The hottest Mathematics Substack posts right now

And their main takeaways
Category
Top Science Topics
lcamtuf’s thing β€’ 2332 implied HN points β€’ 12 Mar 24
  1. The discrete Fourier transform (DFT) is a crucial algorithm in modern computing, used for tasks like communication, image and audio processing, and data compression.
  2. DFT transforms time-domain waveforms into frequency domain readings, allowing for analysis and manipulation of signals like isolating instruments or applying effects like Auto-Tune in music.
  3. Fast Fourier Transform (FFT) optimizes DFT by reducing the number of necessary calculations, making it more efficient for large-scale applications in computing.
Marcus on AI β€’ 4772 implied HN points β€’ 19 Oct 23
  1. Even with massive data training, AI models struggle to truly understand multiplication.
  2. LLMs perform better in arithmetic tasks than smaller models like GPT but still fall short compared to a simple pocket calculator.
  3. LLM-based systems generalize based on similarity and do not develop a complete, abstract, reliable understanding of multiplication.
TheSequence β€’ 1106 implied HN points β€’ 18 Jan 24
  1. Discovering new science is a significant challenge for AI models.
  2. Google DeepMind's FunSearch model can generate new mathematics and computer science algorithms.
  3. FunSearch uses a Language Model to create computer programs and iteratively search for solutions in the function space.
Wood From Eden β€’ 816 implied HN points β€’ 23 Dec 23
  1. Philosophy is the art of clarifying concepts and finding links between them.
  2. Philosophy is similar to mathematics in that it explores relationships between concepts, just as mathematics explores relationships between numbers.
  3. Concepts in philosophy change over time, making it a field that evolves constantly unlike mathematics which is built on stable concepts.
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Logging the World β€’ 299 implied HN points β€’ 07 Mar 24
  1. Using interesting anecdotes or 'Malcolms' at the beginning can engage a wider audience and make complex topics more appealing.
  2. Balancing academic style writing with engaging storytelling can make science communication more effective and impactful.
  3. Integrating rhetorical tricks and interesting facts can drive curiosity and encourage broader audiences to explore complex subjects.
News Items β€’ 471 implied HN points β€’ 18 Jan 24
  1. AlphaGeometry AI system solves complex geometry problems as well as a human Olympiad gold-medalist.
  2. AlphaGeometry combines neural language model with a rule-bound deduction engine for reasoning.
  3. Development of AlphaGeometry highlights AI's logic reasoning progress and ability to discover and verify new knowledge.
Asimov Press β€’ 270 implied HN points β€’ 20 Feb 24
  1. The concept of viewing time differently through the lens of the Minute Man and the Millennium Man prompts questions about our understanding of speed and time in the world.
  2. Biological processes at the cellular level can occur at astonishing speeds, with enzymes performing millions of chemical reactions per second and protein 'motors' spinning thousands of times a minute.
  3. Scientists use innovative experiments to directly observe rapid biological processes, such as watching ATP synthase spin or tracking ribosomes moving along messenger RNA strands, to gain a deeper understanding of the intricate workings of life.
Logging the World β€’ 538 implied HN points β€’ 02 Dec 23
  1. Understanding exponential growth in infection rates can help predict future COVID trends.
  2. Individual growth rates of different strains impact the overall daily growth rate, following a weighted average principle.
  3. Market share of strains, not just reaching a specific percentage threshold, influences overall infection growth.
Compounding Quality β€’ 216 implied HN points β€’ 08 Feb 24
  1. Isaac Newton is famous for his Laws of Motion in physics and mathematics.
  2. Newton's Laws of Motion are fundamental to classical mechanics and still widely used today.
  3. This post about Newton's Laws of Motion is for paid subscribers.
bad cattitude β€’ 165 implied HN points β€’ 22 Feb 24
  1. Mathiness can make people feel more confident, especially if they aren't familiar with math.
  2. Adding complex math or 'mathiness' to information can influence how people perceive its quality, especially if they lack knowledge in math and models.
  3. It's important to be cautious of trusting information just because it includes numbers or complex equations; don't assume accuracy or rigor without verifying.
Defender’s corner β€’ 79 implied HN points β€’ 27 Mar 24
  1. In math, understanding the meaning and representation of variables like 'X' is crucial for problem-solving.
  2. Teaching effectively often involves asking questions and understanding the learner's mental model.
  3. Using metaphors and real-life scenarios can help clarify complex concepts and improve understanding.
Technology Made Simple β€’ 159 implied HN points β€’ 05 Feb 24
  1. The Lottery Ticket Hypothesis proposes that within deep neural networks, there are subnetworks capable of achieving high performance with fewer parameters, leading to smaller and faster models.
  2. Successful application of the Lottery Ticket Hypothesis relies on iterative magnitude pruning strategies, with potential benefits like faster learning and higher accuracy.
  3. The hypothesis works due to factors like favorable gradients, implicit regularization, and data alignment, but challenges like scalability and interpretability remain towards practical implementation.
CPU fun β€’ 121 implied HN points β€’ 22 Feb 24
  1. Floating point arithmetic can be more complex than expected, especially due to limited mantissa bits, affecting the accuracy of calculations.
  2. Complaining about OpenMP reductions giving 'the wrong answer' is misguided; the issue likely existed in the serial code and is now being exposed.
  3. Changing the type of the accumulator to 'double' can help resolve issues with floating point arithmetic and accuracy during sum reductions.
Wednesday Wisdom β€’ 113 implied HN points β€’ 21 Feb 24
  1. Experience and age often bring wisdom, knowledge, and a unique perspective.
  2. In technology, while tools and capabilities have evolved, fundamental principles like people dynamics, math, and physics remain constant.
  3. Despite advancements, people still struggle with basic math, concurrent programming, and effective communication in group settings.
moontower: a stoner dad explains options trading to his kids β€’ 117 implied HN points β€’ 11 Feb 24
  1. Kids often learn from their parents through modeling and osmosis rather than direct instruction.
  2. Teaching someone else's child may sometimes be more effective in imparting knowledge and lessons.
  3. Finding learning moments in everyday activities or tailored to a child's interests can help them grasp concepts effectively and make the lessons their own.
Confessions of a Code Addict β€’ 288 implied HN points β€’ 12 Nov 23
  1. A new method to compute Fibonacci numbers using a closed-form expression without having to resort to floating point arithmetic.
  2. Representation of irrational numbers using two parts can be done in code allowing for precise computation of Fibonacci numbers.
  3. Understanding rings and implementing arithmetic operations within it can help in computing Fibonacci numbers without any loss of precision.
α΄‹ΚŸα΄€α΅Ύs β€’ 628 implied HN points β€’ 15 Jun 23
  1. Former government officials have revealed details about UFO crash retrieval programs involving non-human intelligence and advanced materials.
  2. The use of topological materials in UFO technology could explain exotic properties, like strange isotopes and materials able to deform into higher dimensions.
  3. Connections between the human brain's multi-dimensional functions and UFO phenomena could suggest a link between consciousness and unexplained aerial phenomena.
A Piece of the Pi: mathematics explained β€’ 60 implied HN points β€’ 15 Mar 24
  1. The number pi has now been calculated to 105 trillion decimal places using the Chudnovsky algorithm over 75 days.
  2. Ramanujan's formula for pi has been expanded and improved upon over the years, with the Chudnovsky brothers developing a formula that computes pi to 13 decimal places.
  3. Bellard's formula and the BBP formula provide ways to compute specific digits of pi without having to calculate all earlier digits, making validations faster and more efficient.
Logging the World β€’ 418 implied HN points β€’ 23 Aug 23
  1. New COVID variant BA.2.86 has mutations that suggest fast growth, but estimating its growth rate is tricky.
  2. Statisticians use models and likelihood functions to estimate parameters like growth rates, but uncertainty exists in the estimates.
  3. The work of statistician C.R. Rao, like the Fisher information, shows fundamental limits to parameter estimation and the role of geometry in statistics.
Mathworlds β€’ 569 implied HN points β€’ 22 Jun 23
  1. Students often feel worse about math class compared to other subjects because of the pressure to only have one correct answer for each question.
  2. Math should be taught as a creative discipline that embraces human subjectivity, not just a set of memorized steps.
  3. Teachers can help students deconstruct the idea of one right way to do math by introducing activities that show multiple paths lead to the same solution.
Logging the World β€’ 418 implied HN points β€’ 15 Aug 23
  1. The proposal for compulsory math education until age 18 in the UK received mixed reactions, highlighting the importance of making math appealing and accessible to a wide audience.
  2. Implementing math education until 18 requires consideration of factors like shortage of math teachers and effective delivery methods such as leveraging online resources.
  3. Math education should cover areas such as practical number skills, understanding uncertainty and randomness, and exploring connections between math and other subjects like art and music.
Logging the World β€’ 418 implied HN points β€’ 05 Jul 23
  1. Genius can be found in lesser-known figures like Kolmogorov, who made significant contributions to mathematics and other fields.
  2. Kolmogorov's work on probability theory and the Kolmogorov-Arnold theorem had a lasting impact on mathematics and even underpins modern AI algorithms.
  3. Kolmogorov's life was not only marked by academic achievements but also by navigating personal challenges, such as opposing Lysenkoism and living as an openly gay man in Stalinist Russia.
Insight Axis β€’ 276 implied HN points β€’ 11 Sep 23
  1. Math education should focus on real-world problems to make it interesting and meaningful for students.
  2. Students should be taught a structured process of defining, abstracting, computing, and interpreting problems in math.
  3. School math should prioritize applied mathematics to show the practical utility of math, cater to the majority, and prepare students for the future.
Silicon Reckoner β€’ 98 implied HN points β€’ 11 Jan 24
  1. Mathematicians have two sides to their work: creating new ideas and proving statements.
  2. Artificial General Intelligence (AGI) could potentially encompass all human competences, including mathematical creativity.
  3. Artificial Intuition is being explored to assist mathematicians in generating new ideas and collaborating with AI.
Mathworlds β€’ 373 implied HN points β€’ 26 May 23
  1. Math class often focuses on moving students towards abstract concepts, neglecting the value of concrete understanding.
  2. Teachers who can help students transition between concrete and abstract knowledge effectively engage students in math.
  3. Including both concrete and abstract elements in math problems can make learning more engaging and effective.
Metarational β€’ 59 implied HN points β€’ 13 Feb 24
  1. The problem involves repeatedly selecting balls from an urn, inspecting their color, putting them back, and adding another of the same color. The goal is to find the probability that the majority of balls in the urn will be white after a large number of repetitions.
  2. To solve the problem, it was analyzed that there must be at least half white draws to achieve a white majority. Calculations led to a final result of 11/16 as the probability limit.
  3. The solution involved understanding the probabilities of different color sequences and using Riemann sums to simplify and find the answer, showcasing an intricate application of mathematics to a probability riddle.
Confessions of a Code Addict β€’ 158 HN points β€’ 05 Nov 23
  1. A linear algebra technique can be applied to compute Fibonacci numbers quickly with a logarithmic time complexity.
  2. Efficient algorithms like repeated squaring can compute powers of matrices in logarithmic time, improving performance for Fibonacci number calculations.
  3. A closed form expression using the golden ratio offers a direct method to compute Fibonacci numbers, showing different approaches with varied performance.
Logging the World β€’ 199 implied HN points β€’ 28 Sep 23
  1. The book 'Four Ways of Thinking' by David Sumpter discusses four philosophies that map onto the four types of cellular automata identified by Stephen Wolfram, with historical anecdotes and life lessons.
  2. The book explores statistical, interactive, chaotic, and complex ways of thinking, connecting topics like cellular automata, chaos theory, and modern statistics with practical applications.
  3. David Sumpter's book introduces the complexity of modern mathematical research, showcasing the emergence of complicated behavior from simple rules and the fascinating concept of quantifying complexity in patterns.
Quantum Formalism β€’ 59 implied HN points β€’ 02 Feb 24
  1. QF has introduced an Advanced Mathematics GPT as a learning assistant for graduate-level mathematics.
  2. The new GPT covers advanced branches of pure mathematics like Abstract Algebra, Algebraic Geometry, and Differential Geometry, allowing users to ask questions on various topics.
  3. Access to the Advanced Mathematics GPT is currently restricted to users with ChatGPT Plus or higher subscription plans.
Splitting Infinity β€’ 59 implied HN points β€’ 28 Jan 24
  1. The type of income distribution models used like Pareto or lognormal can impact total utility calculations in economics
  2. There is an interesting relationship observed where the degree of inequality doesn't directly correlate with total utility in certain scenarios
  3. Introducing more risk-averse utility functions can bring the focus back on the importance of inequality in calculations
Quantum Formalism β€’ 59 implied HN points β€’ 26 Jan 24
  1. QF GPT is a learning assistant tool for those studying quantum mechanics and quantum information science, especially those struggling with mathematical definitions.
  2. QF GPT utilizes ChatGPT's capabilities to provide accurate responses most of the time and encourages users to correct errors to solidify their understanding.
  3. Access to QF GPT is currently limited to users with ChatGPT Plus or higher subscription plans, but the hope is to make it accessible to the entire QF community in the future for advanced mathematical learning in QM and QIS.