Science and education is based on an assumption/belief, that the physical World ultimately is governed by mathematical laws imposed by the Creator of the World, which scientists can uncover by digging into the machinery of the World. This view is can be decribed as logical empirism, where the assumption is justified a posteriori by a perceived/observed mathematical nature of the World. In postmodern philosophy this is turned around and the mathematical nature is seen instead rather as a construction following from an a priori stipulation that nature has to be mathematical.
The dispute in the late 19th century between Kronecker and Cantor about the foundations and nature of mathematics prepared the big fight between constructivists and formalists in the 1920s leading into todays unfortunate splitting between pure and computational mathematics.
We show that an effect of not understanding mathematics and the nature mathematics, can lead to believe that mathematics is magical with magical power. We give examples of such magical thinking from science including special relativity, quantum mechanics, gravitation and fluid mechanics.
Mathematicians no longer understand mathematicians.
The ferocious academic battle in the 1920s about the foundations of mathematics between the formalists/logicists and the constructivists/intuitionists, ended with a formal victory for the constructivists, which however in practice were defeated by being expelled from the mathematics departments. The battle continues today between pure/analytical and computational mathematicians.
The formulation of the Clay Mathematics Institute millennium problem on the Navier-Stokes equations is questioned and a possible approach towards reformulation and resolution is presented.Mathematics/Science Education