It's not just in mathematics that this is false. Controlled experiments are one of doing science. By the definition of the author of the original article, combing through existing genomic data to identify SNPs possibly associated with disease isn't science. By his definition, identifying comets or asteroids or planetoids by examining collections of astronomical images taken by others isn't science. By his definition, the work of theoretical physicists who do not perform experiments isn't science. By his definition, identification of new anatomical structures by anatomists performing dissections isn't science. When the author gets it so wrong in his opening sentence, I am reluctant to take the remainder of what he says very seriously.