I don't know what you folks are talking about on this thread branch (what with "efficient markets") but Keynesian Economics is the "theory" that suffers from this "illusion of accuracy".

I don't believe in efficient anything, but I know Free Markets Theory involves no Math (only deductive methods like Praxeology).

That's actually not a good sign. Math is refined thinking. If your theory doesn't involve math, it's probably little more than handwaving and could be significantly improved by being formalized a little more.

There is always the risk that people confuse the map with the territory, but it's present regardless of whether you have a differential equation handy for everything or you're just sharing campfire stories.

> Math is refined thinking.

No, Mr. Poet. Math is an abstract science that can be applied to concrete fields. So far no one has been able to meaningfully apply mathematics to economics, or we would have computers that can simulate markets like we can simulate tornadoes.

That only proves those problems are incredibly hard - and require incredible resources and work to think about in a formal, precise way. It's also worth noting that you are therefore no more likely to be a good economist by guessing and waving hands than you're likely to be a good meteorologist by spinning make-believe stories about which way the weather should be. Failure to understand the meaning of this point is a source of tremendous amount of stupid decisions and pointless politics.

Also, don't confuse logic with math. The former is just a subset.