In the history of mathematics that has been passed down for thousands of years, the conjecture has been the relic of geniuses.
There are only dozens of important mathematical formulas discovered in the last 100 years. Also, many mathematicians are devoted to creating a formula. However, the situation is changing recently. Artificial intelligence (AI) has begun to take over.
On the 10th, the US scientific journal’ZME Science’ reported that the artificial intelligence developed by Technion Israel Institute of Technology in 2019 began to generate’conjectures’ as the original goal. This suggests that computers can take the place of new guesses for mathematicians.
The’Ramanujan Machine’, an artificial intelligence algorithm that generates hypotheses (guesses) in mathematics, has begun to unearth and organize the hypotheses that genius mathematicians have been doing recently. ⒸGetty Images
What math geniuses have done AIOn behalf of
In July 2019, Technion announced that it developed the “Ramanujan Machine,” an algorithm that generates hypotheses (guesses) in mathematics.
This set of algorithms is named after Indian mathematician Srinivasa Ramanujan. He is a prodigy who came up with many mathematical guesses, proofs, and solutions to equations that were not solved before 1887.
Unlike other mathematicians, he had an excellent sense of numbers and patterns, and he produced up to 6165 hypotheses.
According to Live Science on the 15th, the Ramanujan Machine is proposing a new equation hypothesis through constant values that do not change, rather than derive new results based on previous mathematical knowledge like the genius mathematician Ramanujan.
“I don’t care if it’s easy or difficult to prove the formula, and I’m extracting mathematical patterns (like Ramanujan) from only the numbers of mathematical constants,” said Professor Ido Kaminer of Technion, who is involved in the study.
Already, some researchers are working on theorems of conjectures generated using this algorithm. Researchers are using a process called automated theorem proving to prove hypotheses.
Machine learning, in which algorithms detect patterns of large amounts of data, has been applied in a variety of ways, from image recognition to discovery of new drugs. However, this is the first time that artificial intelligence has been put into the leading role in a more fundamental area, a theoretical study between numbers and numbers.
The research team said, “The idea extracted through artificial intelligence can lead to the development of mathematical hypotheses in all areas of mathematics in the future, and will be of great help in the overall study of mathematics” through a paper published in the journal Nature on the 3rd. It is expected to be.
The title of the paper is’Generating conjectures on fundamental constants with the Ramanujan Machine’.
100Generate over ten interesting hypotheses
A hypothesis is an assumption made to explain a fact or deduce a system of theory.
When the theoretically derived result from this is proved by observation or experiment, it deviates from the position of hypothesis and becomes valid truth within certain limits.
Theorem means proving that a hypothesis is true. In ancient times, examples include the Pythagorean theorem, and Fermat’s Last Theorem, a French genius mathematician from the 17th century.
The mathematics geniuses presented a hypothesis that they could hardly solve at the time, and then organized (proved) that the hypothesis was true while others could not prove the proposition.
The work of the Technion research team also follows a similar appearance to these genius mathematicians. In the meantime, algorithms have been scanning a large number of potential equations to find patterns that could indicate the existence of a formula representing a constant that is the default value in the equation.
The artificial intelligence algorithm first scans a limited number of 5 to 10 numbers, then records and expands the match to see if the pattern repeats more. When a promising pattern emerges, we move on to the stage of theorem, which proves the conjecture, which is still being done by humans.
“To date, over 100 interesting hypotheses have been generated, dozens of which have been proven by scholars,” said Medtronic Hadard.
The research team is currently opening a website’RamanujanMachine.com’. It is intended to collect tried proofs from everyone who wants to share the hypothesis that the algorithm generates and discover new theorems.
“We are hoping that the’Ramanujan Machine’ will help change the way math is done,” said Hadard. It is difficult to say how the development of number theory will translate into practical applications, but we are judging that we are getting closer to that goal.
“The project is still in its infancy, but its potential is starting to emerge,” in an email sent to Live Science. “When new patterns and concepts become commonplace in math and physics, or in other scientific fields, new research I believe that you can bring out.”
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