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How the “Frontier” Became the Slogan of Uncontrolled AI
Artificial intelligence (AI) has been billed as the next frontier of humanity: the newly available expanse whose exploration …
From Gödel's Lost Letter and P=NP
Transposing
On the arithmetic complexity of the matrix transpose [ KKB ] Michael Kaminski, David Kirkpatrick, and Nader Bshouty are complexity theorists who together and separately...
From Gödel's Lost Letter and P=NP
A Tiebreak Win and the Problem of Draws
Carlsen impressed in fast chess, but what of classical? Cropped from AFP/Getty source (Irish Times) Magnus Carlsen retained his title of World Chess Champion on...
From Gödel's Lost Letter and P=NP
A Thanksgiving Treat
Another proof that there are an infinite number of primes of a special form Cropped from Packard Fellow src Trevor Wooley is a professor of mathematics at the University...
From Gödel's Lost Letter and P=NP
A Mathematical Auction
A real auction that is happening soon. Crop from BestArts auction history source Samuel Baker and James Christie founded the two premier auction houses in the world...
From Gödel's Lost Letter and P=NP
A Dumb Group Theory Question
A question on finite simple groups Cropped from Schock Prize src Michael Aschbacher is a professor of mathematics at Caltech. He was a leading figure in the classification...
From Gödel's Lost Letter and P=NP
Micro Barriers To Diversity
And perhaps how to remove them Cropped from Monash interview src Elizabeth Croft is Dean of Engineering at Monash University in Australia. She was previously at...
From Gödel's Lost Letter and P=NP
The Inscribed Square Problem
A remark on an open problem with an application of the Lebesgue Density Theorem [ Toeplitz ] Otto Toeplitz was a mathematician who made key contributions to functional...
From Gödel's Lost Letter and P=NP
Watching Over the Zeroes
How confident should we be that the Riemann Hypothesis is true? Composite of src1, src2 Andrew Odlyzko and Herman te Riele, in a 1985 paper, refuted a once widely...
From Gödel's Lost Letter and P=NP
Reading Into Atiyah’s Proof
The Todd function method MacTutor biography source John Todd was a British geometer who worked at Cambridge for most of his life. Michael Atiyah took classes from...
From Gödel's Lost Letter and P=NP
Preview of the Atiyah Talk
Why the Riemann hypothesis is hard and some other observations. ICM 2018 “Matchmaking” source Michael Atiyah, as we previously posted, claims to have a proof that...
From Gödel's Lost Letter and P=NP
Abelian Groups, Mostly
Simple probabilistic arguments that apply to monoids too Famous Mathematicians source Niels Abel is of course a famous mathematician from the 19th century. Many...
From Gödel's Lost Letter and P=NP
Limits On Matrix Multiplication
Can 2.3728639 be best? Personal site; note puzzles Josh Alman is a graduate student at a technical school in the Boston area. He is working on matrix multiplication...
From Gödel's Lost Letter and P=NP
Power Circuits
Not anything to do with electrical engineering Alexei Miasnikov, Alexander Ushakov, and Dong Wook Won are the authors of a brilliant paper, “Power Circuits, Exponential...
From Gödel's Lost Letter and P=NP
Winner Of 2018 Knuth Prize Is:
A great choice Cropped from 2016 KTH grant news source Johan Håstad is the winner of the 2018 Donald E. Knuth Prize. We were going to keep you in suspense, but...
From Gödel's Lost Letter and P=NP
Desperately Seeking Integers
A few twists on Turing’s proof of undecidability of predicate calculus Princeton thesis source Alan Turing presaged Stephen Cook’s proof of -completeness of Turing...
From Gödel's Lost Letter and P=NP
A Quest For Simple Hard Statements
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...
From Gödel's Lost Letter and P=NP
Group Theory Is Tough
Some musings on group theory Isaacs honorary conference source Martin Issacs is a group theorist emeritus from the University of Wisconsin, Madison. I just picked...
From Gödel's Lost Letter and P=NP
You Cannot Do That
How hard is it to prove certain theorems? Maruti Ram Murty is a famous number theorist at Queen’s University in Kingston, Canada. He is a prolific author of books...
From Gödel's Lost Letter and P=NP
Hilbert’s Irreducibility Theorem
A pretty neat paper about a pretty neat theorem [ GLL edited ] Mark Villarino, William Gasarch, and Kenneth Regan are terrific writers. Bill is a co-author of a...
From Gödel's Lost Letter and P=NP