Posted by: dschneid2010 | November 3, 2008

## Early Math

I was feeling very nostalgic so I decided I’d do some research on the oldest records of mathematics. I found some cool stuff on Wikipedia and other websites that I’ll talk about here:

So apparently humans began counting not long after language developed, probably starting with fingers and thumbs (ever wonder why so much stuff involves a base of 10?).

Notches in a stick or stone were the first ways of keeping track, and in the earliest surviving traces of a counting system, numbers are built up with a repeated sign for each group of 10 followed by another repeated sign for 1. The problem with arithmetic is that it requires a 0 (apparently a concept that was difficult to think of?) and place value. If I had been living at this time I definitely would have mentioned this to someone.

Thus, math began with geometry and algebra. The two in a sense mirror each other, aka, a number expressed as two squared can also be described as the area of a square with 2 as the length of each side. Equally 2 cubed is the volume of a cube with 2 as the length of each dimension.

Early Stuff: Babylon and Egypt From 1750 BC

The first surviving examples of geometrical and algebraic calculations derive from Babylon and Egypt in about 1750 BC, with the Babylonians as far more advanced. A typical Babylonian math question will be expressed in geometrical terms, but the nature of its solution is essentially algebraic. Their numerical system was base 60…yikes…so calculation depends largely on tables (sums already worked out, with the answer given for future use), and many such tables survive on the tablets.

An early example of Babylonian math is called the Plimpton 322. The name and number are just related to very modern things (name of owner or something). What’s important is that the tablet was believed to have been written about 1800 BCE and appears to be a listing of Pythagorean triples. It’s Babylonian. Check it out!

Egyptian mathematics is less sophisticated than that of Babylon; but an entire papyrus on the subject survives. Known as the Rhind papyrus, it was copied from earlier sources by the scribe Ahmes in about 1550 BC. It contains brainteasers like “What is the size of the heap if the heap and one seventh of the heap amount to 19”?

Another example of Egyptian mathematics that I came across is called the Moscow Mathematical Papyrus. Again, don’t let the name fool you, it dates back to the 11th dynasty of Egypt (2134BC – 1991BC) (nothing to do with Moscow), and contains about 25 problems, the most famous of which is probably the 14th. The 14th problem of the Moscow Mathematical calculates the volume of a frustrum, how frustrating…no really, it’s the only ancient example finding the volume of a frustum of a pyramid or cone. Very Egyptian, no?

The text of the example runs like this: “If you are told: a truncated pyramid of 6 for the vertical height by 4 on the base by 2 on the top: You are to square the 4; result 16. You are to double 4; result 8. You are to square this 2; result 4. You are to add the 16 and the 8 and the 4; result 28. You are to take 1/3 of 6; result 2. You are to take 28 twice; result 56. See, it is of 56. You will find (it) right”

Anyways, that about wraps up the history of math (okay, not so much, but a few things nonetheless).

## Responses

1. Thanks for a great post! I like your observation about the connection between algebra and geometry. Both myself and my boyfriend are in some sense algebraic geometers (I’m usually called an arithmetic geometer instead, but we are fairly close in what we do). Algebraic geometry, simply speaking, is just the connection between algebra and geometry you see everytime you graph a function or draw a square. Pythagorean triples are the very start of my field of mathematics.

2. Ten isn’t the only one that’s been used. Five (one hand) and twenty (count on your toes, too) have been used, too. 12 is also countable on one hand (four fingers with three segments; use the thumb as a marker), and of course 12 survives in quite a few places.

With a little thought, I can come up with a way to count from 0 through 242 on one hand. though it requires a modern positional-value system, so of course it wasn’t used in the ancient world where 0 hadn’t been invented yet.

If you’re interested in the history of numbers, Georges Ifrah’s he Universal History of Numbers goes quite in depth.

3. For hand counting with positional value, check out Chisanbop, which I enthusiastically learned from a library book as a child and still use today if I have to count while my brain is engaged in something else (you can do multiplication and everything — it’s a kind of hand-abacus). Speaking of counting while your brain is doing something else, does anyone have any tricks? For example, doing situps in the morning, you might want to listen to the news. So you need a way to count that doesn’t use your auditory system, which is busy with the words on the radio. I imagine dots, like on dominoes, and my boyfriend imagines a clock, so the visual system is engaged, which doesn’t interfere with the auditory system. I sometimes use chisanbop if I don’t need my hands.