may have previously remained "hidden" or may have been misidentified. Now it is made explicit, and built into the primitive conjecture as a condition. The theorem - the improved conjecture - supersedes the primitive conjecture with the new proof-generated concept as its paramount new feature. He goes on and gives further stages that might sometimes take place: Proofs of other theorems are examined to see if the newly found lemma or the new proof-generated concept occurs in them: this concept may be found lying at cross-roads of different proofs, and thus emerge as of basic importance. The hitherto accepted consequences of the original and now refuted conjecture are checked. Counterexamples are turned into new examples - new fields of inquiry open up. Publication history The 1976 book has been translated into more than 15 languages worldwide, including Chinese, Korean, Serbo-Croat and Turkish, and went into its second Chinese edition in 2007. Impact on teaching A number of mathematics teachers have implemented Lakatos' method of proofs and refutations in the classroom, when teaching other mathematical topics. The method has been applied to the analysis and presentation of problem solving in mechanics by high school to college level students. The Mathematical Association of America has included this book on a list of books that they consider to be "essential for undergraduate mathematics libraries". Notes References & . John Worrall & Elie Zahar were the editors of this posthumous book. Gábor Kutrovátz, Imre Lakatos’s Philosophy of Mathematics, Eötvös Loránd University, 2005. 1976 non-fiction books Science studies Philosophy of science literature Mathematics books Dialogues