Today I'm going to a Math Festival. Like a coming out fest for geeks. I use the term affectionately, since I have always been fond of intellectual smarty pants. I love the high foreheads, the furrowed brows, the inability to engage in small talk, the frenetic bursts of laughter at inappropriate moments. Very cool. The festival is named for one of my old professors, Julia Robinson. Her rise to fame was for solving one of David Hilbert's 23 unsolved problems in mathematics. Hilbert had presented 10 of these problems in 1900 at the International Congress of Mathematicians (aka the World Cup of Geeks), later publishing 23 in total for mathematicians of the 20th century to ponder. To date, here's the score:
Solved or disproved: 1, 2, 3, 7, 9, 10, 14, 17, 18, 21
Partially Solved: 5 and 6
Still Being Pondered: 4, 8, 11, 12, 13, 15, 16, 19, 22
My great grandfather spent most of his life tackling #8.
Julia Robinson got #10 started and it was eventually put to rest in 1970 by Yuri Matiyasevich. It's all explained in his book, Hilbert's Tenth Problem (MIT Press, 1993). I love it that there are books published about one math problem. Can you feel the universe of geeks expanding beyond your wildest dreams? Can you prove that this universe is infinite? If so, you are in that universe.
So what was problem 10?
Question: Are diophantine equations solvable?
Answer: No
Fantastic!
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