People had apparently known that for millennia. From what I understand, Columbus was a moron whose personal calculations concluded that the Earth is much smaller than it actually is, which is why he dared the journey to "Asia". And if there hadn't been a continent in the way that he didn't know about, he would have starved to death on the way.
So just why is this idea so widespread?
A lot more could certainly be said on the subject, but there are a number of excellent prior answers on this subject that may be of interest to you. In particular, see the two posts by /u/terminus-trantor discussing in detail the issues around Columbus and the size of the earth: here and here. Then there is /u/Georgy_K_Zhukov's post here detailing the work of the key propagator of this myth, Washington Irving. Finally, I have written in the past about some of the reasons why the myth of a medieval flat has been so persistent into the twentieth century here. (There is also a section of the FAQ devoted to the issue.)