"Pierre de Fermat showed that any prime number that could be divided by four with a remainder of one was also the sum of two square numbers.

So 41 is a prime, can be divided by four with one left over and is 25 (five squared) plus 16 (four squared).

e.g.
5(4+1), 13(4+9), 17(16+1), 29(4+25), 37(36+1), 41(16+25), 61(36+25)

So if it has remainder one it can always be written as two square numbers - there's something beautiful about that.

It's unexpected why should the two things [primes and squares] have anything to do with each other, but as the proof develops you start to see the two ideas become interwoven like in a piece of music and you start to see they come together.

He said it was the journey not the final proof that was exciting; like in a piece of music it's not enough to play the final chord."