If you failed math, please see the below post on indulgences.  At any rate, this is a review of an interesting looking book about the nature of math–whether it simply exists or it is constructed.   I’d like to think it’s really real, that mathematical structures exist and that the universe has a logic and truth to it that we can discover and know.  I’m not sure that’s true, but I’d like for it to be.  Anyways, the question here:

On one side of the debate are all those remarkable constants that crop up, the makings of the ideal yet hidden world posited by Plato. In addition, there’s what the physicist Eugene Wigner, in a seminal 1960 essay, called the “unreasonable effectiveness” of mathematical theorems: the astounding ability of math to predict unimagined results. Wigner was picking up on ideas explored earlier by Einstein, and Einstein’s general theory of relativity remains one of the best examples: His predictions about how gravity can cause ripples in space-time was recently corroborated by measuring radio waves from a distant set of compact, high-energy stars called double pulsars, using technology unknown in Einstein’s day. Doesn’t all this indicate that the mathematical structure of the world is out there waiting to be discovered?

On the other hand, math cannot explain many situations, and chaos theory suggests that it may never be possible to predict the weather or the stock market with accuracy. Recent research has pointed to basic mathematical constructs in the human brain, suggesting that we impose numbers and forms on the world, not vice versa. In addition, mathematics is less stable than it appears to us in grade school. At the higher reaches of the field, there is constant ferment and debate. If the “truths” discovered through mathematics are always changing, doesn’t that indicate they are a product of human study and manipulation, rather than something fixed and eternal?