There are Infinitely Many Carmichael Numbers/Historical Note

Historical Note on There are Infinitely Many Carmichael Numbers
When first identified in $1910$ the existence of what are now called Carmichael numbers, he expressed his belief that there were infinitely many.

This was the general (although unproven) belief in the mathematical community, up until $1994$, when, and  finally proved it.

However, this information took some time to be widely disseminated, and in $1997$, was still reporting in his   that:
 * It is widely believed, but not proved, that there are an infinite number of Carmichael numbers, but they are rare.