While Hawking became “officially famous” with “A Brief History of Time,” among physicists he was more renowned for the

**singularity theorems**. In his 1960s work together with Roger Penrose, Hawking proved that singularities form under quite general conditions in General Relativity, and they developed a mathematical framework to determine when these conditions are met.

Before Hawking and Penrose’s work, physicists had hoped that the singularities which appeared in certain solutions to General Relativity were mathematical curiosities of little relevance for physical reality. But the two showed that this was not so, that, to the very contrary, it’s hard to avoid singularities in General Relativity.

Thanks to this seminal work, physicists understood that the singularities in General Relativity signal the theory's breakdown in regions of high energy-densities. In 1973, together with George Ellis, Hawking published the book “The Large Scale Structure of Space-Time” in which they laid out the mathematical treatment in detail. Still today it’s one of the most relevant references in the field.

A somewhat lesser known step in Hawking's career is that already in 1971 he wrote

**one of the first papers on the analysis of gravitational wave signals**. In this paper together with Gary Gibbons, the authors proposed a simple yet path-leading way to extract signals from the background noise.

Also Hawking’s – now famous –

**area theorem for black holes**stemmed from this interest in gravitational waves, which is why the paper is titled “Gravitational Radiation from Colliding Black Holes.” This theorem shows that when two black hole horizons merge their total surface area can only increase. In that, the area of black hole horizons resembles the entropy of physical systems.

Only a few years later, in 1974, Hawking published a seminal paper in which he demonstrates that black holes give off thermal radiation, now referred to as “

**Hawking radiation**.” This evaporation of black holes results in the black hole information loss paradox which is still unsolved today. Hawking’s work demonstrated clearly that the combination of General Relativity with the quantum field theories of the standard model spells trouble. Like the singularity theorems, it’s a result that doesn’t merely indicate, but prove that we need a theory of quantum gravity in order to consistently describe nature.

While the 1974 paper was predated by Bekenstein’s finding that black holes resemble thermodynamical systems, Hawking’s derivation was the starting point for countless later revelations. Thanks to it, physicists understand today that black holes are a melting pot for many different fields of physics – besides general relativity and quantum field theory, there is thermodynamics and statistical mechanics, and quantum information and quantum gravity. Let’s not forget astrophysics, and also mix in a good dose of philosophy. In 2017, “black hole physics” could be a subdiscipline in its own right – and maybe it should be. We owe much of this to Stephen Hawking.

In the 1980s, Hawking worked with Jim Hartle on the

**no-boundary proposal**according to which our universe started in a time-less state. It’s an appealing idea whose time hasn’t yet come, but I believe this might change within the next decade or so.

After this, Hawking tried several times to solve the riddle of black hole information loss that he posed himself, alas, unsuccessfully. It seems that the paradox he helped create finally outlived him.

Besides his scientific work, Hawking has been a master of science communication. In 1988, “A Brief History of Time” was a daring book about abstract ideas in a fringe area of theoretical physics. Hawking, to everybody’s surprise, proved that the public has an interest in esoteric problems like what happens if you fall into a black hole, what happed at the Big Bang, or whether god had any choice when he created the laws of nature.

Since 1988, the popular science landscape has changed dramatically. There are more books about theoretical physics than ever before and they are more widely read than ever before. I believe that Stephen Hawking played a big role in encouraging other scientists to write about their own research for the public. It certainly was an inspiration for me.

Good bye, Stephen, and thank you.