The Inca had a relatively sophisticated mathematical system that could handle division, multiplication and fractions.

Here's a paper demonstrating a calculating device used by the Inca. http://etnomatematica.org/v5-n2-agosto2012/Catepillan_Szymanski.pdf

I think the Maya are generally considered to have had the most sophisticated mathematical system in the Americas -- tied very closely to their calendric system. They had zero (possibly an invention from a previous civilization, but earlier than pretty much anywhere else on Earth), a concept of fractions, a unique numeric symbology. However it's unclear if their system was ever used with multiplication and division. Later mathematicians have tried to figure out systems they could have used, but it's presently not know if any of the proposed systems were actually used.

Their system was also positional, which is a major achievement in numeric representation. Most civilization's systems never achieved positionality, which makes representing arbitrarily large numbers difficult or impossible and complex calculations even harder (for example, try multiplying two large Roman numerals vs. two modern "Arabic" numbers).

https://math.ucsd.edu/programs/undergraduate/history_of_math_resource/history_papers/math_history_07.pdf

http://www.authenticmaya.com/mathematics.htm

http://www.storyofmathematics.com/mayan.html

https://www.youtube.com/watch?v=Ybvb7oy_WV0

https://en.wikipedia.org/wiki/Dresden_Codex

edit: gold! thanks!

Certainly by ~250 CE, the Hopewell in what is now Ohio understood pi and how to calculate the circumference and area of circles, as well as the perimeters and areas of other shapes. This is demonstrated by the inclusion of a square enclosure in one of their most famous monuments, which has the same perimeter as one of the two circular enclosures and the same area as the other. Since I'm short on time, I'll just link to a post where I discussed this recently.

Math as we use it is a relatively modern invention. However, one of the more frequent computations we do are based of our calendar. We know the Mayans had a very advanced calendar system that was used all over Mesoamerica: http://en.wikipedia.org/wiki/Mesoamerican_Long_Count_calendar From recently reading 1491 by Charles Mann they apparently had a 0 date, although what exactly this date is isn't quite clear. 0 is an oddity as we generally start counting when you have something, and you don't count yourself as having 0 of something if you don't have an object - that is to say it's a slightly different concept. Not only is it this fundamental part of our numbering system, it is also used a placeholder (this is conceptually similar to starting with zero when counting) when expressing larger numbers. The oldest long count date possible is Aug 11, 3114 BCE which is really long ago. The oldest definite recorded date is December 6, 36 BCE which would show a well developed concept of 0 by that date. This is centuries before people in the old world came up with the concept of 0. Additionally, the Maya have a very sophisticated system of public in addition to their astronomy, which is probably best showcased by the temple in Chichen Itza where the sun produces the shadow of a snake on the steps. This alone requires of lot calculation and accuracy in order to pull off, although Old World civilizations pulled off similar tricks a few other times. This is not direct knowledge, but it shows they had a system of comparable complexity to what Europe had at the time. Unfortunately in 1562 Diego de Landa burned all of the Mayan (codices) documents so we can't know for certain exactly where they were, but it is clear they got pretty far

I don't want to shut down the discussion of your awesome question, but there is an issue with the way you phrased it. Of course there have been Native American mathematicians after Columbus, just like there have been Native American mechanics and accountants.

Lots of people only think of Native Americans as something that existed in the past, and neglect the fact that there are still thousand of Native Americans living completely contemporary lives. I know that it's implied you were looking for historical examples, but denying the modernity of present Native Americans is a big enough problem that I felt the need to chime in.

Okay, back to the great discussion!

The Anasazi in Chaco Canyon created very impressive set of rocks to mark the summer and winter solstices and equinoxes by using the placement of the sun to travel through slits in tilted rocks, which then projected beams of light onto wall carvings. Which wall carving the beam of light would hit would indicate what solstice/equinox was happening. The math this must have taken would have been... astronomical.

I saw this in a video in a Native American history course. Trying to find sources online that are legitimate have proven tough. I learned about it from I believe This Video. Though there are a few other websites that can tell you a bit more about it.

The city of Teotihuacan is a testament to Mathematics. Every single staircase is masterfully made at consistent angles, and perfectly level. It truly is a testament to ancient engineering, and a clear representation that complex math must have been present in the Americas prior to any western influence.

I've heard Native Americans in what is now North America had not "invented" the wheel when Europeans arrived and had no written language. Is that true?

I know the mayan* and and Aztec were advanced, how about the tribes that lived in what we now know of as America and Canada?

Or were these groups more hunter gatherers (i.e. less dependant on agriculture) and had less of a need to predict seasons?

Edit - auto correct mangled mayan