Those fields aren't the issue, and not what he is discussing in the article. The two fields he mentions, bio-chem (the DNA sequencing) and quantum physics (higgs), both require large amounts of funding to progress. Think the large hadrom collider was cheap? Think a DNA sequencing machine is cheap?
Math is only limited by computer power, and our own personal mental computing power. Computer science, similarly. Those two fields are different from the rest of science as we know it today.
It's true that certain aspects of science are very expensive. We're generating a lot of data these days through DNA sequencing, particle collision, and various other expensive scientific measurement techniques.
But there's a lot of work to be done in making sense of that data. It doesn't cost anything to play with data that's already been collected.
The biggest breakthroughs come from people thinking differently.
Obviously experimental physics can be extremely expensive, but coffee-and-chalk theoretical physics positions like (afaik) Higgs' have roughly the same costs as most math or humanities posts. And apparently theoretical physics has huge problems of PhD oversupply.
Does this disprove your implicit point though? The problem is any position which doesn't cost a lot is attracting way too many people for the amount of possible work.
Meanwhile, the expensive parts - i.e. all the applied physics needed to prove or disprove theoretical physics, is not receiving appropriate funding.
Math is only limited by computer power, and our own personal mental computing power. Computer science, similarly. Those two fields are different from the rest of science as we know it today.