Mathematics and computer science: Triggers software soon people from? – SPIEGEL ONLINE

We humans are lousy computer. For tasks such as 141 by 3 we must briefly consider. 120 by 3 – that’s 40. And 21 is 7 by 3 – adds up to 47. Each computer, every 20 year old calculator is faster. But when it comes to more than blunt adding or dividing, encounter computer to its limits.

Which program about might consider pushing a button, whether the approach of a student in the written Abiprüfung true? And what software can prove conjectures, where already generations of mathematicians are desperate? Without the human spirit, it seems, is very little.

But there are computer scientists and mathematicians, write the brains only a minor role in the future of mathematics. Timothy Gowers of the University of Cambridge about, founder of the platform Polymath, says: “In 25 years, computers will be useful assistants of mathematicians In 50 years, computers are better than people doing mathematics..” If the institution of the prestigious Fields Medal right?

On this question discussed more than a hundred scientists at the congress CADE-25 in Berlin, which ended on Friday. Most of them are computer scientists. And they know that the way of doing math, will change in the coming years. Geniuses who solve alone with pen and paper great mystery, there will soon be perhaps only rarely.

Formal Logic suitable

“We are approaching the situation in which Software scientific articles reviewed,” says Christoph Müller Benz from the Technical University Berlin. He recently reconstructed together with colleagues a proof of God of Kurt Gödel on the computer. From a few basic assumptions and using strict logic the software headed ago that God “necessarily” exist. “Such formal logic-based evidence are particularly well suited for implementation on the computer,” explains Benzmüller. Find

evidence is now possible via software, as long as the evidence is not more mathematical subdivisions such as algebra and group theory would have to be combined. “This is a revolution,” adds Reiner Hähnle of the TU Darmstadt. “Evidence existed for centuries to convince others with precise arguments.” Now get software into play that much less prone to error is as a person.

When evidence via software, there are two varieties. Either a program checks an existing, found usually by people solution (Proof Checker). Or, and this is much more demanding, software searches independently for a proof (theorem prover). She has to try different ways and can also take advantage of ideas of earlier evidence, with which it has previously been fed.

balls tight pack

The mathematician Thomas Hales has already demonstrated that software can crack very difficult problems. In 1999 he proved the Kepler conjecture with complicated computer calculations. This involves the question of how close you can pack spheres in space. Hales reduced the problem to 2500 different ball arrangements, which he then did a computer check of individually. However, the work was no real recognition among colleagues because they could hardly understand what the software had done exactly.

 
 
 

Andreas Loos / FU Berlin

Kepler guessed correctly: So let bullets stack perfectly in space

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The Hales rankled so much that he 2014 his computer evidence reviewed in 1999 with a Proof Checker. He was able to demonstrate that each individual proof step was logically consistent – and thus the entire proof.

Despite such achievements remains skeptical about some mathematicians computer evidence, because they do not quite fit for their own self-image. Hélène Esnault from the Free University of Berlin holds little about the hype: “mathematics is an intellectual process and is first and foremost in the mind.” The creative, innovative ideas that you need to solve difficult math problems, she dares computer programs so far to little.

Christoph Benzmüller disagrees: “The fact that computers are not intuitive, no one has been proven.” His euphoria was not shared by all conference participants in Berlin. “We will not experience so fast that computer the better mathematicians,” says Reiner Hähnle of the TU Darmstadt. Programs would be intelligent assistant that could decrease mathematicians many routine tasks. “True creativity to develop, but is still a great challenge.”

In the short term are likely to provide the greatest assistance Proof Checker mathematicians. Such evidence could auditor namely solve one of their most pressing problems: check the ever more extensive and more complicated proofs.

The Japanese Shinichi Mochizuki about 2012 had submitted a multi-hundred pages of evidence for an ancient number puzzles – the ABC conjecture. But his work is recognized to this day. Work through the 500 pages critically, is a time-consuming endeavor. Could take this test computer, all would be helped.