In principle you ought to be able to go to experts in each area of specialization, ask how many species there are in their fields, then add the totals. Many people have in fact done so. The problem is that seldom do any two come up with matching figures. Some sources put the number of known types of fungi at 70,000, others at 100,000 — nearly half as many again. You can find confident assertions that the number of described earthworm species is 4,000 and equally confident assertions that the figure is 12,000. For insects, the numbers run from 750,000 to 950,000 species. These are, you understand, supposedly the known number of species. For plants, the commonly accepted numbers range from 248,000 to 265,000. That may not seem too vast a discrepancy, but it's more than twenty times the number of flowering plants in the whole of North America.
Putting things in order is not the easiest of tasks. In the early 1960s, Colin Groves of the Australian National University began a systematic survey of the 250-plus known species of primate. Oftentimes it turned out that the same species had been described more than once — sometimes several times — without any of the discoverers realizing that they were dealing with an animal that was already known to science. It took Groves four decades to untangle everything, and that was with a comparatively small group of easily distinguished, generally noncontroversial creatures.