Desperately Seeking Integers
6 August 2018 | 5:25 pm

A few twists on Turing’s proof of undecidability of predicate calculus By permission of Rich Longmore, artist, blog source Alan Turing presaged Stephen Cook’s proof of -completeness of Turing reduced the halting problem for his machines to the decision problem of the first-order predicate calculus, thus showing (alongside Alonzo Church) that the latter is undecidable. […]

A Quest For Simple Hard Statements
28 July 2018 | 10:42 pm

Made-to-order statements that are not so simple Harvey Friedman is a long-standing friend who is a world expert on proofs and the power of various logics. This part of mathematics is tightly connected to complexity theory. This first mention of his work on this blog was a problem about the rationals that says nothing of […]

Group Theory Is Tough
18 July 2018 | 9:01 pm

Some musings on group theory Isaacs honorary conference source Martin Isaacs is a group theorist emeritus from the University of Wisconsin, Madison. I just picked up a copy of his 2008 book, Finite Group Theory. Simple title; great book. Today I want to make a few short comments about group theory. I always hated group […]

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