Mathematicians don’t do experiments in a way that biologists, chemists or physicists do in the lab.
Though we do thought experiments in our heads, which we really enjoy, or on a computer.
The latter can also lead to beautiful mathematics, such as fractals, which are the results of numerical
experiments done on a computer some decades ago. An other similar example is chaotic dynamics, like the Lorenz attractor, first studied by a meteorologist in the 60’s again on the computer, solving a simplified mathematical model of air convection in the earth’s atmosphere. It is really fascinating, you can have a look here: http://paulbourke.net/fractals/lorenz/