Why does 2 + 2 = 4?

We begin with a question that seems almost too obvious to ask: is 2+2=4 really true?

In everyday life it feels immediate—two apples and two apples make four apples. But mathematics asks a deeper question: how do we actually know something is true?
One way is through proof. A proof starts from a few basic statements and rules, and step by step derives a new statement from them. The key challenge, then, is choosing the right starting points. Mathematicians eventually chose sets—simple collections of objects—as the most fundamental building blocks. From a few basic assumptions about sets, we can define numbers, define addition, and gradually build the entire structure of mathematics.

Even a statement as simple as 2+2=4 can therefore be derived from these basic principles. In this session we will not focus on technical details, but on understanding the overall structure of the idea. The reasoning can be followed in simple terms, even by non-mathematicians, and it reveals something remarkable: from a small number of simple starting points, an enormous world of mathematical knowledge can be built.

Along the way, we will also look at the historical path that led to this view—how mathematicians gradually refined these ideas over centuries in an intellectual quest to understand the foundations of mathematics.

This session will be led by Jordi Molins.

Bring wine/beer/drinks/food/snacks/whatever if you want to.

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Press the buzzer marked Semi sotano 2 (bottom left on the panel) to be let in. It's down the stairs, first door on the right.

Image: Ptolemy, in the School of Athens by Raphael.