Martin Gardner |

In an article published in

**magazine in 1985, Martin Gardner wrote this:***Discover*

*As it happens, the thousandth decimal of pi is 9... The question: Was [this assertion] true before the 1949 calculation? To those of the realist school, the sentence expresses a timeless truth whether anyone knows it or not... [Others] prefer to think of mathematical objects as having no reality independent of the human mind.*
This problem is quite old, as we have been
discussing it for over two thousand years. The question about whether
mathematical objects really exist or are a pure creation of our mind is a
particular case of another problem, much more general, that debates whether
ideas and concepts (like the

**) really exist, or just***dog species***and***this dog***exist. This is***that dog***, famous in the Middle Ages, which has not yet been solved to everyone’s satisfaction. In fact, at present, this debate is more virulent than ever.***the problem of universals*