One of the earliest known examples of math homework

It's stuff like this that makes me love archaeology. Turns out, we can trace the concept of math homework back to at least 2300 B.C.E., in ancient Mesopotamia.

In the early 20th century, German researchers found several clay tablets at the site of Šuruppak. (Today, that's basically the Iraqi city of Tell Fara.) Some of the tablets appear to be the remains of math instruction, including two different tablets that are working the same story problem.

A loose translation of the problem is: A granary. Each man receives 7 sila of grain. How many men? That is, the tablets concern a highly artificial problem and certainly present a mathematical exercise and not an archival document. The tablets give the statement of the problem and its answer (164571 men - expressed in the sexagesimal system S since we are counting men - with 3 sila left over). However, one of the tablets gives an incorrect solution. When analyzing these tablets, Marvin Powell commented famously that it was, "written by a bungler who did not know the front from the back of his tablet, did not know the difference between standard numerical notation and area notation, and succeeded in making half a dozen writing errors in as many lines."

That comes from a site set up by Duncan Mellville, a math professor at St. Lawrence University in Canton, NY. He's actually got a whole collection of essays on Mesopotamian mathematics. I am certain, that by posting this, I've just ruined somebody's productivity for, like, a week.

Image is not THE cuneiform tablet in question. Just A cuneiform tablet. I couldn't find a picture of those specific ones:Marks and signs, a Creative Commons Attribution Share-Alike (2.0) image from nicmcphee's photostream.

Via John Baez

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  1. There must have been a previous problem that established how big a granary is. The way the problem is stated on the tablet I can’t see how there’s enough information to solve it.

    Of course, even with that information I don’t think I could solve it using the methods they expect. I suck at sexagesimal  long division. Cinch in base ten though

      1. Looks like it is 1152000 sila of grain. Which is 3840 gur of grain. In base 60 that’s 140, which seems equally as memorizably odd as the conversion factors for Imperial units.

        Conversions using:http://books.google.com/books?id=3ullzl036UEC&pg=PA86&lpg=PA86&dq=sila+of+grain&source=bl&ots=OUjySOkDiA&sig=NwXsofvbsGdNdc28_ch5-ZEEYck&hl=en&ei=kDHYTvy9LoPe0QH_sYngDQ&sa=X&oi=book_result&ct=result&resnum=2&ved=0CCwQ6AEwAQ#v=onepage&q=sila%20of%20grain&f=false 

    1. “The way the problem is stated on the tablet I can’t see how there’s enough information to solve it.”

      That never slowed down one of my math professors. :/

  2. I’ve seen some tablets with math problems on them. They pop up whenever it’s the Yale Babylonian collection’s turn to put things in the display cases at the Sterling. Maybe next time I’ll take a photograph.

  3. Marvin Powell commented famously that it was, “written by a bungler who did not know the front from the back of his tablet, did not know the difference between standard numerical notation and area notation, and succeeded in making half a dozen writing errors in as many lines.”

    Mr. Powell, it’s easy for you to say since you’ve never inscribed anything on a stone tablet… the iPad of old days.

  4. Some poor Sumerian kid’s secret fear that future archeologists will find their old homework and think they were stupid just came true.

  5. It’s stuff like this that makes me love archaeology. Turns out, we can trace the concept of math homework back to at least 2300 B.C.E., in ancient Mesopotamia.

    Nice !

  6. One of the best introductions to Mesopotamian Mathematics is Eleanor Robson’s Mathematics in Ancient Iraq: http://press.princeton.edu/titles/8834.html
    You can find photographs of most of the tablets here: http://cdli.ucla.edu/

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