Eight years after Dyson and Lenard's first rigorous proof (1967, see separate entry dyson-lenard-stability-of-matter-1967), mathematical physicist Elliott Lieb, at Princeton, and Austrian physicist Walter Thirring, at the University of Vienna, publish "Bound for the Kinetic Energy of Fermions Which Proves the Stability of Matter" (Physical Review Letters, 1975). Their strategy is radically different from their predecessors': instead of chaining together a long series of technical inequalities with no clear physical interpretation, Lieb and Thirring start from a deep physical understanding of the problem — based on Thomas-Fermi theory and a result known as the "no-binding theorem" — and from there build the mathematical language needed to make that intuition rigorous. First they bound above the sum of the negative energies of a single particle in a potential, which in turn implies a lower bound for the kinetic energy of N fermions; from this they obtain a much shorter, more transparent proof of the stability of matter. The practical result is notable: while the proportionality constant Dyson and Lenard obtained was on the order of 10¹⁴ — vastly far from the expected physical value, on the order of 1 — Lieb and Thirring's turns out to be approximately 5, much more realistic and physically informative. Freeman Dyson himself would acknowledge years later, in the foreword to a collection of Lieb's works, the fundamental difference between the two approaches: "our proof was so complicated and so unilluminating that it stimulated Lieb and Thirring to find the first decent proof... why was our proof so bad and theirs so good? The reason is simple. Lenard and I started with mathematical tricks and hacked our way through a forest of inequalities without any physical understanding. Lieb and Thirring started with physical understanding and then found the appropriate mathematical language to make the understanding rigorous. Our proof was a dead end. Theirs was a gateway to a new world." The Lieb-Thirring inequality would indeed become the starting point of an entire new line of research in mathematical physics on the stability of matter, which Lieb himself would continue developing for decades, including extensions to systems with magnetic fields.