Formal Proof Systems Reveal Overlooked Ambiguities in Advanced Mathematics

Formalisation is uncovering subtle gaps in modern mathematical proofs, from implicit conventions to non-canonical constructions that demand new rigor. #mathematicallogic

Canonical Isomorphisms In More Advanced Mathematics

Canonical isomorphisms in advanced math aren’t as canonical as they seem. This article explores sign choices, Langlands theory, and why formalism falls short. #mathematicallogic

Reexamining Canonical Isomorphisms in Modern Algebraic Geometry

A critical look at how mathematicians use the word “canonical,” revealing how informal shortcuts obscure the real constructions behind key theorems. #mathematicallogic

Universal Properties In Algebraic Geometry

Universal properties promise abstraction, but localisation shows where they fail—especially in formal proofs. Learn why algebraic geometry needs concrete models #mathematicallogic

The Problem With Grothendieck’s Use Of Equality

Grothendieck’s “canonical” equalities work on paper but clash with formal proof systems like Lean, exposing a subtle gap in algebraic geometry’s foundations. #mathematicallogic

Category Theory Explains a Common Oversight in Everyday Mathematics, Study Finds

Why common product notation hides deep structural issues in set theory, and how category theory resolves ambiguities mathematicians often overlook. #mathematicallogic

Inside the Logic of “Products” and Equality in Set Theory

A clear, accessible explanation of universal properties, equality, and why mathematicians treat many different constructions as “the same” object. #mathematicallogic

Why Mathematicians Still Struggle to Define Equality in the Computer Age

A mathematician explores why equality in mathematics resists formal definition, and how computer theorem provers expose gaps in our foundational intuition. #mathematicallogic

Grothendieck, Equality, and the Trouble with Formalising Mathematical Arguments

How mathematicians use equality conflicts with formal proof systems. This article explores why canonical isomorphisms break down in computer-checked maths. #mathematicallogic

‘Reverse Mathematics’ Illuminates Why Hard Problems Are Hard When it comes to hard problems, computer scientists seem to be stuck. Consider, for example, the notorious problem of finding the shortest round-trip route that passes through every city on a map exactly...

‘Reverse Mathematics’ Illuminates Why Hard Problems Are Hard #Science #Mathematics hashtag 1: #ReverseMathematics 2: #HardProblems 3: #MathematicalLogic

Unravelling Cyclic First-Order Arithmetic
Dominik Wehr, Graham E. Leigh
Paper
Details
#CyclicFOA #LogicAndComputability #MathematicalLogic

The Boolean Compactness Theorem for $\mathrm{L}_{\infty\infty}$
Juan M Santiago Suárez, Matteo Viale
Paper
Details
#BooleanCompactnessTheorem #L_inftyinfty #MathematicalLogic

#Wittgenstein’s #Cambridge seminar on the foundations of mathematics included a brilliant young mathematician, #AlanTuring, who was giving his own course that term on the same topic. Turing too had been excited by the promise of #mathematicallogic
time.com/archive/6735...
youtu.be/lVQNSsuvEg8?...

PHOTOSTORY DRY AS DUST / SPECIAL EPISODE the theory of derivation trees #dryasdust #logic #TV #show #math #mathematicallogic #protocephalopod #comic

PHOTOSTORY DRY AS DUST / SPECIAL EPISODE

the theory of derivation trees

#dryasdust #logic #TV #show #math #mathematicallogic #protocephalopod #comic