Freeman Dyson, at the Institute for Advanced Study in Princeton, becomes interested in a problem the mathematician Andrew Lenard, then at Princeton's Plasma Physics Laboratory, poses to him from his own work in plasma physics: why doesn't ordinary matter — composed of negatively charged electrons and positively charged nuclei, which attract each other electrically — collapse in on itself? Although physicist Lars Onsager had already sketched in 1939 a physically correct but non-rigorous argument, no complete mathematical proof had existed until then. In "Stability of Matter I" (Journal of Mathematical Physics, 1967), Dyson and Lenard rigorously prove that the total energy of a system of N charged particles has a negative lower bound proportional to N — not to N² as a naive count of all possible pairwise interactions would suggest — as long as the particles belong to a fixed number of fermion species (particles, like the electron, subject to the Pauli exclusion principle). The central and most surprising result is that this stability depends crucially on the Pauli exclusion principle, formulated by Wolfgang Pauli in 1925 (see separate entry pauli-exclusion-principle-1925), and not on electromagnetic repulsion between the outer-shell electrons of atoms, as might intuitively be assumed: it is the Pauli principle applied to electrons and protons that ultimately generates the normal macroscopic force preventing two stacked wooden blocks from fusing into one. If the particles were bosons instead of fermions — with no Pauli restriction — the system's energy would scale far more drastically, anticipating collapse. The proof, which Dyson would retrospectively describe as "hacking one's way through a forest of inequalities", required a long chain of mathematical inequalities with a final proportionality constant on the order of 10¹⁴ — far from the expected physical value, on the order of 1, but sufficient to rigorously establish the qualitative result for the first time. Dyson and Lenard would publish a second part refining the result the following year ("Stability of Matter II", 1968). Independently, Elliott Lieb and Walter Thirring would arrive years later (1975) at an alternative, more efficient proof of the same physical result.