``WHAT THE KNOWLEDGE OF THE HISTORY OF MATHEMATICS AND OF THE PARTICULAR SUBJECT CAN OFFER US:

• A human vision of science and of mathematics: not just truths, methods, techniques coming from nowhere, not just facts and skills without soul, without history, but the results of the efforts of persons motivated by deep interest and passion; not as godlike science, but human and so incomplete and fallible; the human side of the great discoveries and discoverers.
• A frame in which all elements appear in their right place: not facts centuries apart in their origin presented together in the same bag without a single remark, but explorations in their own context and with their own motivation; past fashions in order to be able to understand present fashions; the deep connections along time of the different leitmotivs of the mathematical symphony.
• A dynamical vision of the evolution of mathematics: the motivation and driving forces at the roots of the ideas and methods of the subject; the primordial creativity around each particular subject, its genesis and its progress, with all the light it throws upon its true nature; a flavor of adventure and thrill; a creative immersion into the difficulties of the past in order to better understand our own problems; a possibility towards extrapolating towards the future; the realization of the tortuous ways of genuine creativity, in ambiguity, obscurity, twilight, towards the shaping of the first torsos; a guide for a dynamical sense in our educational tasks.
• The intertwining of mathematical thought and culture in human society (mathematics as an important part of human culture); the influence of the history of mankind upon mathematics; the impacts of mathematics upon mankind, its culture, philosophy, technology, arts, ¼ .
• A more profound technical comprehension: the initial simplicity of a theory is a strong help to understand it; technical complications coming later make a theory opaque unless one knows their motivations; the lines of development until the present offer good suggestions toward the future and guide us in our research.
• The peculiar life of each mathematical theory: birth at some specific time by the most diverse motivations (curiosity, applications, expansion, completion, ¼); growth: each theory in its own style, through expectations, false expectations, false starts, ¼; strongly influenced in its particular development by its local atmosphere, social and personal.''

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