In 1798, the French mathematician Adrien Marie Legendre he was in his study, staring at the blackboard on which he had written an endless sequence of prime numbers. Suddenly, he understood what the link between them might be and that it was therefore possible to give a rough description of a classic mathematical problem: how prime numbers are distributed. It is the first formulation of the prime number theorem. Which does not arise from a cold application of the rules, but on the contrary, from something that we could define as an illumination, an epiphany. An intuition.
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It is not a unique case: also Kepler, at the beginning of the seventeenth century, he said he found himself in an “almost dreamy” state while imagining the elements from which Kepler’s Laws relating to the movement of the planets were born. These two anecdotes help us understand how mathematics, at the highest and most theoretical levels, works in a very different way from how we laymen might imagine: “It is a process that requires a lot of imagination and creativity“, Explains to ItalianTech Petar Veli? Kovi?, Serbian researcher of DeepMind (one of the most advanced research laboratories on artificial intelligence, owned by Google) while he is in Rome on the occasion of an event organized by Pi Campus, a fund of venture capital dedicated to the more concrete applications of artificial intelligence. “Sometimes this process requires a leap of faith: the mathematician is convinced that he has understood what are the connections, for example, between two mathematical objects and then he must be able to formalize them, to demonstrate their existence. And often doing all this is extremely difficult “,
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This is where the deep learning model designed within DeepMind that Petar Veli?kovi? and his colleagues who won the cover of Nature: an algorithm capable of supporting mathematicians in the phase that leads from intuition to proof. In short, after a scholar has formulated his hypothesis, the deep learning model is able to generate the data necessary to identify correlations within the mathematical framework under study, helping the researcher to understand if he is following the right path and also narrowing the field, focusing his attention on the most important elements.
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“In some cases, the algorithm that tries to predict the connection between X and Y could already provide a response with a certain accuracy, such as to encourage one to go directly to the demonstration phase,” continues Veli? Kovi ?. “In other cases we can instead interrogate the machine learning model, asking it, for example, to highlight in a graph which was the most important area that allowed it to identify the possible link between the two mathematical objects. On this basis, the algorithm provides us with a portion of the graph, perhaps going from a few thousand elements to 10-15, thus making it easier to inspect them with the naked eye and understand what the link between them is “.
Despite the evident potential in the scientific field, there are still a lot of progress to be made: “Our interrogation techniques are still in their infancy and there is a lot of ‘noise’ (or disturbances in the signals sent by the machine, ed) in the answers it gives us”, continues the 28-year-old DeepMind researcher. “The mathematicians we work with, and to whom we show the graphs that are returned to us by the algorithm, are however often able to distinguish the signal from the noise, helping us again to improve the results we can obtain”.
The DeepMind algorithm has already been put to work on extremely complex mathematical problems such as the Kazhdan-Lusztig polynomials or the theory of nodes, managing to identify new relationships between the traits (or “invariants”) of the nodes (i.e. intertwined closed curves in space) that could have applications in fields such as physics, chemistry and biology. “It is still a tool: a kind of pocket calculator extremely advanced that allows you to zoom in on a particular issue and understand which are the most important parts, thus facilitating the identification of connections ”, explains Veli? kovi ?.
It is a collaboration between man and machine in which the most creative part and the final phase of the discovery still belong integrally to the human being. The algorithm is a support that allows to identify the most promising areas on which to focus attention, thus “increasing” the ability of researchers to have the right intuition. However, an open question remains: what exactly is intuition? “When you use these terms in a paper on machine learning there is always a risk of being misunderstood,” admits Veli? Kovi ?. “Let’s say that, in mathematical termsintuition is the ability to observe very complicated problems, make a leap of mental faith on what the fundamental element of the problem is and then work to demonstrate the correctness of our idea “.
The work done by DeepMindmoreover, it seems more generally to go in a very specific direction: artificial intelligence will not replace human beings, but will increase their capabilities. “It is a synergy that makes the human being more efficient, just like a super calculator. Of course, depending on how the technology is used it can also replace some tasks, but this is normal. We must be attentive to how we use it, to the fact that it is fair and free of prejudices, but if used correctly it allows us to empower the human being “.
It is an even more important interpretation, in a phase in which we have begun to talk about sentient artificial intelligences and the possibility of achieving superintelligence through deep learning: “Neither psychologists nor neuroscientists have yet a precise definition of what it is. sentience: some definitions satisfy someone but not others, and in the meantime all the programs that have passed the Turing test have always done so through some tricks “, explains the researcher of DeepMind, a company whose mission is by statute, that of creating general artificial intelligence. “If you look at all the errors of these systems you understand that that level is still a long way off: for example, you can ask an algorithm to prove you a false mathematical statement and it will do it, obviously incorrectly. There is a difference between language modeling, that is, statistically predicting how to complete a sentence, and being part of the human knowledge. Having said that, I think that sooner or later we will conquer the breaking latest news (general artificial intelligence, human level). But we must not be afraid of it, we must first think about how to use it responsibly ”.