Mathematical objects

We all use numbers every day of our lives, and most of us fail to appreciate how mysterious they are. What exactly is a number? You can't trip over the number 4, it has no physical properties, so in what sense can it be said to exist? If it's just a symbolic representation, then why are numbers and other mathematical objects so effective in the real world - in solving scientific problems, in helping cicadas to evade predators, and so on?