Bad math in Linnaeus’ Philosophia Botanica

János Podani, András Szilágyi

In Philosophia Botanica (1751), Carolus Linnaeus (1707-1778) presented a calculation of the number of plant genera that may be distinguished based on his taxonomic concepts. In order to derive that number, he relied upon the organs of fructification, which represent the flower and the fruit, by selecting over 30 elements from them, and then assuming that each could vary by four dimensions. However, while Linnaeus was good in counting stamens and pistils, he and many of his followers who edited or translated Philosophia Botanica were less careful, basing their calculations of the number of possible genera on flawed assumptions, or even introducing basic arithmetic errors. Furthermore, although mathematics was quite advanced in the eighteenth century, the gap between combinatorial and botanical thinking was too deep, preventing Linnaeus to seek a reasonable solution to the problem he raised. The authors demonstrate this by a historical analysis of 15 editions of Philosophia Botanica, plus many references to it, and conclude that the desired number almost always appeared in error during the past 265 years. The German botanist J. G. Gleditsch (1714-1786) was the most successful with respect to Linnaeus' original intention. Elementary mathematics demonstrates that if Linnaeus' assumptions were taken seriously, then the possible number of genera would be astronomical. The practice he followed in Genera Plantarum (1754) shows, however, that the fructification dimensions served as a universal set for Linnaeus from which he chose only the relevant ones for describing a particular genus empirically. Based on the corrections and modifications implemented in reworked editions, we suggest an evolutionary network for the historical and modern versions or translations of Philosophia Botanica.