> Calculus was created by a physicist who didn't even bother it since he just published the resulting physics
Calculus was discovered by a number of people. I'm assuming you're thinking of Newton, who was a professor of mathematics and whose advisor was a mathematician. Remember the fundamental theorem of calculus had been proven by mathematicians Gregory and Barrow (Newton's advisor) before Newton, not to mention the work of people like Fibonacci. Calculus as we know it today was mainly developed by the mathematician Leibniz independently of Newton.
> Fourier analysis was created by a physicist etc
Joseph Fourier was a mathematician whose advisor was mathematician Joseph-Louis Lagrange whom he succeeded at ENS.
> Mathematicians first and foremost formalizes things after they were created, they don't create many useful tools to begin with. Very few fundamental tools were made first by mathematicians.
This is wildly wrong and contrary to history.
> They often call physicists/polymaths mathematicians after it happened since they published a lot of math
The people I'm calling mathematicians, like Newton and Fourier, are people who trained in mathematics and had mathematical advisors. What other definition do you want of a mathematician other than one who does math, studied math, is employed to do and teach math, and whose advisor was a mathematician?
For example, while Wikipedia calls Fourier a mathematician and physicist, Britannica just calls him a mathematician. Britannica does mention that he was also an Egyptologist but never calls him a physicist.
> generalized functions where done by physicists
Distributions have been used by mathematicians since the 19th century. I'm aware of no examples of physicists claiming priority. Physicists do often use them incorrectly, for example a lot of physicists view the Dirac delta "function" as a function despite the fact that no functions have those properties. They sometimes confuse that, as you seem to do, with thinking that mathematicians don't understand what generalized functions are about.
Calculus was discovered by a number of people. I'm assuming you're thinking of Newton, who was a professor of mathematics and whose advisor was a mathematician. Remember the fundamental theorem of calculus had been proven by mathematicians Gregory and Barrow (Newton's advisor) before Newton, not to mention the work of people like Fibonacci. Calculus as we know it today was mainly developed by the mathematician Leibniz independently of Newton.
> Fourier analysis was created by a physicist etc
Joseph Fourier was a mathematician whose advisor was mathematician Joseph-Louis Lagrange whom he succeeded at ENS.
> Mathematicians first and foremost formalizes things after they were created, they don't create many useful tools to begin with. Very few fundamental tools were made first by mathematicians.
This is wildly wrong and contrary to history.
> They often call physicists/polymaths mathematicians after it happened since they published a lot of math
The people I'm calling mathematicians, like Newton and Fourier, are people who trained in mathematics and had mathematical advisors. What other definition do you want of a mathematician other than one who does math, studied math, is employed to do and teach math, and whose advisor was a mathematician?
For example, while Wikipedia calls Fourier a mathematician and physicist, Britannica just calls him a mathematician. Britannica does mention that he was also an Egyptologist but never calls him a physicist.
> generalized functions where done by physicists
Distributions have been used by mathematicians since the 19th century. I'm aware of no examples of physicists claiming priority. Physicists do often use them incorrectly, for example a lot of physicists view the Dirac delta "function" as a function despite the fact that no functions have those properties. They sometimes confuse that, as you seem to do, with thinking that mathematicians don't understand what generalized functions are about.