Yes, it’s quite necessary because things can be inaccessible. You really need a good formal grounding, especially in maths. On the other hand, once you have that grounding, many things in various fields like aerodynamics or genetics become accessible.
Yes, I have a master’s degree in physics (4 year course). If you want a job as a scientific researcher, it is nearly always necessary to have a degree in science (or possibly in maths instead). For more general science jobs, you will usually need to have a degree but it doesn’t always need to be in one the the main sciences like chemistry, biology, or physics. For example, one of my best friends from school did geography at university and now she works studying data for the NHS!
I do yes, in theoretical physics. However as Savannah has mentioned it can depend exactly what sort of science you want to do – it’s definitely possible to have a “science-y” job without a science degree, but if you wanted to work specifically in Physics you’d need something closely related otherwise there are a lot of concepts, equations, even language that you wouldn’t know.
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