Better math and even computation doesn't necessarily help in some cases. Take for instance the problem of making better solar cells and batteries.
We can't necessarily make a mathematical model useful for understanding the processes that happen during the manufacturing and operation of solar cells/batteries. In fact in many cases determining just what processes are happening is a problem in and of itself. We don't necessarily understand how batteries degrade or why adding a certain component or using a certain process makes batteries degrade less. Determining this often can only be done with real world experimentation.
One problem relevant to making organic solar cells is determining how organic constituents crystallize. A talk I saw looked into doing this computationally, but claimed it to be intractable. The problem was that the same compound, but with a different isotopic composition crystallized completely differently. This meant that nuclear motion mattered and that the already computationally expensive crystallization sim being done needed to be made orders of magnitude more computationally expensive to get useful results.
This isn't to say that math isn't useful, it's just that math isn't necessarily as useful when real world experimentation is necessary. That being said, math can still be quite effective in the natural sciences.
We can't necessarily make a mathematical model useful for understanding the processes that happen during the manufacturing and operation of solar cells/batteries. In fact in many cases determining just what processes are happening is a problem in and of itself. We don't necessarily understand how batteries degrade or why adding a certain component or using a certain process makes batteries degrade less. Determining this often can only be done with real world experimentation.
One problem relevant to making organic solar cells is determining how organic constituents crystallize. A talk I saw looked into doing this computationally, but claimed it to be intractable. The problem was that the same compound, but with a different isotopic composition crystallized completely differently. This meant that nuclear motion mattered and that the already computationally expensive crystallization sim being done needed to be made orders of magnitude more computationally expensive to get useful results.
This isn't to say that math isn't useful, it's just that math isn't necessarily as useful when real world experimentation is necessary. That being said, math can still be quite effective in the natural sciences.