Cecilia Neve Jiménez: The fifth arithmetical operation and its origins

The talk is a part of the speaker´s stay with the research group PragMatika

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Cecilia Neve Jiménez: The fifth arithmetical operation and its origins

Abstract
A well-known quote states that "there are five fundamental operations in mathematics: addition, subtraction, multiplication, division and modular forms". Inspired by this, in this talk we consider a variant, taking modular transformations as the fifth mathematical fundamental operation. This approach allows us to examine and revisit, from a historical perspective, various contexts in which this operation is relevant, along with the processes—both theoretical and practical—that give rise to it. Moreover, we trace their usage back to Lagrange's works on number theory, in which we can identify their emergence as the result of a process through a series of works.

Cecilia is a PhD candidate in Mathematics at the University of Seville (US) who for the last three months has been carrying out a stay with me and my team under the auspices of the Erasmus+ Traineeships programme. Her stay is part of our official collaboration with the History and Philosophy of Physical and Mathematical Sciences research group at the US, the head researcher of which is José Ferreirós, one of Cecilia’s supervisors. During autumn this year, in fact, José Ferreirós will also carry out a research stay with us, on the occasion of which he will give a talk that we will announce in due course.