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If you want to give a mathematician something to try to wrap their head around, a Klein bottle is a good place to start. It is an object with no inside and no outside that can only exist in 4 dimensions. These glass models exist in 3, which means that unlike the real thing, they can actually hold liquid.The difference between the models and the real thing is that by adding an extra dimension, you can make it so that the neck of the bottle doesn’t actually intersect the side of the bottle.

Klein bottle If you want to give a mathematician something to try to wrap their head around, a Klein bottle is a good place to start. A real Klein bottle is an object with no inside and no outside.