If they don't exist, how is it that physicists can apply theorems about these non existent things in geometry to physical space and get consistent, even when unexpected, results? Why does trigonometry from ancient days long before physics, give consistent results even today? Why can Einstein work out the math of general relativity even a century before verification? Why does reality agree with ideas in our head, instead of disagreeing?

And if they do exist, they are not made of matter, energy or information, so how can they exist