They would be replaced by the incompetent who want to shine in the new limelight. That happened in Germany after the Machtergreifung. The new government got rid of the unwanted in science and mathematics and many others quit in protest. The gaps were quickly filled by science backbenchers and cranks who would get rid of all the theories they didn't understand (e.g. parts of number theory) and replaced them by what they called Aryan mathematics and Aryan this or that, towing the line of the people who got them into their new position.