honestly, the very title speaks to the problem.
Mathematics is based on boolean logic, if it aint right, it's wrong. Then they start with assumptions and start trying to see what conclusions can be had with the requirement that all such conclusions be self-consistent (meaning, no conclusion can disagree with another conclusion, ever).
Which is really useful, but the issue is that the real world isn't always that black and white. To be successful is often about being 'less wrong' than the other guy, but less wrong isn't something that mathematics understands. There are systems put in place to try and quantify such things, in particular bayesian probability and multi-valued logic systems ('fuzzy logic' is one such example).
And they're extremely useful, fuzzy logic in particular is really fun to think about imo, but at the end of the day, mathematics is a philosophy with a requirement to be self-consistent, not to be in any way useful or applicable to the world as we know it (PI cannot exist in our physical reality, only an approximation of it, for example).
I haven't read the book, so I cannot really talk to the contents, but I take issue with the idea represented by the title. It isn't about mathematical thinking, and it sure as hell isn't about 'not being wrong'. In the real world, it's about being effective, and that means being better than the other guy. Mathematics in general is about perfection and purity.