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Augustus' Age

Stage: 2 Challenge Level: Challenge Level:2 Challenge Level:2

In 1871 a mathematician called Augustus De Morgan died.
De Morgan made this puzzling statement about his age: he said that he was $x$ years old in the year $x^2$.

Can you discover which year De Morgan was born in?

Do you think anyone living at this time can say the same thing about their age and the year they were born? (That doesn't mean that they have to have been born the same year as De Morgan!)

Man.

This is a cartoon of De Morgan drawn by one of his students.