L ‘artificial intelligence It already surpasses humans in many areas of technology, including solving certain mathematical problems. Recently, an AI rejected about five mathematical hypotheses. An exploitation that makes some people happy and scares others.
Mathematical jets are theories that are not evaluated or rejected. Many assumptions in various branches of mathematics have been established over the centuries. They therefore represent an ideal challenge for testing the capabilities of new algorithms and neural networks developed in recent years.
A research team from the University of Tel Aviv in Israel, led by Adam Salt Wagner, used a systemGene editing For examples that refute long-term assumptions in graph theory, the field of mathematics that involves the study of objects constructed using nodes and links. The original mathematicians believed these assumptions to be true but could not prove them.
Neural networks and machine learning
For each assumption, Wagner and his team created a measure of the distance between an example and its negation. For example, if a ject hum suggests that a particular problem cannot be solved in five steps, a six-step example will be closer to a discipline than a seven-step one, and a four-step solution will act as a counter. ject hikan example, allows its rejection.
They programmed a neural network to create random examples and used those measurements to assess their suitability as a standard sample through machine learning. AI eliminated the worst examples and replaced them with other random examples before starting. In dozens of cases, AI failed to find an example that would disprove the theory, but in five cases, a solution was found to show that ject hum was false.
« We avoid bad examples and learn from the best in each iteration , Wagner explains. ” This is basically the simplest thing possible, architecture. Nothing unusual .
Wagner has been running AI on his laptop for the past 5 years, and it took a few hours to a few days to discard each of the five. In his opinion, the results were often counter-intuitive. ” You have given me hundreds of years but I will never find these creations on my own The details were posted on the preprint server arXiv.
“The Great Advantage of Artificial Intelligence”
« That’s really remarkable », Declares Leslie Hogen, From Iowa State University, AI refuted one of his assumptions. ” From a mathematical point of view, we see here a great advantage of artificial intelligence. She finds things for us as a very insightful person would want. Opposite samples are the needles in the hashtags .
If AI has succeeded in disproving Ject Hangs, it will be very difficult to prove them. To reject an idea, you need to create and test a large number of solutions to see if a mechanical task that can be automated is antithetical to the ject, but the evidence is creative work, which requires careful action and precision, and the sequence includes many reflections.
The first theory proven by a computer was the four-color theory, which states that any map cut into areas using only four different colors can be colored. So two adjacent areas that are connected – an entire border (and not just a point) in general – always adopt two different colors. A computer was used to examine a comprehensive list of examples of evidence found in 1976. Some at the time considered it irrelevant, but the use of computers to solve mathematical problems became more widespread.
However, Hogan believes that it is still important for mathematicians to be able to follow computer proof. ” Personally, I would never have a problem with a discipline (Via computer) You can check it out. However, computer evidence that cannot be verified by hand can give me some problems personally. .
Timothy Gourzs from Col കൊs de France in Paris Announced on Twitter That the approach is an interesting proof of the idea. ” Maybe turn it into a simple ess trading tool that will be very useful for mathematical researchers. He wrote.
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