The Euphorbia genus was named and described by Carl von Linnaeus in Species Plantarum in 1753.
Euphorbia is a very diverse genus of flowering plants in the Euphorbiaceae Family commonly known as the spurge family.
Plants of the World Online lists 2004 accepted species of Euphorbia. The 2013 version of The Plant List named 2,046 species (plus an additional 144 accepted infraspecific names), 3,522 synonyms of species rank (plus 1,592 infraspecific synonyms), and 94 unresolved names. The Plant List is now unmaintained but it is still a great source of information. You can compare it with current statistics to see progress. WCSP lists 5,401 names but most are synonyms. I am not going to go down the list and count all the accepted names.
There is a lot of useful information online about many genera and species in this family. I am not going to do an extensive write up at this time, but the following links are a good place for you to start. The links take you directly to the information on the genus Euphorbia.
If you have any comments, questions or suggestions, I would like to hear from you.