CascadiaPrime Cognition

A 21st Century Lens on Artificial Intelligence

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CascadiaPrime Cognition - Mathematics

Advances in mathematical understanding can lead to sudden spurts of innovation and technological discontinuities. Mathematical insight can therefore lead to strategic surprise that can provide economic, scientific and technological breakthroughs which can have profound geopolitical significance.

Major global players as well as some of the smaller ones place such emphasis on mathematics research.

There are several possible developments that might lead to the Singularity - a mathematics breakthrough is one of them.

Recently there have been notable breakthroughs in the algorithms that underlie AI that I hope to capture here.

And then there is just the mystery, beauty and elegance of this lens on the universe and perhaps what lies beyond.

  arxiv: FineMath: A Fine-Grained Mathematical Evaluation Benchmark for Chinese Large Language Models (March 12, 2024) How do neural networks learn? A mathematical formula explains how they detect relevant patterns (March 12, 2024)
  Science: Mechanism for feature learning in neural networks and backpropagation-free machine learning models ADITYANARAYANAN RADHAKRISHNAN, DANIEL BEAGLEHOLE, PARTHE PANDIT, AND MIKHAIL BELKI (March 7, 2024)
  Average gradient outer product as a mechanism for deep neural collapse, Daniel Beaglehole,Peter Suken, Marco Mondelli,Mikhail Belkin (February 21, 2024)
  Machine Learning and Information Theory Concepts towards an AI Mathematician, Yoshua Bengio and Nikolay Malkin (March 07, 2024)
  arxiv: Average gradient outer product as a mechanism for deep neural collapse (February 23, 2024)
  arXIV: Physics-enhanced deep surrogates for PDEs(December 14, 2023)
  Nature: Mathematical discoveries from program search with large language models (December 14, 2023)
  Data Structures and Optimization for Fast Algorithms (Simons Institute) (December 8, 2023)
  Data Structures and Optimization for Fast Algorithms Optimization and Algorithm Design Simons Institute 23 videos (Simons Institute) (November,December 2023)
  Scott Aaronson: The Greatest Unsolved Problem in Math (December 22, 2022)
  Sir Timothy Gowers talk at G-Research's Computer Guided Mathematics Symposium (December 5, 2023)
  Mathematical Introduction to Deep Learning: Methods, Implementations, and Theory, Arnulf Jentzen, Benno Kuckuck, Philippe von Wurstemberger (October 31, 2023)
  Institute for Pure & Applied Mathematics (IPAM) Workshop: Machine Assisted Proofs (February 13 - 17, 2023)
  Google's Tony Wu - Autoformalization with Large Language Models - IPAM at UCLA (February 16, 2023)
  Mathematician develops equations that seek to bridge the micro and macro realms (February 7, 2023)
  YT Talk: Weinan E: A Mathematical Perspective on Machine Learning (July 8, 2022)
  Stephen Wolfram: " Finally We May Have a Path to the Fundamental Theory of Physics and Its Beautiful (April 14, 2020)
  Lex Fridman interview with Donald Knuth: Algorithms, Complexity, Life, and The Art of Computer Programming | AI Podcast (December 30, 2019)
  Wiki: Calculus
  Nature: Simple artificial-intelligence problem puts researchers up against a logical paradox discovered by famed mathematician Kurt G del. (January 8, 2019)
  MIT OpenCourseware: Lecture: Mathematics of Big Data and Machine Learning (November 9, 2018)
  Institute for Quantum Computing: A Universal Training Algorithm for Quantum Deep Learning (October 15, 2018)
  The Mathematics of Machine Learning (July 8, 2016)
  Differentiable Programming (December 2015)
  Why Machine Learning needs statistics (December 2015)
  Causal Thinking in the Twilight Zone Judea Pearl (July 2015)
  Claimed Breakthrough Slays Classic Computing Problem; Encryption Could Be Next (November 2015)
  Critical Algorithm Studies: a Reading List (November 2015)
  New general-purpose optimization algorithm promises order-of-magnitude speedups on some problems (October 2015)
  P vs. NP and the Computational Complexity Zoo
  Avi Wigderson on the "P vs. NP" problem - Efficient computation, internet security & the limits to human knowledge
  Major advance reveals limits of computation - Maybe?
  Sebastian Seung's Quest to Map the Human Brain - Mathematics
  Algorithms for the Satisfiability (SAT) Problem: A Survey (1996)
  Amoeba-inspired computing system outperforms conventional optimization methods
  Complexity No Bar to AI
  Stephen Wolfram: Computation and the Future of Mathematics
  Stephan Wolfram: Is Mathematics Invented or Discovered
  Stephan Wolfram:The Background and Vision of Mathematica
  Aaron Sloman: "Evolution, robots and mathematics"
  Common Probability Distributions: The Data Scientist s Crib Sheet (December 2015)
  Gunnar Carlsson: The Shape of Data - Topological Mapping (September 2015)
  The Banff International Research Station (BIRS)
  Institute for Pure & Applied Mathematics (IPAM)
  Pacific Institute for the Mathematical Sciences (PIMS, Canada)
  Mathematical Sciences Research Institute (MSRI, Berkeley, USA)
  Institute of Applied Mathematics (UBC, Canada)
  Simons Foundation - Advancing Research in Basic Science and Mathematics
  Wolfram MathWorld
  Austin Fowler: Quantum computing and the need for new algorithms
  The Achampong Theorem and national security
  Unconventional Computing - beyond Von Neuman and Turing - MULTI-level logic variables
  Method to shortcut simulations to reach previously unreachable timescales & ID practicable problems
  Godel's Lost Letter and P=NP (with Blogroll)
  Efficient discovery of overlapping communities in massive networks
  The Baffling and Beautiful Wormhole Between Branches of Math - Euler s identity
  Live Fourier Transform demo, showing small-angle scattering patterns for some structures
  Look at Nothing - Blog on small-angle scattering
  Stanford University: Lecture 1 | The Fourier Transforms and its Applications
   Scott Aaronson - Thought experiments: Is There Anything Beyond Quantum Computing?
  Primes - a visual tribute The Riemann Hypothesis
   Perhaps we can rigorously develop a science of when large sections of proofs can be effectively handwaved
  The real 10 algorithms that dominate our world
  Wolfram Mathworld
  Algorithmia - Open Marketplace for Algorithms
  Axiomatic method is not fully adequate to the current mathematical practice argued
  International Mathematical Union
  Clay Mathematics Institute
  Simons Foundation
  Dusa McDuff
   The research interests of Henry Cohn
  Gil Press - A short history of digitization
  Encyclopedia of Integrer Sequences (OEIX) - Sloane
  See Also the Artificial Intelligence Section of Cascadiaprime
  See Also the Quantum Computing Section of Cascadiaprime
  See Also the Neuroscience Section of Cascadiaprime