# Age of Augustus

The English mathematician Augustus de Morgan has given his age in algebraic terms. Can you work out when he was born?

The English mathematician Augustus de Morgan, who died in $1871$, claimed that he became $x$ years old in the year $x^2$. When was he born?

If you liked this problem, here is an NRICH task which challenges you to use similar mathematical ideas.

**Answer**: 1806

Square numbers near 1871 (year of death)

40$\times$40 = 1600 too small

42$\times$42 = 1764, but if he was 42 in 1764 then by 1871 he was older than 140

43$\times$43 = 1849, 22 years before he died in 1871, which is reasonable

44$\times$44$\gt$1871 so there are no more possibilities

So he was born 43 years before 1849, in 1806