So I have a history/philosophy of science class, and the professor explained that for the ancient Greeks, one one hand what was beyond the moon was considered philosophically as the domain of gods, and thus the precise and true science of mathematics was applicable (the use of maths to describe the orbits of planets); and on the other hand, it was viewed as inappropriate and of poor taste to apply maths to more down to earth science, such as medicine, biology, chemistry... And still according to my professor, it wasn't until the 17th century and Copernic that the status quo changed and that applied maths developed to what they are today.
I truly find hard to believe the idea that maths was seen as unscientific when applied to chemistry or physics before. So how true is it? (I couldn't really find helpful information on Google) Thanks in advance for the answers
Ps: sorry for potentially awful formatting, I'm on mobile, and sorry for potentially awful English, I'm not a native speaker.
Maths was certainly applied to engineering in the ancient world (including by the Greeks). For example, numerical methods for calculating cube roots were developed for designing military catapults (see Hart, V. G. “A Greek Cube-Root Device.” The Mathematical Gazette, vol. 66, no. 438, 1982, pp. 294–296).
Maths was also applied to physics (other than astronomy). For example, optics made much use of geometry (and still does today). Outside optics, most physics only made simple use of mathematics (ratios and proportional relationships), and much physics - including much of mechanics - was qualitative rather than quantitative. For example, the newtonianisation (i.e., the switch from qualitative explanation to mathematical modelling in the modern sense) of electricity and magnetism only dates to the mid 18th century (Franz Aepinus, Tentamen Theoriae Electricitatis et Magnetismi; the translation in R. W. Home, Aepinus's Essay on the Theory of Electricity and Magnetism, Princeton University Press, 2015, includes a long introductory monograph on this process of newtonianisation).
The other sciences were even less quantitative, often remaining focussed on taxonomy and classification even into modern times (thus Rutherford's quote "All science is either physics or stamp collecting", shortly before his Nobel Prize in stamp collecting (i.e., chemistry)). The lack of mathematics in biology and chemistry was not due to it being "poor taste to apply maths to more down to earth science", but due to those sciences not yet being in the position where mathematical modelling was seen as useful.
Ignoring simple mathematics (ratios and proportions), and calling astronomy a branch of mathematics rather than a science, ignoring engineering and technological applications as "non-science", and economics, and surveying as more non-sciences, and ignoring optics, your history teacher might be correct.