Interview with Luciano Boi. What is topology? Mathematics, science, philosophy and art
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References
BOI, Luciano (1992). "The 'revolution' in the geometrical vision of space in the nineteenth century, and the
hermeneutical epistemology of mathematics”. En D. Gillies (ed.). Revolutions in Mathematics. Óxford:
Clarendon Press, pp. 183-208.
___________ (1994). “Mannigfaltigkeit und Gruppenbegriff. Zur den Veränderungen der Geometrie im 19.
Jahrhundert”. Mathematische Semesterberichte, vol. 41, núm. 1, pp. 1-16.
___________ (1995). Le problème mathématique de l'espace. Une quête de l'intelligible. Preface de René Thom.
Hiedelberg/Berlín : Springer/Verlag.
___________ (2005). Geometries of Nature, Living Systems and Human Cognition. Singapur: World Scientific.
___________ (2006). "The A leph of S pace. O n s ome e xtension of geometrical and topological concepts in the
twentieth-century mathematics: from surfaces and manifolds to knots and links”. En G. Sica (Ed.). What is
Geometry? Milán: Polimetrica Inter. Sci. Publ., pp. 79-152.
___________ (2006). "Mathematical Knot Theory". Encyclopaedia of Mathematical Physics, vol. 3. En J.-P. Françoise,
G. Naber, T. S. Sun (Eds.). Óxford: Elsevier, pp. 399-406.
___________ (2006). "From Riemannian Geometry to Einstein's General Relativity Theory and Beyond: Space-Time
Structures, Geometrization and Unification”. En J.-M. Alimi & A. Füzfa (Eds.). Proceedings Albert Einstein
Century International Conference. Melville: American Institute of Physics, pp. 1066-1075.
___________ (2009). “Ideas of geometrization, geometric invariants of low-dimensional manifolds, and topological
quantum field theories”. International Journal of Geometric Methods in Modern Physics, vol. 6, núm. 5, pp.
701-757.
___________ (2011). Morphologie de l'invisible. Limoges : Presses Universitaires de Limoges.
___________ (2011). The Quantum Vacuum. The Geometry of Microscopic World, from Electrodynamics to Gauge
Theories and String Program. Baltimore: The John Hopkins University Press.
___________ (2011). "When Topology Meets Biology for Life. The Interaction Between Topological Forms and
Biological Functions". En C. Bartocci, L. Boi & C. Sinigaglia (Eds.). New Trends of Geometry. Their Interactions
with the Natural and the Life Sciences. Londres: Imperial College Press, pp. 243-305.
___________ (2012). Pensare l'impossibile: dialogo infinito tra scienza e arte. Milán: Springer/Verlag, Milano.
___________ (2016). "Imagination and Visualization of Gometrical and Topological Forms in Space. On Some
Formal, Philosophical and Pictorial Aspects of Mathematics". En O. Pombo & G. Santos (Eds.). Philosophy of
Science in the 21st Century – Challenges and Tasks, Documenta núm. 9. Lisbon: Editions of CFUL, pp. 28-54.
___________ (2019). "Some mathematical, epistemological and historical reflection on space-time theory and the
geometrization of theoretical physics, from B. Riemann to H. Weyl and beyond". Foundations of Science, vol.
24, núm. 1, pp. 1-38.
__________ (2019). "H. Weyl Deep insights into the mathematical and physical worlds. His important contribution
to the philosophy of space, time and matter". En C. Lobo & B. Julien (Eds.). Weyl and the Problem of Space.
Basel: Springer, pp. 231-263.
*
ALEXANDROFF, P. (1961). Elementary Concepts of Topology. Nueva York: Dover Publications.
CONNES, A. (June 2010). "A View of Mathematics". París : Institut des Hautes Etudes Scientifiques.
___________ (7 novembre 2017). "Un topo sur les topos". Texte de la conférence donnée dans le cadre du
séminaire "Lectures grothendieckiennes". París : Ecole Normale Supérieure.
GROMOV, M. (2000). "Space and Questions". En N. Alon et al. (Eds.). Visions in Mathematics, GAFA, Geom. Funct.
Anal., Special Volume, Part I., pp. 118-161.
HILBERT, D. & COHN-VOSSEN, P. (1999). "Geometry and Imagination”. Americal Mathematical Society [First
German edition, Anschauliche Geometrie, Springer-Verlag, Berlín, 1932].
MANIN, Yu (1981). Mathematics and Physics. Boston: Birkhäuser.
POINCARÉ, H. (1902). La science et l'hypothèse. París : Flammarion.
___________ (1913). "Pourquoi l'espace a trois dimensions?". Dernières pensées. París : Flammarion.
PRASOLOV, V.V. (1995). Intuitive Topology. American Mathematical Society. Providence.
RIEMANN, B. (1990). "On the Hypotheses Which Lie at the Bases of Geometry". Collected Mathematical Works. S.
Chandresekhar (Introduction). Nueva York/Leipzig: Springer/Teubner [Habilitatioschrift,
Göttingen, 1854].
ROLSFEN, D. (1976). Knots and links. Berkely, CA.: Publish or Perish.
THOM, R. (1977). Stabilité structurelle et morphogenèse. París : Inter Editions.
___________ (1980). "Topologie et signification". Modèles mathématiques de la morphogenèse. París : C. Bourgois.
THURSTON, W. P. (1997). Three-Dimensional Geometry and Topology, vol. 1. Princeton: Princeton University
Press.
___________ (1998). "How to see 3-manifolds". Classical and Quantum Gravity, vol. 15, núm. 9, pp. 2545-2571.
WEEKS, J. R. (1985). The Shape of Space. Nueva York: Marcel Dekker.
WEYL, H. (1949). Philosophy of Mathematics and Natural Sciences. Princeton: University Press.
hermeneutical epistemology of mathematics”. En D. Gillies (ed.). Revolutions in Mathematics. Óxford:
Clarendon Press, pp. 183-208.
___________ (1994). “Mannigfaltigkeit und Gruppenbegriff. Zur den Veränderungen der Geometrie im 19.
Jahrhundert”. Mathematische Semesterberichte, vol. 41, núm. 1, pp. 1-16.
___________ (1995). Le problème mathématique de l'espace. Une quête de l'intelligible. Preface de René Thom.
Hiedelberg/Berlín : Springer/Verlag.
___________ (2005). Geometries of Nature, Living Systems and Human Cognition. Singapur: World Scientific.
___________ (2006). "The A leph of S pace. O n s ome e xtension of geometrical and topological concepts in the
twentieth-century mathematics: from surfaces and manifolds to knots and links”. En G. Sica (Ed.). What is
Geometry? Milán: Polimetrica Inter. Sci. Publ., pp. 79-152.
___________ (2006). "Mathematical Knot Theory". Encyclopaedia of Mathematical Physics, vol. 3. En J.-P. Françoise,
G. Naber, T. S. Sun (Eds.). Óxford: Elsevier, pp. 399-406.
___________ (2006). "From Riemannian Geometry to Einstein's General Relativity Theory and Beyond: Space-Time
Structures, Geometrization and Unification”. En J.-M. Alimi & A. Füzfa (Eds.). Proceedings Albert Einstein
Century International Conference. Melville: American Institute of Physics, pp. 1066-1075.
___________ (2009). “Ideas of geometrization, geometric invariants of low-dimensional manifolds, and topological
quantum field theories”. International Journal of Geometric Methods in Modern Physics, vol. 6, núm. 5, pp.
701-757.
___________ (2011). Morphologie de l'invisible. Limoges : Presses Universitaires de Limoges.
___________ (2011). The Quantum Vacuum. The Geometry of Microscopic World, from Electrodynamics to Gauge
Theories and String Program. Baltimore: The John Hopkins University Press.
___________ (2011). "When Topology Meets Biology for Life. The Interaction Between Topological Forms and
Biological Functions". En C. Bartocci, L. Boi & C. Sinigaglia (Eds.). New Trends of Geometry. Their Interactions
with the Natural and the Life Sciences. Londres: Imperial College Press, pp. 243-305.
___________ (2012). Pensare l'impossibile: dialogo infinito tra scienza e arte. Milán: Springer/Verlag, Milano.
___________ (2016). "Imagination and Visualization of Gometrical and Topological Forms in Space. On Some
Formal, Philosophical and Pictorial Aspects of Mathematics". En O. Pombo & G. Santos (Eds.). Philosophy of
Science in the 21st Century – Challenges and Tasks, Documenta núm. 9. Lisbon: Editions of CFUL, pp. 28-54.
___________ (2019). "Some mathematical, epistemological and historical reflection on space-time theory and the
geometrization of theoretical physics, from B. Riemann to H. Weyl and beyond". Foundations of Science, vol.
24, núm. 1, pp. 1-38.
__________ (2019). "H. Weyl Deep insights into the mathematical and physical worlds. His important contribution
to the philosophy of space, time and matter". En C. Lobo & B. Julien (Eds.). Weyl and the Problem of Space.
Basel: Springer, pp. 231-263.
*
ALEXANDROFF, P. (1961). Elementary Concepts of Topology. Nueva York: Dover Publications.
CONNES, A. (June 2010). "A View of Mathematics". París : Institut des Hautes Etudes Scientifiques.
___________ (7 novembre 2017). "Un topo sur les topos". Texte de la conférence donnée dans le cadre du
séminaire "Lectures grothendieckiennes". París : Ecole Normale Supérieure.
GROMOV, M. (2000). "Space and Questions". En N. Alon et al. (Eds.). Visions in Mathematics, GAFA, Geom. Funct.
Anal., Special Volume, Part I., pp. 118-161.
HILBERT, D. & COHN-VOSSEN, P. (1999). "Geometry and Imagination”. Americal Mathematical Society [First
German edition, Anschauliche Geometrie, Springer-Verlag, Berlín, 1932].
MANIN, Yu (1981). Mathematics and Physics. Boston: Birkhäuser.
POINCARÉ, H. (1902). La science et l'hypothèse. París : Flammarion.
___________ (1913). "Pourquoi l'espace a trois dimensions?". Dernières pensées. París : Flammarion.
PRASOLOV, V.V. (1995). Intuitive Topology. American Mathematical Society. Providence.
RIEMANN, B. (1990). "On the Hypotheses Which Lie at the Bases of Geometry". Collected Mathematical Works. S.
Chandresekhar (Introduction). Nueva York/Leipzig: Springer/Teubner [Habilitatioschrift,
Göttingen, 1854].
ROLSFEN, D. (1976). Knots and links. Berkely, CA.: Publish or Perish.
THOM, R. (1977). Stabilité structurelle et morphogenèse. París : Inter Editions.
___________ (1980). "Topologie et signification". Modèles mathématiques de la morphogenèse. París : C. Bourgois.
THURSTON, W. P. (1997). Three-Dimensional Geometry and Topology, vol. 1. Princeton: Princeton University
Press.
___________ (1998). "How to see 3-manifolds". Classical and Quantum Gravity, vol. 15, núm. 9, pp. 2545-2571.
WEEKS, J. R. (1985). The Shape of Space. Nueva York: Marcel Dekker.
WEYL, H. (1949). Philosophy of Mathematics and Natural Sciences. Princeton: University Press.
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Published
2020-05-06
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Romero Contreras, A. (2020). Interview with Luciano Boi. What is topology? Mathematics, science, philosophy and art. Tópicos Del Seminario, 1(43), 213–265. https://doi.org/10.35494/topsem.2020.1.43.666
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