Giuseppe Longo

Longo earned his Italian doctorate in mathematics from the University of Pisa in 1971, with a thesis titled, "Complessità di calcolo delle funzioni ricorsive". He then pursued a three-year doctoral scholarship (perfezionamento) in "Logica e calcolabilità".

Following his university education in Pisa, Longo began his academic career as an assistant professor in 1973 in Applied Mathematics, then associate professor of Mathematical Logic in 1981 and a professor of Computer Science at the University of Pisa in 1987. He held four one-year appointments as young researcher at U. C. Berkeley in 1980 and M.I.T. in 1981, then as Invited Professor at Carnegie Mellon University in 1987 and Ecole Normale Supérieure in 1989.. From 2013 to 2019, he served as an adjunct professor in the School of Medicine at Tufts University in Boston, USA and as fellow, in 2014, at Institut d'Etudes Avancées, Nantes, France.{{Cite web|url=https://www.iea-nantes.fr/en/chercheurs/longo-giuseppe_275|title=Giuseppe LONGO – Fellows – Nantes Institute for Advanced Study Foundation|website=www.iea-nantes.fr}}

Longo held the position of Research Director at Centre National de la recherche scientifique (CNRS) from 1990 to 2012 and has been serving as a Research Director Emeritus since 2012, always affiliated at ENS, Paris.

During his early research career, Longo focused on analyzing the syntactic and semantic properties of fundamental functional programming languages including Lambda Calculus and Combinatory Logic. He integrated his research findings into a broader framework that explored the connections between diverse mathematical theories like recursion theory, type theory, category theory, and denotational semantics, and their practical implementation in functional languages.{{cite journal|url=https://www.di.ens.fr/users/longo/files/PhilosophyAndCognition/church-notes.pdf|first=Giuseppe |last=Longo|title= The Lambda-Calculus: connections to higher type Recursion Theory, Proof-Theory, Category Theory|journal=Annals of Pure and Applied Logic|date=1988}}{{psc|date=November 2024}}

He then took an interdisciplinary approach to explore the role of physics in biology to comprehend extended criticality,{{Cite journal|title=The Inert vs. the Living State of Matter: Extended Criticality, Time Geometry, Anti-Entropy – An Overview|first1=Giuseppe|last1=Longo|first2=Maël|last2=Montévil|date=June 1, 2012|journal=Frontiers in Physiology|volume=3|page=39 |doi=10.3389/fphys.2012.00039 |doi-access=free |pmid=22375127 |pmc=3286818}}{{psc|date=November 2024}} anti-entropy,{{cite journal |last1=Bailly |first1=Francis |last2=Longo |first2=Giuseppe |title=Biological Organization and Anti-Entropy |journal=Journal of Biological Systems |date=March 2009 |volume=17 |issue=1 |pages=63–96 |doi=10.1142/S0218339009002715 |url=https://ens.hal.science/hal-03319785/file/2021_08_13_anti-entropy.pdf }}{{psc|date=November 2024}} and biological time.{{cite book |doi=10.1007/978-3-642-35938-5_4 |chapter=Protention and Retention in Biological Systems |title=Perspectives on Organisms |series=Lecture Notes in Morphogenesis |date=2014 |last1=Longo |first1=Giuseppe |last2=Montévil |first2=Maël |pages=99–119 |isbn=978-3-642-35937-8 }}{{psc|date=November 2024}} Later, his research was directed toward the epistemology of theoretical biology, and Interfaces of Physics, Biology, and Computing.{{cite book |doi=10.1007/978-3-319-30526-4_38 |chapter=Comparing Symmetries in Models and Simulations |title=Springer Handbook of Model-Based Science |date=2017 |last1=Longo |first1=Giuseppe |last2=Montévil |first2=Maël |pages=843–856 |isbn=978-3-319-30525-7 }}{{psc|date=November 2024}}

Longo used an interdisciplinary research approach to explore the relationship between several mathematical theories and computer science, particularly by investigating the mathematical semantics of programming languages.{{Cite web|url=https://www.narcis.nl/publication/RecordID/oai:repository.ubn.ru.nl:2066%2F17250|title=Equality of lambda terms in the model T omega (1980) {{pipe}} www.narcis.nl}} His research contributed to constructing a mathematical framework regarding the theory of programming and generated results related to syntax and semantics. In related research he explored the structural properties of the set-theoretical models of lambda-calculus{{Cite journal |title=Lambda-calculus models and extensionality |first1=R. |last1=Hindley |last2=Longo |first2=G. |journal=Zeitschrift für Mathematische Logik und Grundlagen der Mathematik |year=1980 |volume=26 |issue=19–21 |pages=289–310 |doi=10.1002/malq.19800261902 }}{{psc|date=November 2024}} and established new links to Recursion in Higher Types.{{cite web|url=https://repository.ubn.ru.nl/bitstream/handle/2066/17252/13269.pdf|title=Recursion theoretic operators and morphims on numbered sets}}{{cite journal |last1=Giannini |first1=Paola |last2=Longo |first2=Giuseppe |title=Effectively given domains and lambda-calculus models |journal=Information and Control |date=July 1984 |volume=62 |issue=1 |pages=36–63 |doi=10.1016/S0019-9958(84)80009-1 |doi-access=free }}{{psc|date=November 2024}} Collaborating with E. Moggi he characterized hereditary effective operations (HEO) and Kleene-Kreisel countable functionals.{{cite web|url=https://www.di.ens.fr/users/longo/files/FourLettersKreisel.pdf|title=Four letters by Georg Kreisel}}{{cite journal |last1=Longo |first1=G. |last2=Moggi |first2=E. |title=The hereditary partial effective functionals and recursion theory in higher types |journal=Journal of Symbolic Logic |date=December 1984 |volume=49 |issue=4 |pages=1319–1332 |doi=10.2307/2274281 |jstor=2274281 }}{{psc|date=November 2024}} In 1986, with S. Martini, he further analyzed the computability in higher types and proved a completeness theorem for type checking using a model that was created based on the idea of recursion theory.{{cite journal |last1=Longo |first1=G. |last2=Martini |first2=S. |title=Computability in higher types, Pω and the completeness of type assignment |journal=Theoretical Computer Science |date=1986 |volume=46 |pages=197–217 |doi=10.1016/0304-3975(86)90030-7 }}{{psc|date=November 2024}}

Longo's research in the field contributed towards the development of technical tools for polymorphism{{Cite web|url=https://www.researchgate.net/publication/221442802|title=The Finitary Projection Model for Second Order Lambda Calculus and Solutions to Higher Order Domain Equations}} and emphasized the connections between concepts utilized in computer science and mathematical structures derived from generalized recursion, demonstration theory, and category theory.{{cite journal |last1=Longo |first1=Giuseppe |last2=Moggi |first2=Eugenio |title=A category-theoretic characterization of functional completeness |journal=Theoretical Computer Science |date=January 1990 |volume=70 |issue=2 |pages=193–211 |doi=10.1016/0304-3975(90)90122-X }}{{psc|date=November 2024}} Between 1991 and 1993, he researched ad hoc polymorphism and demonstrated the characteristics of "parametricity" of second order systems{{cite journal |last1=Longo |first1=Giuseppe |last2=Milsted |first2=Kathleen |last3=Soloviev |first3=Sergei |title=The genericity theorem and parametricity in the polymorphic λ-calculus |journal=Theoretical Computer Science |date=December 1993 |volume=121 |issue=1–2 |pages=323–349 |doi=10.1016/0304-3975(93)90093-9 |url=https://ens.hal.science/hal-03316293/file/2021_08_10_genericity-theorem.pdf }}{{psc|date=November 2024}} as well as developed extension of classical functional systems.{{cite book |doi=10.1007/BFb0037101 |chapter=A semantics for λ &-early: A calculus with overloading and early binding |title=Typed Lambda Calculi and Applications |series=Lecture Notes in Computer Science |date=1993 |last1=Castagna |first1=Giuseppe |last2=Ghelli |first2=Giorgio |last3=Longo |first3=Giuseppe |volume=664 |pages=107–123 |isbn=978-3-540-56517-8 }}{{psc|date=November 2024}}{{Cite journal|title=A Calculus for Overloaded Functions with Subtyping|first1=G.|last1=Castagna|first2=G.|last2=Ghelli|first3=G.|last3=Longo|date=February 15, 1995|journal=Information and Computation|volume=117|issue=1|pages=115–135|doi=10.1006/inco.1995.1033|doi-access=free}}{{psc|date=November 2024}} In addition, he proposed a novel analysis of the "invariance levels" of proofs through the concept of Prototype Proofs within Type Theory{{cite journal |last1=Longo |first1=Giuseppe |title=Prototype Proofs in Type Theory |journal=MLQ |date=May 2000 |volume=46 |issue=2 |pages=257–266 |doi=10.1002/(SICI)1521-3870(200005)46:2<257::AID-MALQ257>3.0.CO;2-V }}{{psc|date=November 2024}} which was later applied to investigate the concrete incompleteness theorem.{{cite journal |last1=Longo |first1=G. |title=Reflections on Concrete Incompleteness |journal=Philosophia Mathematica |date=October 2011 |volume=19 |issue=3 |pages=255–280 |doi=10.1093/philmat/nkr016 }}{{psc|date=November 2024}}

In 1993, Longo made a thematic change in his research and elaborated the relatability of cognitive phenomena to the foundations of mathematical knowledge. He examined concepts such as mathematical continuity, infinity, computational representations{{cite web|url=https://www.di.ens.fr/users/longo/files/PhilosophyAndCognition/the-continuum.pdf|title=The Mathematical Continuum: From Intuition to Logic* Giuseppe Longo CNRS and Ecole Normale Sup Иerieure 45, rue d'Ulm 75005 Par}}{{cite journal |last1=Longo |first1=G. |title=Mathematical intelligence, infinity and machines: beyond Godelitis |journal=Journal of Consciousness Studies |date=November 1999 |volume=6 |issue=11–12 |pages=191–214 |url=https://www.ingentaconnect.com/content/imp/jcs/1999/00000006/F0020011/997 }} and also investigated the significance of action and movement in shaping the understanding of geometric space.{{cite journal |last1=Longo |first1=Giuseppe |title=Géométrie, mouvement, espace : cognition et mathématiques |journal=Intellectica. Revue de l'Association pour la Recherche Cognitive |date=1997 |volume=25 |issue=2 |pages=195–218 |doi=10.3406/intel.1997.1564 |url=https://ens.hal.science/hal-03318277/file/2021_08_16_cogni-geometrie.pdf }} His work provided insights into the role of order and symmetries in the cognitive foundations of mathematics.{{cite journal |last1=Longo |first1=Giuseppe |last2=Viarouge |first2=Arnaud |title=Mathematical Intuition and the Cognitive Roots of Mathematical Concepts |journal=Topoi |date=April 2010 |volume=29 |issue=1 |pages=15–27 |doi=10.1007/s11245-009-9063-6 }} Furthermore, he explored the relationship between the invention of perspective in painting and its connection to the foundations of geometry and the concept of infinity in mathematics.{{Cite web|url=http://openscience.fr/IMG/pdf/iste_artsci19v3n1_7.pdf|title=Mathematical Infinity "in prospettiva" and Spaces of Possibilities}}

Longo's research in the field served as the initiating point for his project titled, Geometry and Cognition.{{Cite web|url=https://www.di.ens.fr/users/longo/geocogni.html|title=Ecole Normale Supérieure|website=www.di.ens.fr}} He has integrated the mathematical organization of space with the concept of causality in physics and natural science.{{Cite book|url=https://www.jbe-platform.com/content/books/9789027295859-aicr.55.10bai|title=Mind and Causality|first1=Francis|last1=Bailly|first2=Giuseppe|last2=Longo|chapter=9. Space, time and cognition: From the standpoint of mathematics and natural science |date=February 25, 2004|publisher=John Benjamins|pages=149–197|via=www.jbe-platform.com}}{{cite book |doi=10.1007/978-1-4020-6710-5_23 |chapter=Laplace, Turing and the "Imitation Game" Impossible Geometry: Randomness, Determinism and Programs in Turing's Test |title=Parsing the Turing Test |date=2009 |last1=Longo |first1=Giuseppe |pages=377–411 |isbn=978-1-4020-9624-2 }} Together with Bailly, he developed a mathematical theory that focused on understanding the notions of complexity and information within geometric structures and evaluated the geometry associated with different levels of the organization.{{cite web|url=https://www.di.ens.fr/users/longo/files/CIM/obj-epi-complex.pdf|title=Objective and Epistemic Complexity in Biology}} In addition, he initiated a team at LIENS called Complexity and Morphological Information which has been responsible for projects like "Physical singularities and effective computability".{{cite journal |last1=Longo |first1=Giuseppe |title=Incomputability in Physics and Biology |journal=Mathematical Structures in Computer Science |date=October 2012 |volume=22 |issue=5 |pages=880–900 |doi=10.1017/S0960129511000569 }}{{psc|date=November 2024}}

Longo has researched theoretical biology in collaboration with biologists and philosophers of biology. His work includes the exploration of the concept of simplexity, which refers to the initiation of simple processes through complex pathways{{Cite book|contribution-url=https://hal.science/hal-01377260|contribution=L'incompressible complexité du réel et la construction évolutive du simple|first1=Giuseppe|last1=Longo|first2=Maël|last2=Montévil|first3=Arnaud|last3=Pocheville|editor1-last=Berthoz|editor1-first= Alain|editor2-last= Petit|editor2-first= Jean-Luc|title= Complexité-Simplexité|publisher= Collège de France|year= 2014|via=hal.science}}{{psc|date=November 2024}} and the study of association between randomness and the growth of biological organization in ontogenesis and evolution, which originated the notion of anti-entropy, following a 2009 paper with Bailly.{{cite book |doi=10.1007/978-3-642-27654-5_22 |chapter=Randomness Increases Order in Biological Evolution |title=Computation, Physics and Beyond |series=Lecture Notes in Computer Science |date=2012 |last1=Longo |first1=Giuseppe |last2=Montévil |first2=Maël |volume=7160 |pages=289–308 |isbn=978-3-642-27653-8 }} Additionally, he introduced the concepts of differential causality and enablement to understand causality in biology and argued that a significant aspect of biological evolution involves the continuous alteration of the relevant phase space.{{cite journal |last1=Longo |first1=Giuseppe |last2=Montévil |first2=Maël |title=Extended criticality, phase spaces and enablement in biology |journal=Chaos, Solitons & Fractals |date=October 2013 |volume=55 |pages=64–79 |doi=10.1016/j.chaos.2013.03.008 |bibcode=2013CSF....55...64L |url=https://hal.archives-ouvertes.fr/hal-01192911/file/Longo-Montevil_2013_Extended-criticality-Enablement_0%20%281%29.pdf }}{{psc|date=November 2024}} His investigations have led to insights on the default state of cells characterized by proliferation, variation, and motility, as well as the proposal of a framing principle involving non-identical iterations of morphogenetic processes.{{cite journal |last1=Longo |first1=Giuseppe |last2=Montévil |first2=Maël |last3=Sonnenschein |first3=Carlos |last4=Soto |first4=Ana M |title=In search of principles for a Theory of Organisms |journal=Journal of Biosciences |date=December 2015 |volume=40 |issue=5 |pages=955–968 |doi=10.1007/s12038-015-9574-9 |pmid=26648040 |pmc=5505559 }}{{psc|date=November 2024}} In 2017, he further explored the dependence of present and future dynamics of life on history, in comparison with path dependence in physics{{cite journal |last1=Longo |first1=Giuseppe |title=How Future Depends on Past and Rare Events in Systems of Life |journal=Foundations of Science |date=September 2018 |volume=23 |issue=3 |pages=443–474 |doi=10.1007/s10699-017-9535-x }}{{psc|date=November 2024}} as part of a theoretical framework to organize principles for biological thinking and experimenting.{{cite journal |last1=Longo |first1=Giuseppe |title=Information and Causality: Mathematical Reflections on Cancer Biology |journal=Organisms. Journal of Biological Sciences |date=7 July 2018 |volume=2 |pages=83–104 Paginazione |doi=10.13133/2532-5876_3.15 }}{{psc|date=November 2024}} Furthermore, he criticized the current uses of the notion of information in biology, within the framework of exploring the relationship between science and technology.{{cite book |doi=10.1007/978-3-030-44018-3_5 |chapter=Information, Science and Democracy, for an Ethics of Scientific Knowledge |title=Trust |series=Studies in Applied Philosophy, Epistemology and Rational Ethics |date=2020 |last1=Longo |first1=Giuseppe |volume=54 |pages=63–79 |isbn=978-3-030-44017-6 }}{{psc|date=November 2024}}

• 1974 – National Award for young mathematicians, Unione Matematica Italiana
• 1992 – Member, Academia Europaea, the European Academy of Sciences

• Categories, types, and structures (1990) ISBN 978-0262011259
• Mathematics and the Natural Sciences: The Physical Singularity of Life (2011) ISBN 978-1848166936
• Perspectives on Organisms: Biological time, Symmetries and Singularities (2014) ISBN 978-3642359378
• Matematica e senso. Per non divenir macchine (2022) ISBN 978-8857587363
• Le cauchemar de Prométhée. Les sciences et leurs limites (2023) ISBN 978-2130843085

• Barendregt, H. P., & Longo, G. (1980). Equality of lambda terms in the model T omega. JR Hindley; JP Seldin (eds.), To HB Curry: essays on combinatory logic, lambda calculus and formalism, 303–337.
• Longo, G., & Moggi, E. (1990). A category-theoretic characterization of functional completeness. Theoretical Computer Science, 70(2), 193–211.
• Longo, G. (2002, February). On the proofs of some formally unprovable propositions and Prototype Proofs in Type Theory. In Types for Proofs and Programs: International Workshop, TYPES 2000 Durham, UK, December 8–12, 2000 Selected Papers (pp. 160–180). Berlin, Heidelberg: Springer Berlin Heidelberg. (revised: in Philosophia Mathematica, 19(3): 255–280, 2011)
• Bailly, F., & Longo, G. (2007). Randomness and determinism in the interplay between the continuum and the discrete. Mathematical Structures in Computer Science, 17(2), 289–305.
• Bailly, F., Longo, G., & Montevil, M. (2011). A 2-dimensional geometry for biological time. Progress in Biophysics and Molecular Biology, 106(3), 474–484.
• Buiatti, M., Longo, G. (2013 ) Randomness and Multi-level Interactions in Biology. Theory in Biosciences, vol. 132, n. 3:139–158.
• Longo, G. (2018 ) How Future Depends on Past Histories and Rare Events in Systems of Life, Foundations of Science, (DOI), 23 (3):443–474.
• Longo, G. (2019). Interfaces of incompleteness. Systemics of Incompleteness and Quasi-systems, 3–55.
• Longo, G., & Longo, S. (2021). Réinventer le corps et l'espace. in "In difesa dell'umano", 2021

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Category:University of Pisa alumni

Category:Italian mathematicians

Category:1947 births

Category:Living people

Category:Research directors of the French National Centre for Scientific Research