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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
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
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
Princeton Is Invariant
Workshop happening this week—anyone can view it live IAS Weyl bio source Hermann Weyl was one of the first members of the Institute for Advanced Study in Princeton...
From Gödel's Lost Letter and P=NP
Almost Fermat Primes
A possible source of interesting primes Study.com source Pierre de Fermat was fluent in six languages. Yes I thought we would talk about Fermat today. Something...
From Gödel's Lost Letter and P=NP
Lost in Complexity
Should we expect simplicity in a theory named for complexity? Amer. Phy. Soc. interview source Sabine Hossenfelder is a physicist at the Frankfurt Institute for...
From Gödel's Lost Letter and P=NP
A New Proof Of An Ancient Result
Triangulating proofs to seek a shorter path Cropped from 2016 Newsday source Mehtaab Sawhney is an undergraduate student at MIT. His work caught my eye on finding...
From Gödel's Lost Letter and P=NP
Finding Coprime Pairs
Deferring or avoiding randomization Great Discoveries in STEM source Claude Bachet de Méziriac was a French mathematician of the early 1600s. He is the first person...
From Gödel's Lost Letter and P=NP
Leprechauns Know What It Feels
To be human, that is Neil L. has graced these pages many times before. Every eve of St. Patrick’s Day he has visited Dick. Sometimes Dick has been hard to find,...
From Gödel's Lost Letter and P=NP
Happy 0x50th Birthday, Donald Knuth
Donald Knuth’s 80th=0x50th birthday was on January 10.
From Gödel's Lost Letter and P=NP
The Lemma Cited From Burnside
How might it be applied in complexity theory? St. Andrews history source William Burnside was a well-known researcher into the early theory of finite groups. Today...
From Gödel's Lost Letter and P=NP
Timing Leaks Everything
Facing the awful truth that computers are physical machines As moderator of RSA 2016 panel Paul Kocher is the lead author on the second of two papers detailing...
From Gödel's Lost Letter and P=NP
P=NP: Perhaps I Change My Mind
An old result put a new way Albert Meyer knows circuit lower bounds. He co-authored a paper with the late Larry Stockmeyer that proves that small instances of the...
From Gödel's Lost Letter and P=NP