In the early 1910s, John Nicholson suggested that all atoms are formed by four basic elementary particles. This theory had a spectacular match with observations: it explained, with an unbelievable accuracy of 0.1, the atomic weights of all 92 elements known at that time. Specifically, it was shown that every atomic weight can be represented, with this accuracy, as an integer combination of four basic atomic weights. However, in a few years, this theory turned out to be completely wrong: atoms consist of protons, neutrons, and electrons, not of Nicholson's particles. This mysterious episode seems to contradict the usual development of science, when an experimental confirmation means that the corresponding theory is true. In this paper, we explain this mystery by showing that, in fact, there was no experimental confirmation, Namely, we prove that any real number larger than 3.03 can be represented, with accuracy 0.1, as a linear combination of four Nicholson's basic weights. So, this past ``experimental confirmation'' has nothing to do with atomic weights or any experimental data at all -- it is simply an easy-to-prove general mathematical result.