More on "Transalgebraic Theories" (a 19th century yoga)? Among the talks at occasion of the Galois Bicentennial, one is about "Transalgebraic Theories". Unfortunately I found only this article describing that fascinating idea as " an extremely powerful 'philosophical' principle that some
mathematicians of the XIXth century seem to be well aware of. In general terms we
would say that analytically unsound manipulations provide correct answers when
they have an underlying transalgebraic background." Do you know more? 
Edit: This text tells a few words more (e.g. "This philosophy can be linked to Kronecker’s ”Judgendtraum” and Hilbert’s twelfth problem, which seems to have remained largely misunderstood.") and refers to a manuscript "Transalgebraic Number Theory". Has someone a copy? 
 A: For the most part "transalgebraic theory" seems an umbrella term for anything that relates (classic, differential, motivic, categorical) Galois theory with periods, trascendence results, special values, regularization...
Here is a compilation of papers which might be of interest.
Yves André


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*Galois theory, motives and transcendental numbers

*Ambiguity theory, old and new

*Idées galoisiennes
Michel Waldschmidt


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*Transcendence of Periods: The State of the Art

*Much more on trascendence on his page.
Alexandru Buium


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*Transcendental numbers as solutions to arithmetic differential equations

*Arithmetic differential equations on GLn, III: Galois groups
Alain Connes


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*Renormalisation et ambiguïté galoisienne
Ricardo Pérez-Marco


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*The "Transalgebraic Number Theory" manuscript still doesn't seem to be avaible online. The author is clearly active (papers on arXiv), so perhaps someone can ask him directly.

*The (only?) relevant online paper was alredy mentioned in the question, Notes on the Riemann Hypothesis.
