Can humans create infallible mathematics?

Mathematics is used to describe everything from the universe to the tiniest particles. But can mathematics provide us with certainty? Researcher Silvia De Toffoli will join Linköping University as a Wallenberg Academy Fellow to study this.

Mathematics is often presented as being entirely logical in nature, as if it is free of human weaknesses. It is often seen as an objective science whose results cannot be rationally doubted. However, the basic assumptions upon which mathematics rests as well as the arguments that mathematicians use have been constructed by people, by mathematicians who are part of the social world.Silvia De Toffoli.Silvia De Toffoli.

Silvia De Toffoli, Doctor of Philosophy and Mathematics, has received funding from the Knut and Alice Wallenberg Foundation for a five-year project about the human side of mathematics. and. Her research lies at the intersection of mathematical perfection and the social world.

“The issues in philosophy of mathematics that interest me the most concern how living, breathing human agents practice mathematics. What intrigues me is the elusive middle ground between the perfect abstract realm of mathematical theories and the messy human world inhabited by mathematicians.  What explains our formidable success in developing ever more complicated theories?” Silvia De Toffoli says.

De Toffoli will study the legitimacy of various methods used to establish new mathematics. She will do this both by analysing the criteria governing the publication of articles and by collaborating with mathematicians and investigating their working conceptions of rigorous proof.

The goal of the project is to develop a theory of how mathematical knowledge is created and shared in practice.

“I suspect that the answer will be different for different mathematical fields. My work will then be to provide a philosophical framework that is not disconnected from practice but will instead help us understand such practice by explicitly spelling out the sometimes implicit norms that govern actual mathematics.”

De Toffoli will conduct the research at the Philosophy and Applied Ethics research environment at Linköping University.

“Given its interdisciplinary focus and its local, national, and international network, the research environment will be a highly suitable platform for my research.  It will also allow me to connect with other relevant disciplines such as cognitive science, educational studies, physics, and sociology”, De Toffoli says.

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