This is the crux of the issue right here. I would argue that the huge breakthrough in modern science came about the time of Galileo, where science started to depend more on experiment and observation than on natural philosophy. From that point forward, "math science" and "experimental science" worked hand in hand, and accomplished far more than either could alone. Tycho handed data to Kepler who found ellipses in it, and handed it to Newton who explained them, who handed the means to make an observational prediction to Halley, and so forth. Faraday handed experiments to Maxwell who handed a theory to Michelson-Morely who handed the data to Einstein, and on it goes. I see the new issue as being whether or not they should turn their back on all that success and go back to the realm of natural philosophy where theory and controlled experiment were highly uncoupled and even in competition (as in the ancient debates between Greek schools of natural philosophy). What an awful step backward for science, in the name of advancing it!
Well, they do the math with the intention of supporting those who do the experiments, it is not necessary that they carry out the observations themselves to be counted as scientists.