By the 1860s chemists had measured the atomic weights of about 60 known elements with reasonable accuracy; at the 1860 Karlsruhe Congress Stanislao Cannizzaro had revived Avogadro's hypothesis and secured agreement on a common scale. Yet the elements remained a long list — there was no explanation for why some behaved alike (lithium, sodium, potassium all react violently with water; fluorine, chlorine, bromine are all sharply coloured toxic gases).

On 6 March 1869 the Russian chemist Dmitri Ivanovich Mendeleev, while organising elements for a chemistry textbook he was writing at St. Petersburg University, made an observation: arranged by atomic weight, the chemical properties of the elements repeated at regular intervals. He cast this intuition into a single table and presented it to the Russian Chemical Society. The same year in Germany, Lothar Meyer independently prepared a broadly similar table; but three bold moves set Mendeleev apart.

First: when certain elements did not fit the pattern, Mendeleev suggested that their atomic weight measurements might be wrong — and in many cases he was right. Second: to preserve the pattern he left empty squares in the table, and for the elements that ought to occupy them — not yet discovered — he gave numerical predictions of atomic weight, density, and the formulas of their oxides. Third: he listed these predictions explicitly in an expanded 1871 paper, naming them "eka-aluminium", "eka-boron", "eka-silicon".

In 1875 Lecoq de Boisbaudran found gallium (eka-aluminium), in 1879 Nilson found scandium (eka-boron), in 1886 Winkler found germanium (eka-silicon) — each with properties in striking agreement with the numbers Mendeleev had set down a decade earlier. The table was no longer a summary but a prediction machine: the strength of a scientific theory lies less in its account of the past than in its ability to anticipate the future.

Mendeleev's ordering rested on atomic weight, which occasionally backfired (the tellurium–iodine and cobalt–nickel inversions). In 1913 Henry Moseley, using X-ray spectra, showed that the true ordering quantity is atomic number — the number of protons in the nucleus. The logic of the periodic table found its full place in quantum mechanics: the repeating properties are a consequence of how electron shells fill. The 118-element table of today still carries Mendeleev's skeleton; every newly synthesised element (oganesson, tennessine) settles into a square that had been left for it.