February 20, 2024

Galileo Galilei said that nature is written in a mathematical language. Today, immersed in a true digital revolution, this statement is more true than ever since, thanks to the promotion of technologies such as artificial intelligence, automatic learning or the big data, mathematics reaches practically all areas: economy, health, environment, sustainable development, urban planning, design and a very long etcetera. “You do math from the moment you wake up. At breakfast you are calculating things; you plan your route to university or work according to traffic; you constantly make decisions… And mathematics is behind every decision we make; nothing is by chance”, affirms Mar Angulo, coordinator of the double degree in Computational Mathematics and Engineering of the software of U-tad. A professional option with a high degree of employability that is also noticeable in access to university studies: at the Complutense University of Madrid, for example, the cut-off mark in 2014 was 5 (out of 10), while this course It is situated between 13 and 14 (the maximum grade), depending on the grade. Yesterday, March 14, the International Mathematics Day (or Pi Day) was celebrated, under the motto “Mathematics for all”.

What do power lines, the catenary on the train tracks and the evolution of a virus or a bacterium, which grows exponentially, have in common? The Sagrada Familia and a certain type of arches and figures in architecture with the profitability of any financial product? The risk of earthquakes with the study of the tides or the prediction of floods? Indeed: mathematics. “Sometimes we are not aware that there is mathematics and creators of algorithms and mathematical models behind everything we use; be it the mobile phone, the credit card, the television screen or the design of characters in a movie or a video game, because there is a lot of geometry there: where we see: “cameras, lights, action” there are matrices and some concepts that may seem unsympathetic or abstract”, says Angulo. Technological advances such as those already mentioned also allow the capture and analysis of huge amounts of data (many times in fractions of a second, thanks to the handling of software) that lead to the development of new tools and methods to solve much more complicated problems and phenomena.

Whether we are aware of it or not, mathematics is found in many spheres of our daily lives: they are, through artificial intelligence algorithms, behind devices that we use every day such as voice assistants, QR codes, smart vacuum cleaners or Instagram filters. They are also present in the field of health, in the resolution and analysis of medical images, in the comparison of new treatments or drugs, and even in the surgical industry, applying virtual reality to surgery simulators. And they were, during the pandemic, making all kinds of predictions in real time about the sick, the deceased, or different treatments. “We all learned to see how much mathematics was in all of that. But it happens in other areas of life. We had a student who told us: “I don’t know why I started this career, if what I like is music.” But in the end, he found a way to make it compatible, because he is developing music recommendation engines based on the facial expression that detects you”, recalls Angulo.

The ubiquitous mathematics

“Today we live in a much more complex society, and that is why other mathematical and statistical models are necessary to help us try to predict where we are going. Now, for example, the stock market is much more complicated than in 1929, because it is more global and more factors interact. And a century ago, who handled three million pieces of data? But today, three million pieces of information are collected by a bank in one day of visa transactions,” says Antonio Brú, dean of the Faculty of Mathematical Sciences at the Complutense University (UCM).

With much more data available, artificial intelligence and machine learning have emerged as two essential tools in which mathematics plays a key role, “because it is the only way to have the capacity to analyze and process that large amount of data , and to be able to obtain the information or predictive power you are looking for”, adds Brú. The popular ChatGPT, which has been talked about so much in recent months, is a perfect example of this predictive capacity: based on a mathematical model of neural networks, this artificial intelligence is capable of generating content: “You pass him a few words or ask him a question and she finds, in all that accumulation of information with which she has been trained, the words that are most likely to follow the ones you have introduced”, explains Angulo.

But artificial intelligence has many other uses: on platforms for streaming Like Prime Video or Netflix, it is used to recommend new series or movies, and it is also used in North American universities such as MIT or Harvard, where teachers make students use it to go faster in studying and acquiring knowledge. “In the city of Los Angeles (California), the police incorporate it to study crime and find out what the fights between the different criminal gangs are like. And it can be used in a similar way for all types of human behavior”, says Brú. In his recent study Hybrid machine learning methods for gender crime risk assessment, that Brú carried out with fellow professors Juan Carlos Nuño (UPM) and Ángel González-Prieto (UCM), found an artificial intelligence algorithm that allows behavior patterns to be developed and more effectively calculates the probability of recidivism of an abuser.

Neural network models

Why are these mathematical models called neural networks? “Because they are based on machine learning, the machine learning. It is about training the machine with statistical and mathematical models so that it can answer a question in a similar way to how our brain does, and continuing to improve it with a backpropagation algorithm so that the answer is better and more precise.” Angulo answers. And all artificial intelligence is also based on that: “ChatGPT works through vector spaces, perhaps one of the least liked subjects when studying in the second year of high school; but the foundations of neural networks and artificial intelligence are already being laid there, and it is tremendously important to know that all this is constantly being used to develop the most complex products”, he adds.

According to the expert, data analysis through mathematical models allows you to examine any type of complex system, make predictions or optimize resources such as programming a hospital emergency network, a fire network or garbage collection through a graph. , so that it passes through all the streets without repeating any; distribute to the people I have to deliver food at home or any other public or private service system. “And with the La Palma volcano, for example, it was necessary to study it day by day, and in that, as in any other environmental phenomenon, in the end, time series intervene where the changes that are produced are studied, data that you analyze to make predictions. This is applicable to any phenomenon and to any sector that you can imagine”, concludes Angulo.

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