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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 Computational Complexity
Favorite Theorems: Learning from Natural Proofs
October EditionI had a tough choice for my final favorite theorem from the decade 2015-2024. Runners up include Pseudodeterministic Primes and Hardness of Partial...
From Computational Complexity
Steven Rudich (1961-2024)
Complexity theorist Steven Rudich passed away on October 29 at the age of 63. His works on Natural Proofs and Program Obfuscation were both highly influential.great...
From Computational Complexity
Higher Education Under Trump
It feels eerie as pretty much everyone seemingly avoided talking about the election. But Trump back in the White House will likely have a profound effect on USonce...
From Computational Complexity
FOCS 2024
Junior/Senior lunch in 80°F Chicago Last summer I attended the Complexity Conference in Ann Arbor for the first time in eight years largely because it was within...
From Computational Complexity
Family Feud vs Pointless
Every now and then I feel like doing a Gasarchian post. This is one of those weeks. I'm going to look at the mathematics behind the American game show Family Feud...
From Computational Complexity
Computing and the Nobels
Herb Simon Herbert Simon while a political scientist in the 1940s at my institution, the Illinois Institute of Technology, developed the theory of bounded rationality...
From Computational Complexity
Fall Jobs Post 2024
In the fall, I write a jobs post predicting the upcoming CS faculty job market and giving suggestions and links. In the spring I used to crowdsource a list of where...
From Computational Complexity
Favorite Theorems: Gradient Descent
September EditionWho thought the algorithm behind machine learning would have cool complexity implications?The Complexity of Gradient Descent: CLS = PPAD ∩ PLSJohn...
From Computational Complexity
LeetCode and AI
I often do LeetCode problems for fun. This site mainly provides short coding problems for students and others to train for the kinds of question that come up in...
From Computational Complexity
Embracing the Future of Manufacturing
Last week I walked around the International Manufacturing Technology Show with 89,000 other participants at the McCormick Center in Chicago. I went to see how AI...
From Computational Complexity
Natural Proofs is Not the Barrier You Think It Is
If there's a position where I differ from most other complexity theorists it's that I don't believe that natural proofs present a significant barrier to proving...
From Computational Complexity
Favorite Theorems: Parity Games
August EditionA quasipolynomial-time algorithm for a long standing open problem. Yes, we have two of them this decade.Deciding Parity Games in Quasi-polynomialCristian...
From Computational Complexity
My Quantum Summer
Rendering of PsiQuantum's facility in Chicago I wasn't looking for quantum this summer but it found me. At various events I ran into some of the most recognized...
From Computational Complexity
The Levin Translation
Earlier this summer I attended a Celebration for Leonid Levin who recently turned 75. To prepare my talk I wanted to go back to Levin's 1971 two-page Russian masterpiece...
From Computational Complexity
Favorite Theorems: Random Oracles
July EditionThis months favorite theorem is a circuit result that implies the polynomial-time hierarchy is infinite relative to a random oracle, answering an open...
From Computational Complexity
Complexity in Michigan
Invited Speaker Nutan Limaye, Conference Chair Valentine Kabanets,2024 PC Chair Rahul Santhanam, myself, 2025 PC Chair Srikanth Srinivasanand 2025 Local Arrangements...
From Computational Complexity
The Story of Shor's Algorithm
The quantum factoring algorithm of Peter Shor (FOCS 1994, SIAM Review 1999) turns thirty this year. Before his algorithm, quantum computing lacked the killer app...
From Computational Complexity
Favorite Theorems: Extracting Ramsey Graphs
June EditionTwo decades ago, I named the recently departed Luca Trevisan's paper connecting extractors to psuedorandom generators as one of my favorite theorems...
From Computational Complexity
Why is called the Turing Award (revisited)?
Avi Wigderson gave his ACM Turing Award lecture last week, and instead of telling his own story, he focused on Alan Turing and his influence on complexity. If you...
From Computational Complexity