Unsurprisingly, infinite was a common them for them. They, in fact, considered different sizes of infinity which they called enumerable, innumerable, and infinite, previewing transfinite cardinals by nearly 2000 years.
The Mayans also had a fascination with large numbers (although not quite that large), and their use in calendars (which were much more mathematically well-constructed than any have been in the West, surely than they were during the first millennium CE, when the Mayans were at their peak). The Mayans kept careful astronomical observations and devised their numeration system around their calendar and astronomical needs.
The Incans wanted a way to deliver recorded information across great distance before they had developed writing. They did so by tying a sequence of knots into linked strings. These were easily transported by runners who delivered them across difficult mountainous terrain. These quipus are from 1400-1550 CE.
There were over a million people living in Cairo of ancient Egypt, often working together as a complicated society. The papyri we have sometimes concern the computations necessary to maintain their many projects. For example, the Reisner papyrus appears to be a set of books for a construction site. They include a list of employees, as well as calculations of volumes and areas. A typical computation is determining the number of workmen needed to excavate a tomb. These documents are from 2000 - 1500 BCE.
Here are some views of the - to give you a sense of what this relic actually
is.
The
Here is a little bit from the .
Some problems from the Rhind and Moscow -
translated. More detailed version.
More sources.
The
The Mesopotamian culture was one of the first agricultural societies. They kept records of this by marking in mud with a stylus and then baking into tablets. These have the advantage of preserving very well. Many of their problems were about canals. They also seem to have an interest in math problems for curiosity sake as well. The works we have are from a range of time from 2500 to 1600 BCE. Suffice to say - very long ago.
Babylonian square root of 2 on
The Nine Chapters of the Mathematical Art is the canonical ancient Chinese textbook (held in the same esteem as Euclid's Elements). It has many problems and sections on diverse practical and instructional topics. It also has many editions through history with a tradition of several different commentators making additions. This work is from about 200 BCE to 200 CE. The "Pythagorean theorem" is well known in many cultures, here we see it was familiar in China in about 500 BCE.
Written Chinese
numeration.
An . Text from nine chapters.
(excuse the Wikipedia link - I do have this in a
print source but this way I don't need to scan it here).
The Indians were also familiar with the "Pythagorean theorem" at least two hundred years before Pythagoras (~600 BCE). Much of their geometry work was used for temple building in ancient India. Indian work with trigonometry in about 500 CE is motivated by astronomy and is mostly computational (as is most early trigonometry). The Lilivati from Bhaskara represents an overview of mathematical achievements at the time throughout their history (~1150 CE).
Numerals
Vedic square doubling
Trig tables
Lilavati contents
Details from Bhaskara
Early Islamic culture in the middle-east was a varied cultural mixing ground, with regular travelers and commerce from Europe, Africa, and the far East. It lead to great wealth and a respect for diversity, which included an attempt to gather and develop ideas from each culture they contacted. Inspi
