If you create new mathematics in order to properly describe a physics phenomena then you are doing science. Similarly if you create a laboratory in order to properly conduct physics experiments to verify your theories you are doing science. How the laboratory was built matters a lot for the experiment, the same as how the math language was built.
Math is a tool, yes, but it is a tool that is very useful to do science in and the act of creating and distributing a tool you use to do science is a large part of science. A shower on the other hand has no direct relationship to science, you don't need to be a physicist to make a shower, it is just a commodity. Calculus however needed to be discovered by a physicist as the math was too strange for mathematicians to find but simple enough that two different physicists found it in parallel.
Math is a tool, yes, but it is a tool that is very useful to do science in and the act of creating and distributing a tool you use to do science is a large part of science. A shower on the other hand has no direct relationship to science, you don't need to be a physicist to make a shower, it is just a commodity. Calculus however needed to be discovered by a physicist as the math was too strange for mathematicians to find but simple enough that two different physicists found it in parallel.