Interdisciplinary Learning Courses

The power of mathematical thinking

The power of mathematical thinking The power of mathematical thinking
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Interdisciplinary Learning CoursesThe power of mathematical thinking

Mathematics offer a clear and precise way of understanding the world, and are very useful to everyone

Mathematical thinking goes beyond operating with fractions, calculating roots of polynomials or learning the formulas of derivatives. It is a way of seeing the world, identifying the key elements that operate in each situation and extracting its defining characteristics; observing the numerical and structural relationships that occur between these objects... and using logic to make our deductions.

Throughout the history of civilization, these tools have been developed and perfected, and configure mathematical thinking. In this course we will pause at some of these great achievements of humanity, which are part of our cultural heritage. Through these examples we will induce reasoning and mathematical analysis, which should be fundamental skills for any person.

Learning objectives

  • 1) Exercise mathematical skills such as abstraction and modeling.
  • 2) Relate mathematical knowledge and our reality, technological advances, other sciences …
  • 3) Extract the basic characteristics of mathematical thinking.
  • 4) Know key moments and people in the history of mathematics.
  • 5) Learn about mathematical research.

Contents of the Subject

The power of mathematical thinking

  • 1. Introduction and organization of the subject
  • 2. Mathematics to measure, relate and sharer (Mesopotamia, Egypt, Mayans...)
  • 3. From magical thinking to mathematical thinking (Thales, Pythagoras).
  • 4. Mathematics that expand our view of the world (Archimedes and Eratosthenes).
  • 5. Formalization of truth: Euclid's concept of demonstration.
  • 6. Represent the abstract: symbols and notation.
  • 7. Thought beyond what is tangible: algebra and other generalizations (Arabic mathematics). Mathematical revival in Europe: duels and small advances.
  • 8. Understanding the movement and predicting the future (Kepler, Newton, Leibniz)
  • 9. Plasticine graphs and geometry (Euler).
  • 10. Geometries of other worlds (Gauss, Riemann).
  • 11. New disciplines: group theory, abstract algebra, chaos theory.
  • 12. Fundamentals and paradoxes (Cantor, Russell, Hilbert and Gödel).
  • 13. Mathematics as a profession (Hilbert problems, Millennium problems, Bourbaki, Noether) and economy engine (computers, signal processing).
  • 14. End of course and closing activity.


Ágata Timón García-Longoria. Professor of The power of mathematical thinking

Ágata Timón García-Longoria.

Responsable de Comunicación y Divulgación del Instituto de Ciencias Matemáticas (ICMAT). Licenciada en Ciencias Matemáticas, es experta en comunicación pública de las matemáticas. Ha formado parte del gabinete de prensa del proyecto Consolider iMATH y del centenario de la Real Sociedad Matemática Española (RSME). Desde su creación en 2012 organiza y coordina las actividades de la Unidad de Cultura Matemática del ICMAT. Es coautora de cuatro libros de divulgación, coordina la sección Café y teoremas, en El País, y ha impartido diversas conferencias sobre comunicación pública de las matemáticas.