In this essay the heuristic method of proofs and refutations, as pre- sented in the book Proofs and refutations by Imre Lakatos, is reviewed and discussed. Some background is given of heuristic methodology in contrast to the deductivist method and then Euler’s polyhedron for- mula is presented. Examples of both local and global mathematical monsters are introduced and handled through the application of the historical progression of Cauchy’s proof of Euler’s polyhedron formula. This leads to show the method of lemma-incorporation as the superior approach. The method is presented in the light of Lakatos’ heuristic philosophy, followed by criticism to his method. It is suggested to use Lakatos’ method as an addition to today’s formal mathematics to increase creativity and expand mathematical theorems further. The conclusion is drawn that Lakatos’ method of proofs and refutations is not prefect, but should utilize the existing criticism to be perfected through its own practice.