benefits of an historical point of view were explained very convincingly
by Miguel de Guzmán, President of the International Commission on
Mathematical Instruction, in his talk at the 7th International Congress
on Mathematics Education1:
``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
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.''
de Guzmán, Origin and Evolution of Mathematical Theories: Implications
for Mathematical Education, Newsletter of the International Study Group
on the History and Pedagogy of Mathematics, 8, March 1993, 2-3.
File translated from TEX by TTH,
On 26 Sep 1999, 20:43.
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Teaching with Original Historical
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