I'm sympathetic to mathematics but also to that view. I explain the apparent contradiction as follows: We have powerful computers nowadays yet many tasks that organic brains perform, such as interpreting what is in a picture, remain unsolved. When you discuss solving such a problem with people who understand the technicalities, you encounter several different attitudes.
One outlook is "All we need is a Manhattan Project". According to this theory, the essential mathematics of how a computer can understand a picture is already known. It is merely a matter of implementing thousands and thousands of details. This will take many computer programmers and technicians, but it is essentially problem of gathering up sufficient resources.
Another outlook is "The problem is already solved". These people will hand you a book on Statistical Pattern Recognition or tell you about Neural Nets and other techniques. But if you take them seriously, you will start to have disturbing doubts. You will wonder: "What's wrong with neural nets?". This happens because you find article after article about Neural Nets., which report success after success in applying them. You sense that if the average undergraduate wanted to do his term project on Neural Nets, that would be a pretty safe bet. He could probably get a Neural Net to recognize something about a set of photos. Yet the solution to a general purpose program to interpret images never appears. Why is this? Is there some secret defect in Neural Nets? Is it a conspiracy by the big oil companies to thwart such a project?
Another outlook (which is the one that I take) is that the problem can only be solved by discovering some yet unknown mathematics. This is the attitude of the treasure hunter. It is the outlook of people who expect to find a rare coin buried in their backyard or discover a rare stamp in their grandmother's attic etc. It is an unlikely possibility, but it is the most fun to imagine.