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This math doesn't work - you're gonna wake up early to have more productive hours, but you'll waste the gain by exercising.

You are right - the amount of time you wake up early may be cancelled out by the amount of time you exercise. Two things to note:

1. The title of the article is "Waking up early", not "how to have more productive hours in the day"

2. I'm personally much more interested in the health benefits gained by exercising so I have no doubt it's worth it.

Presumably, if you exercise then you'll have more days total in which to be productive (that is, you'll live longer)!

Plus, you might find yourself more productive on days when you have exercised. I certainly do.

Working out won't make you healthier. In fact, boosting your metabolism and gaining muscle mass is the sure way to getting cancer sooner.