Why does mathematics work? FilMat 2026 meets in Bologna

A physicist writes down an equation. The equation predicts the existence of a particle nobody has seen. Years later, the particle is found.

Why is that possible?

The question looks innocent but it is the hardest problem in the philosophy of mathematics. In 1960 the physicist Eugene Wigner gave it a name: the unreasonable effectiveness of mathematics in the natural sciences.

That problem sits at the centre of a conference at the University of Bologna from 9 to 11 September 2026.

FilMat 2026 — Philosophy of Mathematics: Applicability, Ontology and Reasoning is the fifth international conference of the Italian network for the philosophy of mathematics. The three words in the title summarise the field's present agenda: applicability, ontology and reasoning.

Three problems#

Applicability#

Is mathematics a system of symbols produced by the human mind, or is it reading the structure of the world?

If the first, then its fit with physics is a miracle awaiting explanation. If the second, we owe an account of where mathematical objects are.

That dilemma feeds every other argument in the field.

Ontology#

One of the keynotes, by Chris Pincock of Ohio State University, goes straight at it: "Do mathematical objects have a nature?"

The question opens like this. What is a mathematician working on when working on triangles? There is no perfect triangle in the physical world — every drawn triangle has sides with thickness. So what is "the triangle"?

The Platonist answer: mathematical objects exist outside space and time, independently of mind. The mathematician discovers rather than invents.

The fictionalist answer: mathematics is a useful fiction. Saying "between two primes…" is like saying "Anna Karenina thought…" in a novel — truth holds inside the fiction.

The structuralist answer: numbers are not objects but positions in a structure. There is no such thing as "2"; there is the second position in the sequence of natural numbers.

The sharpness of Pincock's question lies here: for something to have a nature requires more than for it to exist. Socrates has a nature — being human. What is the nature of the number 7? Or is everything that can be said about 7 exhausted by its relations to the other numbers?

Reasoning#

The third heading is the field's liveliest area: how do mathematicians actually reason?

The classical view treats mathematical proof as a chain of formal inference. Real mathematical practice does not look like that: diagrams are used, "it is clear that" is written, computer-assisted proofs are accepted.

What makes a proof a proof? Does a computer-generated proof that nobody can read from beginning to end give us knowledge?

Why Bologna?#

The venue is symbolic. The University of Bologna is regarded as the oldest continuously operating university, founded in 1088.

And Italy has a particular history in the philosophy of mathematics: Giuseppe Peano's axiomatic programme was among the founding steps in the late nineteenth-century search for the foundations of mathematics.

The FilMat network sets out to carry that tradition forward in contemporary analytic philosophy of mathematics.

Practical details#

• Dates: 9-11 September 2026
• Venue: Department of Philosophy, University of Bologna, Italy
• Organiser: FilMat — Italian Network for the Philosophy of Mathematics
• Keynote speakers include: Chris Pincock (Ohio State University)

The full programme is at filmatnetwork.com.