"A mathematician is a machine that transforms coffee into theorems," said one of those machines, the Hungarian Alfred Rényi. Our Coffee and theorems section takes the name of that exit from Alfred. The case of Hao Huang, a mathematician at Emory University in Atlanta, is slightly different. Hao had the bad fortune of being in Madrid at the end of June, during the first heatwave of the two that have burned Europe this summer. While his wife visited the Institute of Mathematical Sciences (Icmat), Hao locked himself in the hotel and, in the absence of anything better to do, proved a theorem that had been floating in the limbo of conjectures for 30 years. Hao has transformed heat into theorems. And the most amazing of all is that I've done it in just two pages. Read on Matter a very didactic article by Albert Atserias, professor of theoretical informatics at the Polytechnic of Catalonia, about Hao's great achievement and its practical implications.
How is it that a conjecture that had resisted the best theoretical computer scientists for 30 years can be resolved in two pages? If the solution was so concise, why hadn't it occurred to anyone before? Well, here is a key to the advancement of knowledge. During the first half of the twentieth century, febrile activity in genetics laboratories had generated such data overflow that not even the most knowledgeable of specialists could boast having a general idea about their field of study. All that changed radically in 1953, when Watson, Crick and Franklin discovered the double helix of DNA, the ultimate explanation of inheritance, the secret of life. Watson and Crick presented that colossal finding on a page and a half of the journal Nature. The mere geometry of the double helix explained a half a century of unbeatable and paradoxical genetic results, and opened a new continent of research and thought that has completely transformed biology, and partly the world in which we live.
In the 1880s, Maxwell had done the same with the tangle of results that a handful of experimentalists had obtained on electricity and magnetism. In just four equations that can be written on a bar napkin folded in four, Maxwell showed that electricity and magnetism were no more than two ways of looking at a single phenomenon, electromagnetic force, one of the fundamental forces of physics , and discovered in passing that the light was an electromagnetic wave, such as ultraviolet and infrared radiation, X-rays, the microwaves of our oven and the radio waves that we use 16 hours a day for absolutely everything we do.
We will end up remembering that Einstein's doctoral thesis was the shortest in the history of his university, and that Borges said: "I don't know why people write so much." I can think of many more examples, but a compliment of brevity must start by being brief, isn't it?
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