Math and the sciences – Santi Aranguri

4. Sometimes people say that science is growing steadily and plateaus. This is True if you look at predictions. For instance, general relativity only improved the predictions from classical mechanics by a little bit [1], and the first heliocentric models barely improved over the geocentric models. But what generates that small improvement in the predictions is new theories. And the theories do not grow steadily. Instead, new theories usually contradict previous ones and can be much more complicated than the former theories. Quantum mechanics, for instance, proposes that we can’t know the position and velocity of a particle at the same time, though we always assumed we could in classical mechanics. 3. Mathematicians and physicists as the developers of the tool and the ones that use the tool. Mathematicians know the tool better, they don’t commit a mistake when they are doing an integral. They know all about the integral and how it works (Lebesgue integration, forms, etc.) The physicist

4. Sometimes people say that science is growing steadily and plateaus. This is True if you look at predictions. For instance, general relativity only improved the predictions from classical mechanics by a little bit [1], and the first heliocentric models barely improved over the geocentric models. But what generates that small improvement in the predictions is new theories. And the theories do not grow steadily. Instead, new theories usually contradict previous ones and can be much more complicated than the former theories. Quantum mechanics, for instance, proposes that we can’t know the posit