It's not easy to imagine dimensions higher than the three that we exist in, but in math, higher dimensions are used all the time. As pointed out in this video from 3Blue1Brown, there are some downsides to the fact that we can't visualize these dimensions. Putting math into geometric form helps us see how different mathematical ideas connect and discover novel ways to solve problems. How can we do that with higher dimensions that we can't imagine? This video presents one idea. Using number lines to represent axes, we can plot a certain point on a shape regardless of how many dimensions its in. From there, 3Blue1Brown explains how this idea can reveal truths about shapes in higher dimensions.

Source: