• 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