A letter from Lewis Carroll to 14-year-old Wilton Rix:

Honoured Sir,

Understanding you to be a distinguished algebraist (i.e. distinguished from other algebraists by different face, different height, etc.), I beg to submit to you a difficulty which distresses me much.

If x and y are each equal to ‘1,’ it is plain that 2 × (x² – y²) = 0, and also that 5 × (x – y) = 0.

Hence 2 × (x² – y²) = 5 × (x – y).

Now divide each side of this equation by (x – y).

Then 2 × (x + y) = 5.

But (x + y) = (1 + 1), i.e. = 2.

So that 2 × 2 = 5.

Ever since this painful fact has been forced upon me, I have not slept more than 8 hours a night, and have not been able to eat more than 3 meals a day.

I trust you will pity me and will kindly explain the difficulty to

Your obliged, Lewis Carroll