There is someone in the USA who claims that the millionth word of English has recently been coined, but this turns out to be something of a publicity stunt, largely to promote a book he has written on the subject. I won't add to the publicity by telling you his name; but a discussion of this hoax can be found on Language Log here.
I was reminded about the fact that it is not possible to determine how many words there are in English (or any other language) by a recent announcement of a talk at UBD. The abstract starts:
Based on previous reports of the presence of terminal alpha-linked galactosyl residues in the glycoconjugates of the human malaria parasite Plasmodium falciparum, a systematic investigation into the biochemical structure of the glycoconjugates was initiated.It all sounds fascinating stuff; but what does it mean? And should galactosyl, falciparum and glycoconjugates be counted as some of the "million words" of English or not?
In fact, if you start trying to include as words of English all the possible chemical compounds, some of which can be very long and rather obscure, you will easily exceed one million words.
And it is not just in the pure sciences that this issue arises. In my own field of acoustic phonetics, I could talk about formant transitions following the aspiration associated with fortis alveolar plosives. Should these technical terms be counted as some of the million words? For me, they are all perfectly good words of English; but I don't expect you to agree with me (unless, of course, you have studied lots of phonetics).
I hope this helps to illustrate why any discussion of the total number of words in a language is meaningless.