This chapter introduces constructive mathematics and intuitionism, the foundational program of L.E.J. Brouwer. Intuitionism views mathematics as a mental activity of construction, independent of language or logic. We contrast this with classical mathematics, whose reliance on logic leads to non-effective existence proofs. Through “weak counterexamples”, based for example on undecided questions regarding the decimal expansion of Pi, we show that classical principles like the law of trichotomy are not constructively valid. This critique sets the stage for the development of constructive and intuitionistic analysis.