**Mathematicians tend to hold two simultaneous**and incompatible views of the objects they study.**Prime numbers, for example, have surprising relations**with one another that mathematicians are still discovering.**Such explorations, of what appears to be an alien landscape**, encourage the idea that mathematical objects exist independently of humans.**If mathematical objects are real, however**, why can one not touch, see or otherwise interact with them? Such questions often lead mathematicians to postulate that, in fact, the world of mathematical objects is fictitious.

www.scientificamerican.com/article/is-the-mathematical-world-real