Mathematics could be an ideal experimental field for AI, as the data to be worked with is clear and easily accessible. Earlier this year, it was announced that Google's DeepMind AlphaGeometry system combines a language model with a type of artificial intelligence that uses symbols and logical rules to make mathematical inferences. That would be mathematics revolution?
A mathematical conjecture is a statement that, although not proven by mathematics, is nevertheless highly probable. If someone proves a conjecture correct, the conjecture becomes a theory. In this case, it can actually be used during further proofs.
The Eureka Moment is born!
It takes genius, intuition and experience to make a new discovery. Consider the late summer day in 1666 when Newton saw an apple fall straight from a tree in his garden. Not to the side and not to the top. Then came the big idea: The force that causes the apple to fall is the same force that keeps us on the ground. This requires Newton's eye and creative thinking, which AI cannot yet do. But yes to everything else.
In 2017, researchers at the London Institute of Mathematical Sciences conducted successful experiments using artificial intelligence to predict elliptic curves. However, this week holds high hopes for artificial intelligence Millennium problem Also in solving it. Six of these questions are still waiting to be solved, 24 years after the Clay Mathematics Institute announced them with a $1 million reward. If we try our luck, let's consider solutions to the existence and smoothness problems in the Navier-Stokes differential equations that describe fluid motion. Or whether elliptic equations have finite or infinite solutions.
Several years ago Ramanujan machine A computer program called the method was to find fractions whose denominator was a number plus a fraction, and whose denominator was also a number plus a fraction, and so on. Some of these assumptions have since been confirmed.
Another example concerns knot theory, a branch of topology that studies knots whose ends are glued together. If a node is decomposable, it is equivalent to a trivial node. London-based Google DeepMind researchers also came up with a solution: they created a neural network on the data of many different nodes and discovered the relationship between algebraic and geometric structures. But how can artificial intelligence impact mathematics, which relies heavily on creativity? A lot of data can be entered, from number sequences (for example, Fibonacci) to prime numbers and even groups. The Online Encyclopedia of Integer Sequences (OEIS) contains approximately 375,000 sequences, and scientists are already using machine learning methods to search the database to find new relationships.
AI can help you recognize patterns and guess.
At the same time, a seemingly revolutionary discovery may collapse in an instant, if it turns out that it works in vain in a trillion cases, there is one exception. This happened, for example, with the Bolya Conjecture, Hungarian mathematician György Bolya's theory examining prime numbers, which was published in 1919. But in 1960, it turned out that the conjecture was incorrect for the number 906,180,359.
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As British mathematician Godfrey Harold Hardy said in 1940: Mathematician's apology In his article he explains that a good theorem is a component of many mathematical constructions and can be used to prove many types of theses. Those guesses that help us discover new worlds are good, but the connections are difficult for AI to recognize in the absence of connections. Therefore, the vision of important speculations does not yet await technology, although it could be an advantage, accelerating research and opening new paths.
Last year, for example, 2.2 million new crystals is found Graph Networks' new deep learning tool for Materials Exploration (GNoME), including 380,000 stable materials, but it remains to be seen how many of these potential materials are stable, tunable and practically applicable. Only researchers can determine that. Likewise, the imagination and intuition of mathematicians will be needed to understand and process the results of AI tools. Therefore, AI can only act as a catalyst for human creativity, not as a substitute for it.
(Cover photo by Matt Cardy/Getty Images)
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