If you don't use mathematical reasoning, then you'll produce O(n^3) when you could have produced O(n). Any hack can throw together a script that will hobble along with 4 rows of data. Throw a million rows at the same script and it might terminate properly in a few years. Or maybe it just runs out of memory half way through.
Another problem is winding inefficient boolean branching. If you don't understand boolean algebra, you either over specify cases which makes code cluttered and disorganized, or you under specify and some cases are not considered at all... The result in either case is always buggy code that crashes. It becomes like a virus. Other lesser programmers are afraid to fix it, because it's so complicated. Instead, they just tweak the mess to accomplish their own goals, adding more bad boolean logic along the way. It infects everything it touches.
Finally, certain fields of programming, like machine learning, are almost entirely math and statistics. So, yeah, you don't need math to (poorly) do programming (in certain fields).