Francesco dell’Isola (Università di Roma La Sapienza and MEMOCS International Center)

Holm Altenbach (Otto Von Guericke University Magdeburg)

Ugo Andreaus (Università di Roma La Sapienza)

Danilo Capecchi (Università di Roma La Sapienza)

Gianpietro Del Piero (Università di Ferrara and MEMOCS International Center)

Victor A. Eremeyev (South Federal University and South Scientific Center of RasciRostov on Don)

Raffaele Esposito (MEMOCS International Center)

Samuel Forest (Paris-Tech Mines Paris)

Giulio Maier (Accademia dei Lincei and Politecnico di Milano)

Gérard Maugin (Université Pierre et Marie Curie, Paris)

Umberto Perego (Politecnico di Milano)

Giannantonio Sacchi Landriani (istituto Lombardo Accademia di Scienze e Lettere)

Pierre Seppecher (Université de Toulon et du Var)

David Steigmann (University of California at Berkeley)

*Gabrio Piola Works translated in English: a tribute to a great mathematical-physicist who contributed to Italian Risorgimento (Resurgence).*

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* Gabrio Piola scientific papers have been underestimated in the mathematical-physics literature. A careful reading of them proves that his contribution to science has been original, deep and long-ranging. His ingenious spirit was attracted since his first original creations by the Principle of Virtual Velocities (as Lagrange called what has been later called the Principle of Virtual Works).*

*The aim of the whole scientific activity of Gabrio Piola has actually been to demonstrate that Principle can be considered the basis of the Postulation of every Mechanical Theory. Indeed Piola developed by using the Lagrangian Postulation modern continuum mechanics, being the first author who introduced the dual in power of the gradient of velocity in the referential description of a continuous body. The coefficients of this differential form were to be recognized later, after the revolutionary theories introduced by Ricci and Levi-Civita, to identify a double tensor, which has to be named Piola stress tensor. Some of the results presented in Piola’s works (e.g. those concerning continua depending on higher gradients of strain measure) can be regarded even nowadays as the most advanced available in the literature.*

*The mathematics used by Piola is on every aspect modern, except in a very important point. Indeed as Levi-Civita absolute calculus had to be invented many years later, Piola’s presentation proceeds firmly and rigorously but encumbered by a very heavy component-wise notation, which to the eyes of a modern mechanician gives an appearance of primitiveness. The reader should not believe that Piola -were him alive nowadays- would refuse (as some mechanicians still do) to use the powerful tools given to us by Levi-Civita. As proven in the obituary he wrote for honoring his “Maestro” Vincenzo Brunacci, Gabrio Piola knew how important is the choice of the right notation and conceptual tools for the advancement of science and calls ”obscurantists” those who refused the nominalistic and conceptual improvements introduced by Lagrange in Mathematical Analysis.*

*Unfortunately Piola did not had already available the tool he needed to progress more quickly in his research. It is astonishing to discover how much he managed to discover notwithstanding this limit. Piola’s work did not receive the due attention because of a great limit of his works: indeed they are written in Italian. He used a very elegant and erudite style which can be understood and appreciated only by few specialists. A well-founded but yet unproven conjecture about this linguistic choice can be advanced: although Piola was surely fluent in French (he translated into Italian many works by Cauchy) he decided “per la gloria dell’Italia” for the glory of Italy to use his mother language, in an historical climate in which Italian Nation was not independent and able to self-determine its destiny.*

*A patriotic choice which was repaid by a nearly complete neglect of his contribution to mechanical science. For this reason -and for the advancement of science and history of science- the scientific committee of this edition, under the Auspices of the Accademia dei Lincei and the Istituto Lombardo, decided to endorse the scientific effort of translating Piola’s works in English. Of course the commentaries to the translated documents will be published under the scientific responsibility of the authors being indeed intended that all members of the scientific committee consider Piola as one of the most eminent mathematical phycisists of XIX century.*

*Francesco dell’Isola & Ugo Andreaus*