Is there any consensus among mathematicians (or rather philosophers of mathematics) on the concept of a number - what is really a number? This question has quite bothered me recently. Do we left the concept of a number undefined and take it as an intuitive one with no need of definition? Leopold Kronecker wrote "God made the integers; all else is the work of man." (http://en.wikipedia.org/wiki/Kronecker" about Kronecker at Wikipedia). Is this idea prevalent? Are there any recent books that deal with the concept of a number in modern mathematics?