This is a meta-mathematical question—a question about mathematics itself that can be addressed using mathematical methods. In our research, we proved that four assumptions—monotonicity, convexity, ...

Humans have been making symbols for numbers for thousands of years. Different cultures developed their own symbols, but all use addition and multiplication, suggesting arithmetic is a universal truth.

Everyone knows that arithmetic is true: 2 + 2 = 4. But surprisingly, we don’t know why it’s true. By stepping outside the box of our usual way of thinking about numbers, my colleagues and I ...