Where does math come from?

We start out with one and two year olds, teaching them how to count and to recognize shapes. Math is fundamental, but where did the study of math come from?, I asked myself.

“The most ancient mathematical texts available are Plimpton 322 (Babylonian mathematics c. 1900 BC),[2] the Rhind Mathematical Papyrus(Egyptian mathematics c. 2000-1800 BC)[3] and the Moscow Mathematical Papyrus (Egyptian mathematics c. 1890 BC). All of these texts concern the so-called Pythagorean theorem, which seems to be the most ancient and widespread mathematical development after basic arithmetic and geometry.”

Y’all learned this at some point, but I bet nobody remembers it:

In any right triangle, the area of the square whose side is the hypotenuse (the side opposite the right angle) is equal to the sum of the areas of the squares whose sides are the two legs (the two sides that meet at a right angle).

aka:             a^2 + b^2 = c^2\!\,

Plimpton 322 is a Babylonian clay tablet, (see the image above) notable as containing an example of Babylonian mathematics. This tablet, believed to have been written about 1800 BC, has a table of four columns and 15 rows of numbers in the cuneiform script of the period. This table lists what are now called Pythagorean triples, i.e., integers abc satisfying \scriptstyle a^2+b^2=c^2. ”

The one most people remember is 3, 4, 5: three squared (9) plus four squared (16) is five squared (25).

The Rhind Papyrus is named after a Scotsman who bought it, lame imo- should be named after the person or group who wrote it, don’t you think? Stored at the British Museum, which has a nice page dedicated to it, according to Wikipedia, it “is the best example of Egyptian mathematics. It was copied by the scribe Ahmes.” So let’s call it the Ahmes Papyrus. “Ahmes presents the papyrus as giving “Accurate reckoning for inquiring into things, and the knowledge of all things, mysteries…all secrets”. ”

Please take a moment to consider what an amazing idea that is. A man four thousand years ago, whose life span was maybe 35 was searching for an accurate reckoning for inquiring into all secrets. Curiosity and confidence in conclusions has been a desire of humanity for thousands of years. As someone who would start a blog based on learning something new each day, you can easily imagine why this would excite me. 

The Ahemes Papyrus begins with reference tables and some basic problems such as fractions, dividing 10 loaves of bread evenly among various numbers of individuals, some linear equations like solving x + 1/3 x + 1/4 x = 2 for x and arithmetic progressions, which are sequences of numbers such that the difference of any two successive members of the sequence is a constant. For instance, the sequence 3, 5, 7, 9, 11, 13, … is an arithmetic progression with common difference 2. Then it gets into geometry, like how to find the volume of different shapes, areas and then the slopes of pyramids. And it ends with some problem sets like a textbook. 

The final text, the Moscow Mathematical Papyrus is also an ancient Egyptian document from about 1850 BCE, also often named after the guy who bought it, and is in the collection of the Pushkin State Museum of Fine Arts in Moscow, where it remains today. The Moscow Papyrus is thought to be a bit older than the Ahemes, but smaller. The neat thing to me is that the problems are not your basic equations, but rather, for example, “One of the problems calculates the length of a ship’s rudder and the other computes the length of a ship’s mast given that it is 1/3 + 1/5 of the length of a cedar log originally 30 cubits long.” It’s interesting to learn in what contexts they were using the math and what prompted them to discover the relationships of length, area and volume.

This one seems a bit of economic theory to me:

“A pefsu measures the strength of the beer made from a heqat of grain

 \mbox{pefsu} = \frac{\mbox{number loaves of bread (or jugs of beer)}}{\mbox{number of heqats of grain}}
Read this, don’t read this, but I found this pretty funny:
“The pefsu number is mentioned in many offering lists. For example problem 8 translates as:
(1) Example of calculating 100 loaves of bread of pefsu 20
(2) If someone says to you: “You have 100 loaves of bread of pefsu 20
(3) to be exchanged for beer of pefsu 4
(4) like 1/2 1/4 malt-date beer
(5) First calculate the grain required for the 100 loaves of the bread of pefsu 20
(6) The result is 5 heqat. Then reckon what you need for a des-jug of beer like the beer called 1/2 1/4 malt-date beer
(7) The result is 1/2 of the heqat measure needed for des-jug of beer made from Upper-Egyptian grain.
(8) Calculate 1/2 of 5 heqat, the result will be 2 1/2
(9) Take this 2 1/2 four times
(10) The result is 10. Then you say to him:
(11) Behold! The beer quantity is found to be correct.”
Then there are problems dealing with the output of workers and more geometry problems. Interestingly, they used 256/81 to approximate π, which is about 0.5 percent below the exact value, rather than 22/7, which i was taught in school, but is also not a great approximation, (suggested first by a Chinese mathematician in the 5th century CE). 
Anywho, that’s the start of our current knowledge of the history of math. I don’t know whether to be stunned that math was the subject of a written document four thousand years ago or just the opposite, that it wasn’t involved earlier. This is about to become another huge tangent into the history of writing, which I will save for another day. 

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