The Pequeño Instituto de Matemáticas is an initiative aimed at fostering interest and appreciation for mathematics among pre-university students. Launched in 2021 by the ICMAT, it follows the model of mathematical circles, where students, working in groups, attempt to solve complex mathematical problems. On May 31, the second edition of the program concluded, and registrations are now open for the third edition, which will begin in September 2024 and, like the previous ones, will be free for students.

At PIM, groups of four or five students work together to find creative solutions to challenging mathematical problems. Image: Laura M. Iraola/ICMAT
Ágata Timón García-Longoria (ICMAT)
On May 31, the second edition of the Pequeño Instituto de Matemáticas (PIM) concluded with a celebratory event featuring a keynote lecture by the popular science communicator Mates Mike. Participants—this year, around 140 students from 1st-year secondary school to 2nd-year high school, 35% of them female—and their families had the opportunity to bid farewell, at least for a few months, to the ICMAT, where they spent every Friday afternoon doing mathematics.
“The teaching philosophy behind the project is summed up in a simple phrase: ‘Mathematics is not learned by watching, but by doing,’” explains the PIM organizing team. And doing mathematics means attempting to solve difficult problems, exploring different approaches, testing multiple pathways, discussing with others, and comparing ideas. Following the methodology of mathematical circles, students do not learn new concepts in theoretical sessions but work in groups on problem sheets with the support of teachers, mainly predoctoral researchers.
“One lesson we want to convey at PIM is that most real-world problems are challenging and require deep, creative, and thoughtful approaches. This early understanding prepares students to face future situations where problem-solving will not be a trivial task, instilling patience and the ability to tackle complexity effectively,” adds the organizing team.
ICMAT launched PIM in 2022, and after successfully completing two editions, the third one is now underway, set to begin in September 2024. Interested students must take an entrance test—scheduled for June 7 or 14 at 5:30 PM at ICMAT—which serves to determine their starting level and requires prior registration. Those unable to attend the test will have the option to register during the summer by submitting their solutions to a set of problems that will be posted on the registration website in June.

The problems posed at PIM reflect the challenges that STEM professionals face in real life.
Inspiring a love for mathematics and training future researchers
“The problems posed at PIM reflect the challenges that STEM professionals face in real life, showcasing the diverse and multifaceted nature of mathematics. By bringing this experience to students, we aspire to build a strong foundation for their academic and professional future, inspiring the next generation of creative minds passionate about mathematics,” states the organizing team.
One way to get hooked on mathematics is to experience the reward—“the unique satisfaction,” as they describe it—of solving a difficult problem. “When students tackle mathematical challenges that initially seem insurmountable, they discover the joy of persistence, of exploring different strategies, and ultimately finding a solution. In our experience, for the vast majority, this leads to a renewed interest in mathematics,” they add.
Currently, the program is funded by ICMAT and CUNEF Universidad and is free for students. The initiative is also supported by the Universidad Autónoma de Madrid and the Spanish Royal Mathematical Society. “PIM is a creative and determined effort to promote mathematical vocations among young people, which in turn will help cultivate the necessary environment for training the next generation of scientists in Spain,” says Javier Aramayona, director of ICMAT.
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