Hans Bethe passed away last month, last of the living legends of modern physics. He was 98, professor emeritus at Cornell, and still publishing new work. He was born into the greatest age of physics since Newton, just as it began, in 1906, a year after Einstein's paper on special relativity was published. He lived through the three great theoretical upheavals of the 20th century — relativity, atomic physics, and quantum mechanics — not as a spectator, but as an instrumental force. It is not only his accomplishments that bear remembering, but the phenomenon that he represented: he was a personal link between the great physicists who laid the modern foundations of this science, the memorable figures who developed it in the middle of the century, and the theoreticians carrying it forward today. It was all there, housed in one mind, both inventing physics and conveying it across three generations. He was both bridge and steersman of the science that defines our day.
He was one with the great names of science. He headed the theoretical division for the Manhattan Project, working with Fermi, von Neumann, Oppenheimer, and Teller. He taught Wolfgang Pauli and Werner Heisenberg, Freeman Dyson and Richard Feynman. The only major figure I can think of who lay outside his sphere of influence and collaboration was Niels Bohr, who lived and worked in Denmark all his life, even as the war shifted the center of physics from Europe to America.
He did not just span the age and its great ideas. His signal recognition was the Nobel Prize in 1967, but his discoveries comprehended two of the great theoretical achievements of astrophysics, forty years apart They are the two pillars of stellar physics. In 1938 he discovered how stars live by nuclear fusion, and in the late 70s helped formulate how they die in supernovae. He was one of those rare few for whom genius strikes twice in the same place.
When we think of great double discoverers, it is Einstein who usually comes to mind, with the special and general theories of relativity. If that isn't qualification enough, relativity and the photoelectric effect are candidates just as strong, and it was the photoelectric effect, delineating the unsuspected intimacy between light and electricity, that gained him the Nobel in 1921. Before Einstein, only Newton, two hundred years before, comes to mind, who first revolutionized optics and then physics, pausing between the two mostly for the sake of polishing his manuscript.
But rarely is it given to one man to shake the same field twice. Einstein did so, redefining first motion, mass and energy, then space and gravity ten years later. Bethe joins his company. There remains a third, Kurt Gödel.
When Gödel is remembered, accurately or inaccurately, it is for just one thing. But like Einstein, his was a two-fisted accomplishment in logic. In 1929 he submitted as his doctoral thesis the Completeness Theorem for first-order logic. It was something on the order of saying that we do, in fact, live in a perfect world. First-order logic was the dominant language of sets, representations, and proof; it was the language of truth that had been refined from Aristotle up through Boole and Tarski. It had elegance, simplicity and power, and was on its way to becoming the language of thought for logicians and mathematicians alike. It is a beautiful thing, and true. It posits only that there are items that may be true or false, and sets of these items; the ideas of "and", "or", and "not" as truth-modifying operations; and three rules of deducing true statements from other true statements. From this flowed a system capable of expressing and organizing thought on almost anything, and promising the iron rule of truth in doing so.
Gödel proved this: that what is true is also beautiful. That is, not only are the elegant operations of first-order logic guaranteed to derive true statements, but that all true statements expressible in it can also be proved by it. As a system, it was complete and flawless. Proof of completeness was like the demonstration of the sphericity of the earth: that everything we saw was also everything there was, and reachable. In universal gravitation Newton saw the manifestation of God inhabiting all things. In completeness, logicians might now justly claim to see the same.
First-order logic is not yet mathematics, though. We need add but little to make it so: symbols called "numbers", an ordering function on these that lets us move from lesser to greater; and crucially, another rule of deduction to permit proofs over the whole set of numbers. That is all; from this emerges the whole body of mathematics and mathematical theorems. Mathematicians had every hope that this system, too, was as complete as it was logically consistent.
It was not. Only two years after his proof of the completeness theorem, Gödel gave a lecture culminating in proof that any first-order mathematics was incomplete: either it must fail to prove all true theorems, or some of the things it could prove must not be true. Truth and provability could not form a whole and harmonious system. The perfect world that logicians inherited was forever closed to mathematicians.
Despite his double accomplishments, it is for this shattering of mathematical perfection that Gödel is remembered. Einstein gave us the physics that reshaped space, but he is remembered for showing that matter can be energy, and hence that atomic bombs are possible. Bethe showed how stars destroy themselves, but also that the destructive forces behind thermonuclear weapons work to build up stars. When discoverers span both creation and destruction, perfection and imperfection, it is the violent half that seems to become their single legacy. For Bethe, let us have it otherwise, if only as an antidote to the rest of 20th century physics. Like Newton, forgotten for his optics, but remembered for his law of universal gravitation that holds the world together, mark down Hans Bethe as the builder of physicists and the discoverer of how the stars shine.
Hans Bethe by his biographer