The time evolution of various natural phenomena often exhibits sudden changes of state, occurring at certain points where the duration of these disturbances is either null or minimal in comparison to the overall duration of the phenomenon. These sudden changes are referred to as impulses and can be observed in fields such as physics, biology, economics, control theory, and information science.

Impulsive dynamical systems (IDS) are effective mathematical models of real world phenomena that display abrupt changes in their behavior.

At the beginning of the third millennium of our era, Leibniz’s famous expression, “Musica est exercitium arithmeticæ occultum nescientis se numerare animi” (Music is a hidden arithmetical exercise of a mind unconscious that it is counting) can be taken in a broad sense in a contemporary conception of art and science. In the European universities, since the middle ages, Music was part of the studies and Portugal was not an exception. The Studium Generale of Lisbon, instituted by King Dinis in 1290, marking the foundation of the Portuguese University, included the medieval version of the Liberal
Arts of the Trivium (grammar, rhetoric and dialectic) and
the Quadrivium (arithmetic, geometry, astronomy and
music).

The International Conference on Mathematical Analysis and Applications in Science and Engineering (IC-MASC’24) was held on June 20–22, 2024, at the Polytechnic of Porto’s School of Engineering (ISEP) in Porto, Portugal. 

Having appeared at the end of the seventeenth century, the calculus (differential and integral calculi for Leibniz, method of fluxions for Newton) was undoubtedly the most important branch of pure mathematics in the eighteenth century. For all its centrality in eighteenth-century European mathematics, the adoption of the calculus in Portugal was slow. Before 1760, only a few isolated cases can be found of Portuguese individuals knowing about the calculus, and in each case one may wonder how profound was such knowledge.

In four movements — Pythagorean Arithmiusic, Tone Algebra, Harmonisation of Analysis, Digital Musurgia — and through a few examples, we will present a brief introduction to the numerous interactions between mathematics and music throughout history, which can help us understand the modern interpretation of Leibniz’s expression: Musica est exercitium arithmeticae occultum nescientis se numerare animi.

José Francisco Rodrigues, former President of CIM, has been elected President of the Lisbon Academy of Sciences (ACL) for the 2025-2026 term. The election took place at the Academy’s plenary session on December 19, 2024.

The LxDS Spring School 2024, organized by the LxDS-Lisbon Dynamical Systems Group in collaboration with CEMAPRE and CMAF-CIO, took place from May 27 to 29, 2024. The event was held at the Faculdade de Ciências, Universidade de Lisboa (FCUL). This spring school focused on various topics of dynamical systems, providing an opportunity for participants to enhance their knowledge through courses delivered by internationally recognized experts.

In this note we will review the main steps in the proof of Fermat’s Last Theorem and discuss Darmon’s program to tackle the generalized Fermat equation Ax^q + By^r = Cz^p. Finally, we discuss how combining the classical approach with some ideas of Darmon led to recent results for equations of the form x^r + y^r = Cz^p.

Luis Nunes Vicente, member of the scientific council of CIM, has been selected as a Fellow of the Society for Industrial and Applied Mathematics (SIAM). SIAM has over 14,000 individual members in all areas of industrial and applied math. The SIAM Fellows Program recognises members of SIAM who have made outstanding contributions to fields served by the industrial and
applied math community. According to his citation, Luis was selected for ground-breaking contributions to derivative-free and bilevel optimisation, and exemplary leadership in editorial and organisational service to the SIAM community.

Jorge Buescu, a mathematician from the Faculty of Sciences of the University of Lisbon (FCUL), has been awarded the “Grande Prémio Ciência Viva 2024”. This prestigious award, the highest category of the Ciência Viva Prizes, recognises individuals and organisations for their outstanding contributions to scientific and technological dissemination.

The international conference Perspectives in Representation Theory took place at the University of Coimbra, July 1–3, 2024, and it was a Satellite meeting of the 9th European Congress of Mathematics, Sevilla 2024 (see https://ecm2024sevilla.com).

The Combinatorics Days is an itinerant annual conference series that brings together mathematicians working in Combinatorics, widely interpreted, and related fields such as Algebra, Geometry, Probability, Computer Science or Physics.

This short expository note aims to give the minimal amount of Lie theory needed to appreciate the eightfold way in particle physics. We first give a quick but complete account of the finite-dimensional irreducible representations (irreps) of SL(2,ℂ). Then we sketch how the theory generalizes to the irreps of SL(3,ℂ), and close by gesturing at the role of these irreps in the eightfold way.

The 2025 Pedro Nunes Lectures will be given by Michael Christ (University of California, Berkeley), on May 7 and May 9, 2025.