{"id":13694,"date":"2023-10-02T07:53:00","date_gmt":"2023-10-02T05:53:00","guid":{"rendered":"https:\/\/www.ull.es\/portal\/noticias\/2023\/10\/02\/en-clave-matematica\/"},"modified":"2026-10-30T10:48:47","modified_gmt":"2026-10-30T09:48:47","slug":"en-clave-matematica","status":"publish","type":"post","link":"https:\/\/www.ull.es\/portal\/noticias\/en\/2023\/10\/02\/en-clave-matematica\/","title":{"rendered":"In mathematical terms"},"content":{"rendered":"

Despite the fact that almost everyone knows and has even hummed the very well-known song once or twice A Hard Day's Night<\/em> Of all the Beatles, few people know that one of their chords wasn't George Harrison's, Paul McCartney's, or Ringo Starr's. Not even John Lennon's. The Liverpool quartet's third album hid a secret rhythm that not only revealed the existence of the so-called fifth Beatle\u2014or one of the many to whom that 'honor' is attributed, George Martin\u2014but also demonstrated that mathematics and music can go hand in hand.<\/p>\n

The enigma hidden in the song that gave its title to the British group's first film was in a note of just a few seconds that did not fit with the rest of the composition until someone (the American scientist Jason Brown) thought of applying the Fourier transform, an essential mathematical operation with which it is possible to fragment a melody and analyze it to the point of finding out that Martin was responsible for those fleeting piano chords.<\/p>\n

The explanation for this fact was addressed in 2017. the students Airam Exp\u00f3sito and Sarai del Castillo<\/a>. And they did it in 10 minutes, the length of the short math sessions that have been held for years in the Aula Magna of the Physics and Mathematics Departments of the University of La Laguna, an initiative promoted by the professor of Department of Mathematics, Statistics and Operations Research<\/a>, and coordinator of the Educational Mathematics Cultural Classroom<\/a>, Edith Padr\u00f3n<\/a> Fern\u00e1ndez<\/a>.<\/p>\n

\"\"<\/a>Committed to raising awareness of the presence of mathematics in different areas of society, Padr\u00f3n was the first president of the Women and Mathematics Commission of the Royal Spanish Mathematical Society<\/a>. As a good popularizer, she doesn't miss the opportunity to proclaim far and wide that there can be many different (and entertaining) ways to make the science of Pythagoras and Descartes known, one of the reasons why around 2015 she decided to embark on the adventure of creating something different and sparkling with which to involve her first-year undergraduate students.<\/p>\n

\u201cThe \u201dfisquitos\u2019 came about in the silliest way possible, to be honest. I had been involved in cooking workshops that addressed mathematics and in scientific monologues, and it was after their disappearance that the vice-dean of the Mathematics Section, Mar\u00eda Candelaria Gonz\u00e1lez, suggested that I do something so that the first-year students would not become demotivated, since at that time there was little mathematics in the first-year curriculum.\u201d.<\/p>\n

The germ of the fisquitos<\/strong><\/p>\n

It was then, on his walk from home to the university, that he thought he could do something short and engaging with the professors during break time. And that's how "Fisquito de Matem\u00e1ticas" (Little Math Talk) was born. The professors at the University of La Laguna were asked to share a math-related story once a week, with the only requirement being that it be 10 minutes long. It also had to spark curiosity and be entertaining, without requiring anyone to be a math expert to participate.<\/p>\n

The number of people attending the "fisquitos" (little physics talks) quickly grew from 60 to 150, despite the fact that "the 'fisquito' doesn't offer anything in return, no credits, nothing. People come to listen and learn, and the presenter comes to share mathematical knowledge," explains the researcher, emphasizing that after 10 minutes it doesn't matter who's speaking. Whoever it is, the applause signals that the speaker's moment of glory has come to an end, and it's up to the audience to close the presentation.<\/p>\n

The students soon joined the teachers. The mathematics students didn't want to miss the opportunity to design and create their own little show, which they plan, assemble, rehearse, perform, and narrate until it's perfect. "It's a fantastic learning experience that they leave feeling proud and fulfilled for having been able to do it," Padr\u00f3n remarks.<\/p>\n

In fact, the Mathematics Workshop at the University of La Laguna has become a benchmark in the academic world and the best rehearsal for students who are afraid of facing their Final Degree Project (TFG), a preparatory exercise that allows them to unleash their curiosity and solidify their knowledge. \u201cRecently, a student told us that part of mathematics has to do with how to detect human traits, with identifying people. These are things you discover. It hadn't occurred to me, but they find them. Perhaps they find it difficult to delve deeper, but they have that ability to seek out things that surprise them.\u201d.<\/p>\n

The outreach championed by Padr\u00f3n is not limited to finding 'fisquiteros' and 'fisquiteras'. Cultural Classroom of Informative Mathematics<\/a> The department at the University of La Laguna, which she directs and where a dozen professors and just as many students work, promotes exhibitions, talks, and training activities. In addition, there are workshops and an escape room in the classrooms that rivals any professional one. "We have things like that, and I really enjoy those kinds of things.".<\/p>\n

Showing the more playful, little-known, and yet motivating side of mathematics is further proof that this professor enjoys each and every facet of this science, to which she has dedicated four six-year research periods at the University of La Laguna (ULL). Both with her research group, Differential Geometry and Geometric Mechanics, and through the national thematic network Geometry, Mechanics, and Control, outreach has been and continues to be paramount in her professional career. \u201cI'm part of a research network that works very well, but the outreach tools of these networks are perhaps not the most suitable because they are designed in a more general way. What we've envisioned is a thematic outreach network, tailored to each branch, in this case, mathematics.\u201d.<\/p>\n

Mathematical reasoning <\/strong><\/p>\n

The fact that mathematics has not evolved at the same pace as the real world is due, according to the expert, to the fact that it requires "a certain level of personal concentration," and on many occasions that is\"\"<\/a> Impossible in a society interconnected 24\/7. \u201cA mathematician doesn\u2019t reason like everyone else, and that\u2019s something you don\u2019t forget when you go to university. Reasoning processes don\u2019t disappear from your life; they\u2019re fundamental.\u201d.<\/p>\n

And it is these reasoning processes that enable mathematicians to break down problems into smaller parts, a compelling reason why companies are so eager to hire them. Teaching is no longer the only career path for those who choose to pursue a degree in Mathematics. Today, professionals in the field of mathematics have a wide range of career options available to them, from working in multinational pharmaceutical companies to supermarket chains, logistics and transportation companies, production lines, or banking and finance.<\/p>\n

A wide and attractive range of possibilities explains why the unemployment rate in Spain for mathematics graduates barely reaches 41%, according to data published by the National Institute of Statistics (INE)<\/a>. The search for intelligent solutions has led to professionals in this field leaving the classroom to embrace the business world, a fact that has caused a shortage of teachers in this specialty.<\/p>\n

The ability to segment problems that people with a degree in Mathematics possess is a powerful reason why many companies request students from the University of La Laguna for internships. \u201cCurrently, there are many companies where fourth-year students do their internships. Although they may not initially know what they are working on, mathematical methodology helps them solve numerous situations that arise in the business world today.\u201d.<\/p>\n

However, despite the numerous career paths available to graduates, Padr\u00f3n believes that, although it's a successful field with virtually no unemployment, it's primarily a vocation. "I wouldn't recommend studying mathematics to anyone if they don't enjoy it and aren't drawn to it. It must be, above all, a calling.".<\/p>\n

\u201cA mathematics degree is not what you saw in high school; it has nothing to do with it. It involves reasoning processes that must be built. Topology, for example, is pure reasoning, and when students are able to overcome it, despite the effort it takes, they are able to continue taking steps in the right direction,\u201d explains the professor from this academic center.<\/p>\n

Adaptation as a challenge<\/strong><\/p>\n

Despite the "fresh perspective" that students with expertise in numbers bring to the business world, where their well-organized minds lead processes of optimization, distribution, or production,\"\"<\/a> The expert believes that mathematics academics have been unable to adapt to the system. \u201cThe system itself has gone against what mathematics requires, and that is a future challenge we will have to face.\u201d One of these challenges is developing the ability to critically analyze everything digital, an aspect that must be taught in universities so that graduates are able to obtain impartial information, free from societal bias. In this regard, \u201cthere is much to be done in high schools and universities.\u201d.<\/p>\n

\u201c<\/strong>Complicated times are coming, and new generations must make an effort to change many things, not only in the teaching of mathematics but in education in general. Artificial intelligence tools will be the great revolution in everything, in how we teach. You don't teach people about artificial intelligence; they perceive the results.<\/p>\n

The problem, according to the expert, lies in the fact that developing this entire mechanism requires \u201ca number of people to continue doing that deep, focused mathematics. That rigorous, reviewable mathematics. Because a mathematician is like a scientific reviewer, taking steps while constantly verifying what they are doing. They always stop and review, because sometimes, it is in those small details that great discoveries are found, and changing things means taking a different path,\u201d Padr\u00f3n explains.<\/p>\n

In this regard, we cannot ignore the common perception of mathematics: a science where two plus two equals four and everything fits together perfectly, a closed concept that is quite far removed from what it actually is, and from science in general. \u201cWe often think of and teach mathematics as a building constructed from the ground up, where you place the blocks one on top of the other so that everything fits, but it's not like that. As you place the blocks, you realize that perhaps you've put them in the wrong place, and you have to move them around.\u201d.<\/p>\n

However, the professor from the University of La Laguna is aware that, when teaching mathematics, the usual approach is to "present it as something constructed and perfect," and it is this perception of perfection that has permeated society and students, whether in primary, secondary, high school, or university. Facing mathematics is not easy. More often disliked than loved, this science tends to cause many headaches for students.<\/p>\n

Not surprisingly, researchers from University of Nevada<\/a> The United States coined the term arithmophobia to refer to the tension and panic that arises among many students when faced with having to deal with numbers. This uncontrolled fear is due, according to two leading figures in the field, to the Fields Medal (the highest award for a mathematician). Martin Hairer and Cedric Villani<\/a>, Padr\u00f3n partly agrees that the teachers who teach Mathematics sometimes lack sufficient knowledge and speed when delivering the content.<\/p>\n

Learn how to teach <\/strong><\/p>\n

\u201cTeachers need to be taught how to teach. From a self-critical perspective, I think we should be more modern. At the university, we don't teach how to teach mathematics, and many professors feel they aren't qualified to teach it. The education system forces teachers to cover the material outlined in the curriculum, and over time you discover that it doesn't matter what was actually taught in the classroom if the students truly learned what was taught, if they grasped how to solve a problem. But that would require a major overhaul of the system.\u201d.<\/p>\n

The truth is, \u201cif the objectives set are not achieved, it's pointless,\u201d especially when artificial intelligence \u201cis already posing significant challenges.\u201d That's why he believes that young professors now entering university \u201cneed to get their act together.\u201d \u201cThe difference will be that from the outside you can either manage the situation or let it manage you. High-level positions will be in the hands of those who are able to understand how to engage with artificial intelligence on equal terms, not from a position of power.\u201d I give to you and you give to me<\/em>\u201d.<\/p>\n

\"\"<\/a>Padr\u00f3n is aware that mathematics has its own language that makes communication difficult, although that language is not usually a handicap for the students of Bachelor's Degree in Mathematics<\/a>.\u201cIt is true that our mathematics students come with high abilities. I have discovered that their training is not the same as mine, but they do have a great deal of curiosity, and sometimes that is more important than knowing certain things.\u201d.<\/p>\n

That they ask questions, that they want to know, and that they don't abandon their curiosity or dismiss having initiative is paramount for the driving force behind the "fisquitos" (a group of young mathematicians), who insists that they know that mistakes help them grow, "something that isn't taught when learning mathematics. Realizing the mistake you make allows you to look for other paths," different ways to instill this science. And one of them is the hands-on technique.<\/p>\n

\u201cIn mathematics, to learn, it is important to manipulate, to work with objects. We must not lose the hands-on aspect. Creativity is related to manual work. It is true that digital tools give you the answer, however, you have to do the manipulative work yourself,\u201d says Tinerflecta, a group of primary and secondary school teachers who teach mathematics to their students using paper figures that recreate pre-established geometric patterns, referring to the origami display.<\/p>\n

This display of paper figures was one of the activities carried out during the past year by the Cultural Classroom of Informative Mathematics<\/a> from the University of La Laguna, which she leads with the aim of bringing mathematics closer to everyone. Despite it no longer being such a niche field of study as when Edith Padr\u00f3n began her studies, and there were no more than 35 people in the classroom, she is very clear that "success in mathematics lies in being able to make it your own.".<\/p>\n

Although student enrollment has changed substantially in recent years\u201478 people have begun their studies in the Mathematics degree program at the University of La Laguna this year\u2014learning the steps of mathematical reasoning is like learning to drive. \u201cWhen you're learning to drive, you have to think about every step you take, and when you know how, you don't think about them because you've internalized them and made them your own process, a process you understand.\u201d It's an ambitious and complex task that the new students now face.<\/p>\n

Communications Office<\/strong><\/p>\n

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