It looks like one of the easiest math questions in the world: 2+2. It's pretty simple if you're counting something, like screws at the hardware shop. But sometimes the lines aren't clear. If you mix 2 cups of vinegar with 2 cups of baking soda and get 5 cups of a fizzy mess, does that mean that 2+2=5?

We bring our beliefs into the field of math. The easy "counting numbers" (1, 2, 3, etc.) show that there is a gap between how math is thought of and how it is used. Using "2+2=4" as a starting point,

mathematicians are looking into the situations where 2+2 doesn't really equal 4, at least not in a neat way. These interpretations can be applied to bigger questions in epistemology, which is the study of how we know what we know.

As a biostatistics Ph.D. student at Harvard, Kareem Carr started a discussion on Twitter called "Does 2+2 ever equal 5?" He wrote on July 30, 2020, "I don't know who needs to hear this, but if someone says 2+2=5, the right answer is 'What are your definitions and axioms?' not a rant about how Western civilization is falling apart."

It was Carr's point on Twitter that counting numbers "are abstractions of real underlying things in the universe," so we should be aware of how those abstractions change the truth when they are used in real life.

In a textbook, arithmetic works well, but in real life, it often gets stuck on questions that don't take into account parts of a whole, approximations, or more useful vectors.

For instance, if you keep adding whole degrees to an angle, you'll reach a 360-degree angle in the end. But an angle of 360 degrees is the same direction as an angle of 0 degrees.

It depends on the situation whether the angle is measured in degrees or in circles. Also, if you drilled a screw five full turns (1,800 degrees) instead of four (1,440 degrees), the screw would still be facing the same way, but it would be deeper in the wood.