2025-04-22 05:44:32
A team of amateurs recently came together in an online collaboration called the Busy Beaver Challenge to pin down the value of BB(5), the fifth "busy beaver" number — a notoriously difficult problem in theoretical computer science. The busy beaver problem, or “game,” involves finding the Turing machine with a given number of states that runs for the longest series of steps before halting. Using collaborative tools and the Coq proof assistant to verify their work, the team proved that BB(5) equals 47,176,870. The landmark result explores the limits of computation and the boundaries of what is knowable in mathematics.
Read Ben Brubaker's excellent Quanta Magazine Article for more details: "With Fifth Busy Beaver, Researchers Approach Computation’s Limits" https://www.quantamagazine.org/amateur-mathematicians-find-fifth-busy-beaver-turing-machine-20240702/
PAPERS
- Busy Beaver Challenge website https://bbchallenge.org/
- "The Busy Beaver Frontier", S. Aaronson 2020 https://dl.acm.org/doi/10.1145/3427361.3427369
- "On Non-Computable Functions" T. Rado 1962 https://onlinelibrary.wiley.com/doi/abs/10.1002/j.1538-7305.1962.tb00480.x
- "The determination of the value of Rado’s noncomputable function
for four-state Turing machines" A. Brady, 1983 https://www.ams.org/journals/mcom/1983-40-162/S0025-5718-1983-0689479-6/
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CHAPTERS
00:00 What is the Busy Beaver problem?
01:05 How does a Turing machine work?
02:35 Programs that halt versus getting stuck in endless loops: the Halting Problem
04:38 How to play the Busy Beaver game
05:26 BB(1), BB(2), BB(3), BB(4) solutions
06:38 The Busy Beaver Challenge tackles BB(5)
07:31 The history of the search for BB(5)
08:10 The Busy Beaver Challenge methodology
08:48 Coding 'deciders'' to shorten the list of contenders
09:49 Mysterious contributor confirms BB(5) solution
10:09 Coq proof of BB(5)
10:54 Is BB(6) solvable?
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Quanta Magazine is an editorially independent publication supported by the Simons Foundation: https://www.simonsfoundation.org
2025-03-19 00:32:36
Physicist Mario Krenn uses artificial intelligence to inspire and accelerate scientific progress. He runs the Artificial Scientist Lab at the Max Planck Institute for the Science of Light, where he develops machine-learning algorithms that discover new experimental techniques at the frontiers of physics and microscopy. He also develops algorithms that predict and suggest personalized research questions and ideas.
00:00 - The Artificial Scientist Lab
00:59 - The limits of human intuition
02:12 - Building algorithms to design experiments
03:37 - Algorithm makes a discovery about entanglement
06:11 - Collaboration with LIGO (gravitational wave detectors)
07:07 - Using AI to generate research ideas
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Quanta Magazine is an editorially independent publication supported by the Simons Foundation: https://www.simonsfoundation.org
2025-02-21 03:56:14
Mathematicians recently proved a central component of the Langlands program, an ambitious effort to develop a “grand unified theory” of mathematics. The monumental proof of the geometric Langlands conjecture totaled more than 800 pages and marked the culmination of 30 years of work by nine mathematicians. Lead author, Dennis Gaitsgory, is the recipient of the 2025 Breakthrough Prize in Mathematics.
Watch Quanta’s video explainer about the full Langlands program here: https://www.youtube.com/watch?v=_bJeKUosqoY
Read the companion Quanta Magazine article:
https://www.quantamagazine.org/monumental-proof-settles-geometric-langlands-conjecture-20240719/
PAPER
- D. Gaitsgory, S. Raskin D. Arinkin, D. Beraldo, J. Campbell, L. Chen, J. Faergeman, D. Gaitsgory, K. Lin, S. Raskin and N. Rozenblyum (2024) "Proof of the geometric Langlands conjecture" - https://people.mpim-bonn.mpg.de/gaitsgde/GLC/
CORRECTION 02/24/25: In the end credits, "Qaunta Math Writer" is misspelled. It should have been "Quanta Math Writer." (Thanks to Milton Lee for catching that)
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00:00 Introduction
01:01 What is the Langlands Programs?
01:35 Fourier theory and analysis
02:23 Fourier transform, building blocks and labels
04:37 Sheaves as building blocks
05:49 Geometric Langlands and eigensheaves
06:30 Gaitsgory and his fundamental diagram
07:01 Poincaré sheaf and the solution to conjecture
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Quanta Magazine is an editorially independent publication supported by the Simons Foundation: https://www.simonsfoundation.org
2025-02-01 00:52:36
An estimated 1 to 4% of people have aphantasia, a condition where they don’t experience mental imagery or a ‘mind’s eye.’ Neuroscience research into people with aphantasia is now revealing how imagination works and demonstrating the sweeping variety in our subjective experiences.
Correction: February 10, 2025
Joel Pearson is a neuroscientist, not a neurologist.
Read the Quanta article: "What Happens in a Mind That Can’t ‘See’ Mental Images"
https://www.quantamagazine.org/what-happens-in-a-mind-that-cant-see-mental-images-20240801/
PAPERS
- "Loss of imagery phenomenology with intact visuo-spatial task performance: A case of ‘blind imagination’" | https://www.sciencedirect.com/science/article/abs/pii/S0028393209003418?via%3Dihub
- "The critical role of mental imagery in human emotion: insights from fear-based imagery and aphantasia" | https://pubmed.ncbi.nlm.nih.gov/33715433/
- "Hippocampal-occipital connectivity reflects autobiographical memory deficits in aphantasia" | https://elifesciences.org/reviewed-preprints/94916v2
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Chapters:
00:00 What is it like to have aphantasia?
01:29 How aphantasia was identified and named - Adam Zeman
02:32 How the brain forms mental imagery - visual cortex
03:25 VVIQ Questionnaire
04:03 Joel Pearson's new research techniques
04:55 Emotional response and aphantasia
05:52 Cornelia McCormick and memory research
06:26 Memory-aphantasia connection
07:09 Aphantasia spectrum and hyperphantasia
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Quanta Magazine is an editorially independent publication supported by the Simons Foundation: https://www.simonsfoundation.org
2024-12-19 23:56:38
The year's biggest breakthroughs in computer science included a new understanding of what’s going on in large language models (LLMs) and a breakthrough in computing Hamiltonians — models that represent complex quantum systems. Read more at Quanta Magazine: https://www.quantamagazine.org/the-year-in-computer-science-20241219/?swcfpc=1
0:04 - Can Large Language Models Understand?
Are chatbots "stochastic parrots"? A new evaluation called Skill Mix suggests that the biggest large language models seem to learn enough skills to understand the words they’re processing.
Read more: https://www.quantamagazine.org/new-theory-suggests-chatbots-can-understand-text-20240122/
6:14 - Hamiltonian Learning Algorithm
After years of false starts, a team of computer scientists has found a way to efficiently deduce the Hamiltonian of a quantum system at any constant temperature.
Read more: https://www.quantamagazine.org/scientists-find-a-fast-way-to-describe-quantum-systems-20240501/
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2024-12-19 08:37:16
We investigate three of 2024’s biggest breakthroughs in biology including new understanding of the common ancestor of all modern life, a surprising discovery about the connection between the brain and the immune system, and the ongoing impact of AI on the field of biology which led to the Nobel Prize in Chemistry for researchers working on protein structure prediction and protein design.
Read about more breakthroughs from 2024 at Quanta Magazine: https://www.quantamagazine.org/the-year-in-biology-20241218/
00:05 Modern Life's Ancient Ancestor
An interdisciplinary group applied the latest tricks of phylogenetics — using genes and genomes to build evolutionary trees — to trace all of modern life back to our shared ancestor. This ancient cell, or population of cells, is known as LUCA, which stands for “last universal common ancestor,” the one from which everything alive today emerged. The work suggested that LUCA was a surprisingly complex cell and dated LUCA to some 4.2 billion years ago — earlier than researchers had thought.
https://www.quantamagazine.org/all-life-on-earth-today-descended-from-a-single-cell-meet-luca-20241120/
04:50 Surprising Brain-Body Connection
One of the most mind-blowing discoveries of the year is about the integration of the brain and body. Most immunologists have long assumed that the immune system is self-regulating. For the first time, researchers have found a neural circuit, located in the brainstem, that adjusts the immune system. This circuit senses inflammatory molecules in the body and then dials their levels up or down to protect healthy tissues
https://www.quantamagazine.org/the-brainstem-fine-tunes-inflammation-throughout-the-body-20240614/
09:18 AI Transforms Protein Science
In 2024, hardly a week could go by without some big new paper related to Google DeepMind’s AlphaFold2: a neural network that can accurately predict the three-dimensional structure of a folded protein from the one-dimensional string of its amino acid molecules In May, Google DeepMind released AlphaFold3, which predicts the shapes of proteins as they interact with other molecules. Then, in October, the Nobel Prize in Chemistry was awarded to John Jumper and Demis Hassabis from Google DeepMind, the creators of AlphaFold2, and David Baker from the University of Washington, who revolutionized the design of proteins using AI.
https://www.quantamagazine.org/how-ai-revolutionized-protein-science-but-didnt-end-it-20240626/
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