Problem 7 (Mystery Mathematician)

A famous mathematician once said that he was once x years old in the year x2. Who was this mathematician ? First, however, find the possible years (if any) this mathematician was born ?

Solution

There are several candidate mathematicians. We first make the simple observation that if a person had his/her xth birthday in the year x2, then that person was born in the year x² - x. So, we make a table listing the values of x² - x for x = 1, 2, 3, ... to find our candidates. We have

Looking at the table, we see that a person born in the year 0, was 1 year old in the year 1². Looking further down the table to x = 25, we have that a person born in the year x² - x = 600 had his/her 25th birthday in the year x2 = 25² = 625 A.D.. As you can see, persons born in any of the years in the column under the heading x² - x were at one time (if they live long enough) x² - x in the year x² ... in other words persons born in one of the years 0, 2, 6, 12, 20, ... . For example, a person in 1890, would have been 45 years old in the year 45² = 1936.

So, who is the mystery mathematician ? Well, the story goes that the French mathematician Liouville made the claim, but according to our history of mathematics books, Liouville was born in 1809 and not 1806 (which would be a correct year). Hence, you will have to find another mystery mathematician. If you were born in the year 1980, you will be 46 years old in the year 2116, making you 46 years old in the year 46² = 2116.
If you don't have your own "equation" you can make one up. For example, the person writing the words you are now reading was once 2x + 5 years old in the year 3x + 1932. Am I giving my age away ?

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Last modified on Tuesday, January 12, 1999