The role of mathematics in the exploration of reality

In his well?known paper from 1954, Herbert A. Simon sets out to demonstrate that it is possible, in principle, to make public predictions within the social sciences that will be confirmed by the events. However, Simon's proof by means of the Brouwer fixed?point theorem not only rests on an illegitimate use of continuous variables, it is also founded on the questionable assumption that facts ? even on the level of possibilities ? can be established by purely mathematical means. The ?proof? also appears redundant since we already know from past experience that, for instance, the confirmation of a public election prediction is possible