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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
An Old But Cool Result
Solving a type of Fermat Equation Leo Moser was a mathematician who worked on a very varied set of problems. He for example raised a question about “worms,” and...
From Gödel's Lost Letter and P=NP
Primes And Polynomials
A result on the prime divisors of polynomial values Cropped from source Issai Schur was a mathematician who obtained his doctorate over a hundred years ago. He...
From Gödel's Lost Letter and P=NP
A Simple Fact
Can we find a simplest proof? Composite crop from src1, src2 Joseph Wedderburn and Leonard Dickson proved Wedderburn’s “Little” Theorem: that every finite ring...
From Gödel's Lost Letter and P=NP
Jean Bourgain 1954–2018 and Michael Atiyah 1929–2019
A tribute to two premier analysts From Flanders Today src1 and Ryle Trust Lecture src2 Baron Jean Bourgain and Sir Michael Atiyah passed away within the past three...
From Gödel's Lost Letter and P=NP
Predictions For 2019
The problem of predicting ‘when’ not just ‘what’ Cropped from Toronto Star source Isaac Asimov was a prolific writer of science fiction and nonfiction. Thirty-five...
From Gödel's Lost Letter and P=NP
ACM Great Results
A Puck-ish take on promised technological advances Wikimedia Commons source Knecht Ruprecht accompanies Santa Claus in Germany. He brings gifts to good children...
From Gödel's Lost Letter and P=NP
Explanations and Explorations
Comparing proofs for the Jaccard metric BetterExplained source Kalid Azad is the founder of the website Better Explained. It is devoted to explaining mathematical...
From Gödel's Lost Letter and P=NP
Explaining The Jaccard Metric
Why is it a metric? Composite of source 1, source 2 Paul Jaccard was a botanist who worked at ETH in Zurich during much of the first half of the 20th century. He...
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