero. The Mayans almost certainly developed it independently, without any contact with the Old World civilizations.

If some mathematical ideas are culturally contingent (see “Draw a Triangle”), what mathematical concepts are universal? What ideas must develop in any society that has some kind of advanced math, and what ideas could we do without? For example, we think of math as based on proof and logic, but perhaps that’s just a cultural legacy from the ancient Greeks, and not really necessary at all?

I think that proofs are necessary but that theey do not necessarly have to be so rigorous as some cultures have made them out to be. I think that mathematics should be a “playing feild” in which a person comes up with a n idea and then others rebute it or agree with it and together come up with an answer, rather than one person on his own trying to come up with an answer. Some concepts that should be universal are of course the properties of addition, subtraction, division, multiplication and also the properties of shapes. If you have these basic things I think that anyone can come up with ideas and proofs in which other people can universally rebute or agree with.

It hard to find the answer for this question. I think, today all civilization are based on math (computer, satellites, space vehicles, etc.) In my opinion, the modern society needs an advanced math, and there are no ideas that we may live without. Moreover, I agree with previous comment that some mathematical concepts are universal. They are multiplication and division, adding and subtraction.

It’s very interesting that the Maya had a ritual calendar of 260 days with 13 nonths of 20 days numbered from 0 to 19; I have to highlight that they actually used 0 as a number because the days could have been numbered 1 to 20. But, they also had the 365-day civil day calendar that is used universally.

I do believe that some mathematical ideas are culturally contingent for example the concepts of addiction, substraction, multiplication and division are universal since they are what calculation consists of.

In any society that has some kind of advanced math, ideas that are easier and simpler to use should be developed since it would be used nationwide.

I believe the base 20 comes from Mayan culture using counting fingers concept. They had fingers and toes, so their base 20 may come from that notion. And they must of developed their own math by simple understanding of gaining and minus of fingers to apply to trade and commerce.