From the reviews: "This is a book on the history and philosophy of mathematics interpreted as a sequence of linguistic innovations. ... Kvasz has succeeded in producing a book which synthesizes over a quarter of century of his contributions to a linguistic approach to the history and philosophy of mathematics. The book should prove of interest not only to mathematicians. It suggests new directions for the analysis of changes ... resulting from cultural encounters. ... The book also has explicit references ... to obstacles in mathematics education." (U. D'Ambrosio, Mathematical Reviews, Issue 2009 k) "In this book the author expounds his 'linguistic approach' for reconstructing the development of mathematical disciplines from a philosophical and historical point of view. ... Kvasz' approach provides an interesting tool for philosophers and historians which should be further discussed and applied." (Hans Fischer, Zentralblatt MATH, Vol. 1153, 2009)

• Preface.- Introduction.- Re-codings as the first pattern of change in mathematics.- Historical description of re-codings.- Philosophical reflections on re-codings.- Relativizations as the second pattern of change in mathematics.- A Historical description of relativizations in synthetic geometry.- Historical description of relativizations in algebra.- Philosophical reflections on relativizations.- Re-formulations as a third pattern of change in mathematics.- Re-formulations and concept-formation.- Re-formulations and problem-solving.- Re-formulations and theory-building.- Mathematics and change.- The question of revolutions in mathematics (Kuhn).- The question of mathematical research programs (Lakatos).- The question of stages of cognitive development (Piaget).- Notes.- Bibliography.

From the reviews: "This is a book on the history and philosophy of mathematics interpreted as a sequence of linguistic innovations. ... Kvasz has succeeded in producing a book which synthesizes over a quarter of century of his contributions to a linguistic approach to the history and philosophy of mathematics. The book should prove of interest not only to mathematicians. It suggests new directions for the analysis of changes ... resulting from cultural encounters. ... The book also has explicit references ... to obstacles in mathematics education." (U. D'Ambrosio, Mathematical Reviews, Issue 2009 k) "In this book the author expounds his 'linguistic approach' for reconstructing the development of mathematical disciplines from a philosophical and historical point of view. ... Kvasz' approach provides an interesting tool for philosophers and historians which should be further discussed and applied." (Hans Fischer, Zentralblatt MATH, Vol. 1153, 2009)

• Preface.- Introduction.- Re-codings as the first pattern of change in mathematics.- Historical description of re-codings.- Philosophical reflections on re-codings.- Relativizations as the second pattern of change in mathematics.- A Historical description of relativizations in synthetic geometry.- Historical description of relativizations in algebra.- Philosophical reflections on relativizations.- Re-formulations as a third pattern of change in mathematics.- Re-formulations and concept-formation.- Re-formulations and problem-solving.- Re-formulations and theory-building.- Mathematics and change.- The question of revolutions in mathematics (Kuhn).- The question of mathematical research programs (Lakatos).- The question of stages of cognitive development (Piaget).- Notes.- Bibliography.

From the reviews: "This is a book on the history and philosophy of mathematics interpreted as a sequence of linguistic innovations. ... Kvasz has succeeded in producing a book which synthesizes over a quarter of century of his contributions to a linguistic approach to the history and philosophy of mathematics. The book should prove of interest not only to mathematicians. It suggests new directions for the analysis of changes ... resulting from cultural encounters. ... The book also has explicit references ... to obstacles in mathematics education." (U. D'Ambrosio, Mathematical Reviews, Issue 2009 k) "In this book the author expounds his 'linguistic approach' for reconstructing the development of mathematical disciplines from a philosophical and historical point of view. ... Kvasz' approach provides an interesting tool for philosophers and historians which should be further discussed and applied." (Hans Fischer, Zentralblatt MATH, Vol. 1153, 2009)

• Preface.- Introduction.- Re-codings as the first pattern of change in mathematics.- Historical description of re-codings.- Philosophical reflections on re-codings.- Relativizations as the second pattern of change in mathematics.- A Historical description of relativizations in synthetic geometry.- Historical description of relativizations in algebra.- Philosophical reflections on relativizations.- Re-formulations as a third pattern of change in mathematics.- Re-formulations and concept-formation.- Re-formulations and problem-solving.- Re-formulations and theory-building.- Mathematics and change.- The question of revolutions in mathematics (Kuhn).- The question of mathematical research programs (Lakatos).- The question of stages of cognitive development (Piaget).- Notes.- Bibliography.