Definition:Amicable Pair/Historical Note
Historical Note on Amicable Pair
He found over $60$ examples.
There are now over $40 \, 000$ amicable pairs now known, including all such pairs where the smaller pair is under $1 \, 000 \, 000$.
Techniques for generating new amicable pairs from existing ones strongly suggest that there is an infinite number of them, but this still has to be rigorously proven.