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Formal Proof Systems Reveal Overlooked Ambiguities in Advanced Mathematics
The article argues that modern mathematical literature contains subtle but significant gaps—ranging from reliance on non-canonical...
Canonical Isomorphisms In More Advanced Mathematics
The article examines why many “canonical” isomorphisms in advanced mathematics—especially in the Langlands program, class field th...
Reexamining Canonical Isomorphisms in Modern Algebraic Geometry
The article examines how mathematicians casually label maps as “canonical,” why this obscures the constructive content of theorems...
Universal Properties In Algebraic Geometry
Universal properties beautifully describe localisations in theory, but in practice they can’t carry the full weight of algebraic g...
The Problem With Grothendieck’s Use Of Equality
The article examines how Grothendieck’s casual identification of canonically isomorphic objects with true equalities—especially in...
Category Theory Explains a Common Oversight in Everyday Mathematics, Study Finds...
Mathematicians routinely treat different product constructions—like (𝐴×𝐵) × 𝐶(A×B)×C and 𝐴× (𝐵×𝐶)A×(B×C)—as identical, even th...
Inside the Logic of “Products” and Equality in Set Theory
The article explores how universal properties uniquely characterize mathematical objects, explains why different constructions can...
Why Mathematicians Still Struggle to Define Equality in the Computer Age
The article unpacks why the everyday mathematical idea of equality is far more subtle than it appears, showing how attempts to for...
Grothendieck, Equality, and the Trouble with Formalising Mathematical Arguments
The article examines how mathematicians freely identify objects “up to unique isomorphism,” why this practice collapses in formal...
