Irrespective of this:
The issue of how much math is needed for various branches of programming, and the issue of learning via Google searches or other means, are independent concerns. There is of course the correlation that anyone with a math background is more likely to be more systematic about learning to program than to do web searches all the time, but again, these are orthogonal issues.
There are actual people who learned programming without a lot of math background way before Goolge or even Altavista or the internet existed. When I started coding at ten, my math must have been inferior to that of most non-programming graduates of today, yet I could learn stuff just by doing and reading.
Having said that, and my coding benefitting from various areas of mathematics now, there is a lot of value in being able to quickly type in a search query that leads to relevant hits, for any type of UI work, where the IE browser incompatibilities are more of a trial and error than logic. Also, a color name to hex lookup via Google is just a superior alternative to the older method, which was, open the index pages of a book, find the page and go there.