Is aerodynamics science still being discovered(like mathematics for example) or everything has already done?
Aerodynamics science is not a standalone discipline and involves many other aspects that are peculiar to it. In particular, only to cite some:
- Fluid mechanics : fluid mechanics research is very extended, starting from experimental, until the numerical one. Related to it we have all the research related to math (Fluid dynamic equations' nature, specific solver algorithms...), physics (fundamental fluid mechanics, wall cycle, turbulence...) and informatic (HPC architecture, computation efficiency...).
- Design: new designs are considered and developed everyday. Remember for example that an airplane is an assembly of different systems that must cooperate (see the attached comic on the optimal plane by different groups). So engineers must find everyday new designs to satisfy this need of integration. One example is the Zeroe airbus concept, where hydrogen system must be suited in the body and innovative aerodynamic concept (like the blended wing body) are considered. Another case is the car racing world where every year there are new concepts (for basics see for example this book by Katz)
- Drag reduction: Drag reduction research is always active (like the study and development of riblets, only to cite one). This can be related to basic fluid mechanics research of course.
These are some examples, but in general, as all the other science, Aerodynamics is always evolving as the disciplines related to it.
Research in aerodynamics has not stopped. Just in the first ten days of 2022, over a thousand papers have been published.