Follow the ideas that keep turning up in Hacker News discussions.
William P. Thurston
In response to Jaffe and Quinn [math.HO/9307227], the author discusses forms of progress in mathematics that are not captured by formal proofs of theorems, especially in his own work in the theory of foliations and geometrization of 3-manifolds and dynamical systems.
Sébastien Bubeck, Varun Chandrasekaran, Ronen Eldan +11
Artificial intelligence (AI) researchers have been developing and refining large language models (LLMs) that exhibit remarkable capabilities across a variety of domains and tasks, challenging our understanding of learning and cognition.
Martin Kleppmann
The CAP Theorem is a frequently cited impossibility result in distributed systems, especially among NoSQL distributed databases.
Eric Chisolm
This is an introduction to geometric algebra, an alternative to traditional vector algebra that expands on it in two ways: 1.
Tom Leinster
Mathematicians manipulate sets with confidence almost every day, rarely making mistakes.
Ross Mcilroy, Jaroslav Sevcik, Tobias Tebbi +2
The recent discovery of the Spectre and Meltdown attacks represents a watershed moment not just for the field of Computer Security, but also of Programming Languages.
Art Hobson
Quantum foundations are still unsettled, with mixed effects on science and society.
Jon Kleinberg, Sendhil Mullainathan, Manish Raghavan
Recent discussion in the public sphere about algorithmic classification has involved tension between competing notions of what it means for a probabilistic classification to be fair to different groups.
John C. Baez, Mike Stay
In physics, Feynman diagrams are used to reason about quantum processes.
N. David Mermin
A strategy is suggested for teaching mathematically literate students, with no background in physics, just enough quantum mechanics for them to understand and develop algorithms in quantum computation and quantum information theory.
Thurston, William P.
In response to Jaffe and Quinn [math.HO/9307227], the author discusses forms of progress in mathematics that are not captured by formal proofs of theorems, especially in his own work in the theory of foliations and geometrization of 3-manifolds and dynamical systems.
John C. Baez
Our assumption that spacetime is a continuum leads to many challenges in mathematical physics.
Joseph M. Hellerstein, Peter Alvaro
A key concern in modern distributed systems is to avoid the cost of coordination while maintaining consistent semantics.
Mary Phuong, Marcus Hutter
This document aims to be a self-contained, mathematically precise overview of transformer architectures and algorithms (*not* results).
Henry W. Lin, Max Tegmark, David Rolnick
We show how the success of deep learning could depend not only on mathematics but also on physics: although well-known mathematical theorems guarantee that neural networks can approximate arbitrary functions well, the class of functions of practical interest can frequently be approximated through "cheap learning" with exponentially fewer
Max Tegmark
I explore physics implications of the External Reality Hypothesis (ERH) that there exists an external physical reality completely independent of us humans.
Blaise Agüera y Arcas, Jyrki Alakuijala, James Evans +5
The fields of Origin of Life and Artificial Life both question what life is and how it emerges from a distinct set of "pre-life" dynamics.
G. J. Chaitin
We discuss mathematical and physical arguments against continuity and in favor of discreteness, with particular emphasis on the ideas of Emile Borel (1871-1956).
Zhe Jia, Marco Maggioni, Benjamin Staiger +1
Every year, novel NVIDIA GPU designs are introduced.
Michael M. Bronstein, Joan Bruna, Taco Cohen +1
The last decade has witnessed an experimental revolution in data science and machine learning, epitomised by deep learning methods.
Nicolas Gisin
It is usual to identify initial conditions of classical dynamical systems with mathematical real numbers.
Eric Zelikman, Yuhuai Wu, Jesse Mu +1
Generating step-by-step "chain-of-thought" rationales improves language model performance on complex reasoning tasks like mathematics or commonsense question-answering.
Martin Kleppmann, Victor B. F. Gomes, Dominic P. Mulligan +1
We introduce OpSets, an executable framework for specifying and reasoning about the semantics of replicated datatypes that provide eventual consistency in a distributed system, and for mechanically verifying algorithms that implement these datatypes.
Tom Leinster
This short introductory category theory textbook is for readers with relatively little mathematical background (e.g.
Jonathan Bartlett, Asatur Zh. Khurshudyan
Treating differentials as independent algebraic units have a long history of use and abuse.
Cynthia Solomon, Brian Harvey, Ken Kahn +5
Logo is more than a programming language.
DeepSeek-AI, Daya Guo, Dejian Yang +197
General reasoning represents a long-standing and formidable challenge in artificial intelligence.
Saurav Kadavath, Tom Conerly, Amanda Askell +33
We study whether language models can evaluate the validity of their own claims and predict which questions they will be able to answer correctly.
Tanya Khovanova, Alexey Radul
This is a special collection of problems that were given to select applicants during oral entrance exams to the math department of Moscow State University.
Gerard 't Hooft
When investigating theories at the tiniest conceivable scales in nature, almost all researchers today revert to the quantum language, accepting the verdict from the Copenhagen doctrine that the only way to describe what is going on will always involve states in Hilbert space, controlled by operator equations.