So you think you know 2+2? Try again.

ON PAPER, IT’S ONE OF THE SIMPLEST maths problems in the world: 2+2. If you’re counting something, such as screws at the hardware store, it’s pretty straightforward. But the lines blur in other contexts. If you add two cups of vinegar to two cups of baking soda, and the reaction produces five cups of a fizzy mess, does that mean 2+2=5?

- CAROLINE DELBERT

We bring assumptions into the world of mathematics. In this case, the simple ‘counting numbers’ – the whole integers 1, 2, 3, and so on – signify a gulf between math’s abstraction and application. Using ‘2+2=4’ as food for thought, mathematicians are exploring the circumstances in which 2+2 doesn’t actually equal 4, at least not neatly, and we can extend those interpretations to larger questions in epistemology – how we know what we know.

Kareem Carr, a biostatistics PhD student at Harvard University, ignited a ‘Does 2+2 ever equal 5?’ debate on Twitter. On 30 July 2020, he wrote, ‘I don’t know who needs to hear this, but if someone says 2+2=5, the correct response is, “What are your definitions and axioms?”, not a rant about the decline of Western civilisation.’

In his Twitter thread, Carr pointed out that counting numbers ‘are abstractions of real underlying things in the universe’, so we should be mindful of how those abstractions distort truth when introduced to real-world scenarios. Arithmetic works well in a textbook, but practically, it often runs into contextual questions that don’t account for parts of a whole, approximations, or more relevant vectors.

For example, if you’re adding whole degrees to an angle, eventually you’ll circle around to an angle that measures 360°. But a 360° angle has the same orientation as a 0° angle, so whether the angle measures 0° or 360° depends on context. Likewise, if you drilled a screw five full rotations (1 800°) instead of four (1 440°), the screw’s orientation remains the same, but in one case, it’s deeper inside the wood.