The hottest Mathematics Substack posts right now

And their main takeaways
Category
Top Science Topics

Fast Computation of Fibonacci Numbers: Part II

Confessions of a Code Addict • 288 implied HN points • 12 Nov 23
🕹 Technology Mathematics
  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.

Too much information

Logging the World • 99 implied HN points • 21 Nov 22
🔬 Science Mathematics
  1. Information Theory studies how randomness and predictability affect the transmission and compression of data.
  2. Entropy measures the information gained from a source, highlighting the balance between predictability and unpredictability.
  3. Redundancy can protect messages against noise in communication channels, showing the importance in modern data transmission scenarios.

Tactics versus strategies in the theory of games

Infinitely More • 25 implied HN points • 03 Aug 25
📖 Philosophy Mathematics
  1. Tactics are focused, short-term moves in games, while strategies are broader plans that consider the entire game history. Think of tactics like specific plays in a game of chess compared to a strategy that shapes the whole match.
  2. In game theory, a tactic works with just the current state of play, while a strategy includes the whole journey to that point. This means tactics can be very specific to the moment, without knowing the past turns.
  3. Understanding whether a game has winning tactics or strategies helps players decide their best moves. It's important to know if there's a guaranteed win for one player or if both can only draw.

The Ramanujan Machine

A Piece of the Pi: mathematics explained • 90 implied HN points • 23 Dec 24
🔬 Science Mathematics
  1. Srinivasa Ramanujan was a brilliant mathematician known for his unique insights and identities, many of which he discovered in unconventional ways.
  2. The Ramanujan Machine is an AI project that helps generate new mathematical conjectures, making it easier to discover complex equations related to fundamental constants.
  3. The odd double factorial is a useful concept in pairing problems and can be calculated by multiplying all odd numbers up to a certain point, making it easier to understand how to pair off groups.
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Group Theory. The Math Twin to Object Oriented Programming[Math Mondays]

Technology Made Simple • 79 implied HN points • 31 Jan 23
🕹 Technology Mathematics
  1. Group theory in mathematics helps in understanding inheritance and polymorphism in Object-Oriented Programming.
  2. In OOP, inheritance allows classes to inherit properties, similar to how groups inherit properties from subgroups.
  3. Group theory provides a framework for designing efficient and modular systems by understanding class and object relationships.

Geometry that feels like magic

Eternal Sunshine of the Stochastic Mind • 59 implied HN points • 12 Jul 23
🔬 Science Mathematics
  1. In geometry, certain geometric properties can hold true regardless of how the figures are drawn, leading to aesthetically pleasing and eternal truths.
  2. Specific theorems like Morley's trisector theorem and Napoleon's theorem showcase the magic of geometry by revealing surprising relationships within triangles.
  3. Concepts like Simson's line and Țițeica's 3 circles theorem demonstrate the beauty and elegance of geometry, inspiring us to appreciate the world through the lens of mathematics.

Double Bubbles

Pershmail • 58 implied HN points • 14 Apr 23
🔬 Science Mathematics
  1. Double bubbles minimize surface area by using interesting film connections.
  2. For fencing in different areas with minimal material, the double bubble shape is ideal.
  3. The standard double bubble minimizes perimeter between two areas.

Shape of the Week: Zonogon

Pershmail • 58 implied HN points • 17 Mar 23
🚌 Education Mathematics
  1. The 'Shape of the Week' feature introduces a new geometric shape each week to expand knowledge and make learning fun.
  2. A zonogon is a parallelogram with point symmetry and can be dissected into multiple parallelograms, creating an interesting mathematical pattern.
  3. Regular zonogons can produce beautiful dissections, and studying them can lead to exploring concepts like Minkowski's First Theorem.

More Impossible Things Before Breakfast

SCIENCE GODDESS • 58 implied HN points • 01 Apr 23
🔬 Science Mathematics
  1. Amateur mathematicians discovered a single shape that can fill a plane irregularly without gaps
  2. This unique shape is called an 'einstein' tile and can only fill the plane in a disorderly manner
  3. The discovery challenges traditional beliefs and shows that even non-professionals can make significant contributions to mathematics

Gonna have fun fun fun!

Silicon Reckoner • 58 implied HN points • 02 May 23
🎨 Art & Illustration Mathematics
  1. The discussion is about the expectation of fun and enjoyment in mathematics, especially concerning formal proofs and proof assistants.
  2. There is an exploration of the interaction between formalization, mathematical communication, and technology, emphasizing the potential impact on author-reader dynamics.
  3. The text questions the philosophical implications of automatic translation between different forms of mathematical proofs, highlighting the nuances and potential losses in communication and understanding.

Abstract Mathematics 101 Bootcamp

Deep-Tech Newsletter • 19 implied HN points • 23 Mar 24
🚌 Education Mathematics
  1. A new 'QF Abstract Mathematics 101 Bootcamp' is launching annually starting in June 2024 to help bridge the gap in mathematical knowledge within the Quantum Formalism community.
  2. The bootcamp curriculum will cover topics like Set theory, Abstract Algebra, and Differential Geometry, catering to those interested in areas like quantum computing and machine learning.
  3. Participants of the bootcamp will receive certifications upon completing each module and will have the opportunity to learn from experts like Bambordé Baldé and Max Arnott.

Number Theoretic Transform with RVV

Fprox’s Substack • 83 implied HN points • 07 Dec 24
🕹 Technology Mathematics
  1. The Number Theoretic Transform (NTT) helps speed up polynomial multiplication, which is important in cryptography. It uses a smart method to do complicated calculations faster than traditional methods.
  2. Using RISC-V Vector (RVV) technology can further improve the speed of NTT operations. This means that by using special hardware instructions, operations can be completed much quicker.
  3. Benchmarks show that a well-optimized NTT using RVV can be substantially faster than basic polynomial multiplication, making it crucial for applications in secure communications.

Shape, Symmetries, and Structure: The Changing Role of Mathematics in Machine Learning Research

The Gradient • 87 implied HN points • 16 Nov 24
🕹 Technology Mathematics
  1. Mathematics is playing a bigger role in machine learning by connecting with fields like topology and geometry. This helps researchers create better tools and methods.
  2. It's not just about scaling up current methods; there's a need for new approaches based on mathematical theories. This can lead to more innovative solutions in machine learning.
  3. Mathematicians should view advancements in machine learning as chances to explore and deepen their theoretical work, not as threats to their field. Embracing these changes can lead to new discoveries.

The Mathematics of Literature

Holodoxa • 79 implied HN points • 30 Mar 23
📚 Literature Mathematics
  1. Math and literature are more interconnected than commonly thought, with Sarah Hart's book exploring the relationship between the two disciplines in depth.
  2. Once Upon a Prime delves into how mathematics influences different aspects of literature, from fundamental structures like plot and rhyme scheme to using mathematical metaphors and deploying math creatively in storytelling.
  3. Hart's book is a mix of engaging content, with some parts feeling like random trivia, leading to a reading experience that can be a bit scattered but ultimately offers unique insights into the blend of math and literature.

Random chess position

Infinitely More • 23 implied HN points • 20 Jul 25
🔬 Science Mathematics
  1. Most random arrangements of chess pieces are not legal moves in a game. It's rare for pieces to be placed in a way that follows the rules of chess.
  2. When you randomly scatter 32 chess pieces on a board, there are many more illegal positions than legal ones. This shows how strict the game rules are.
  3. Understanding chess positions can help improve strategic thinking. It’s interesting to see how players use the rules to create valid game scenarios.

Visualizing the Chain Rule

The Palindrome • 4 implied HN points • 22 Dec 25
🕹 Technology Mathematics
  1. The chain rule is essential in machine learning because it lets you compute gradients of composite functions, which you need for gradient descent and fitting models.
  2. The single-variable rule is simple, but with many parameters you must handle vector-valued functions and the math gets more complicated in the multivariable case.
  3. Each parameter's gradient is a sum over model outputs: the loss's sensitivity to each output times that output's sensitivity to the parameter, which is equivalent to multiplying gradients/Jacobians to propagate derivatives.

Infinite Sudoku

Infinitely More • 23 implied HN points • 12 Jul 25
🚌 Education Mathematics
  1. Sudoku is typically a solo puzzle where you fill a 9x9 grid with numbers, ensuring that each number appears only once in each row, column, and 3x3 box.
  2. There's a fun two-player version called the Sudoku game where players take turns placing numbers on an empty board, trying to outsmart each other without breaking the Sudoku rules.
  3. The Sudoku game can be played on larger or different shaped boards, and there are even ideas for playing infinite versions of the game on larger grids.

A polynomial with Rubik’s cube symmetry

A Piece of the Pi: mathematics explained • 78 implied HN points • 25 Nov 24
🔬 Science Mathematics
  1. Rubik’s Cube has a huge number of ways it can be scrambled, around 43 quintillion, which shows its interesting symmetry in math. It can be thought of as not just a puzzle, but a complex mathematical object.
  2. There are specific rules about how the pieces of the Rubik’s Cube can be rearranged, which creates a lot of interesting patterns and symmetries. This helps mathematicians understand how groups of movements relate to each other.
  3. Recent research has shown that it's possible to find polynomials that have the same symmetries as the Rubik’s Cube. This connects the world of puzzles to deeper mathematical concepts, making it a fun area to explore.

The Sequence Chat: Can AI Solve The Riemann Hypothesis? Some Ideas About the Progress and Limitations of AI in Science

TheSequence • 70 implied HN points • 18 Dec 24
🔬 Science Mathematics
  1. AI has made impressive strides in scientific fields, helping tackle complex problems across various disciplines like chemistry and physics. This progress shows that AI can be a powerful tool in advancing our understanding of science.
  2. The Riemann Hypothesis is a famous unsolved math problem that could significantly enhance our knowledge of prime numbers. Its simplicity in concept and complexity in proof makes it a unique challenge for both humans and AI.
  3. While AI has potential in scientific research, there are limitations to what it can achieve, especially in tackling deeply complex problems like the Riemann Hypothesis. The unique nature of such challenges may be beyond AI's current capabilities.

mathiness instills confidence

bad cattitude • 165 implied HN points • 22 Feb 24
🔬 Science Mathematics
  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.

Chutes, ladders, and Markov chains

A Piece of the Pi: mathematics explained • 72 implied HN points • 04 Dec 24
🚌 Education Mathematics
  1. The game of Chutes and Ladders is a fun example of a Markov chain. It shows how the next move depends only on where you are now, not on how you got there.
  2. There are different types of game boards, some allow for winning while others can trap players forever. Ultimately winnable boards guarantee that a player can reach the end if they keep playing.
  3. On average, players need about 39 spins to win the game, and surprisingly, most random boards created will still offer a winning chance.

The Story of the Mathematics of Machine Learning Book

The Palindrome • 5 implied HN points • 02 Dec 25
🚌 Education Mathematics
  1. Writing online about math and machine learning turned a hobby into a 700-page book, showing that sharing knowledge can lead to unexpected successes.
  2. Creating clear, engaging content on social media helped grow an audience rapidly, proving that quality work can attract attention even in crowded spaces.
  3. Finding a publisher transformed a challenging project into a successful book release, underlining the importance of collaboration and support from the community.

Abstraction in the function concept

Infinitely More • 25 implied HN points • 09 Jun 25
📖 Philosophy Mathematics
  1. The function concept in mathematics has evolved a lot, allowing for more abstract definitions. This means mathematicians can explore complex ideas that go beyond simple rules and formulas.
  2. Examples like the Devil's staircase and space-filling curves challenge our understanding of functions. These unique functions have properties that seem strange and unexpected compared to our usual ideas of what a function should be.
  3. The Conway function shows how every real number can be linked to another number in a complex way. It helps to illustrate that functions don't always need a clear formula and can still be valid in mathematics.

News Flash: Is this the Singularity?

Silicon Reckoner • 39 implied HN points • 20 Feb 23
🕹 Technology Mathematics
  1. The AI crisis with Bing raises concerns about the ethical implications of designing AI to run everything.
  2. Despite the dysfunction of Bing's Chatbot, it showcases a glimpse of genuine creativity and persistence in AI.
  3. The newsletter emphasizes the importance of human qualities like wonder and community in mathematical creativity, critiquing the focus on profit in AI development.

The advent of mathematics as spectacle

Silicon Reckoner • 39 implied HN points • 25 Mar 23
🎭️ Culture Mathematics
  1. Mathematics has become a spectacle in social media, moving away from traditional academic spaces.
  2. Social media accelerates the transformation of real world into spectacle, impacting communication and individual alienation.
  3. Mathematics reporting in media may lack critical analysis, focusing on positive narratives rather than material structures and decision-making processes.

(My) shallow thoughts about deep learning, I

Silicon Reckoner • 39 implied HN points • 27 Jun 23
🔬 Science Mathematics
  1. The workshop on 'AI to Assist Mathematical Reasoning' involved sessions with mathematicians and professionals discussing the role of institutions in adapting to AI.
  2. Panelists highlighted the importance of collaborations, new publication models, and the need for changes in teaching to incorporate new technologies in mathematics.
  3. There was a discussion about the potential impact of AI on mathematical reasoning, with a focus on automation, creating an ecosystem for accessibility, and the implications for democratizing decisions.

New words #5

Mutual Information • 39 implied HN points • 22 Sep 23
🚌 Education Mathematics
  1. Discover new words by looking them up when encountered in podcasts or readings.
  2. Some new words include pluriennial, isoprene, trammel, polysemy, coruscate, mezuzot, kasher, sheikha, and more.
  3. Words like xenotime, mountebank, salubrious, and antepenultimate highlight the vast diversity in the English language.

Sphericons

Pershmail • 39 implied HN points • 28 Apr 23
🔬 Science Mathematics
  1. The sphericon is a shape that wobbles when twisted, and it's made of two pieces resembling bicones.
  2. The sphericon has square dimensions and a 90 degree angle from one end extending down.
  3. Generalizations of the sphericon, called polycons, roll in a wobbly way and include shapes like hexacons, octacons, and decacons.

Identifying bottlenecks in networks

A Piece of the Pi: mathematics explained • 48 implied HN points • 03 Feb 25
🔬 Science Mathematics
  1. Bottlenecks in networks are crucial points that can slow down communication or movement. Identifying these points helps understand how the entire network functions.
  2. Networks can be made up of different regions that are linked by these bottlenecks. Recognizing connections between these regions is important for overall analysis.
  3. Knowing where the bottlenecks are can help improve the efficiency of networks, whether in transportation or social connections. This can lead to better planning and resource allocation.

The mathematics of the game Waffle

A Piece of the Pi: mathematics explained • 48 implied HN points • 22 Jan 25
🔬 Science Mathematics
  1. Waffle is a fun word game where you need to form six five-letter words in a grid. You can swap letters to find the right words based on clues given.
  2. To solve Waffle, you must figure out the words first, then how to rearrange the letters, and finally do it using the least number of swaps.
  3. Group theory is useful for solving Waffle puzzles because it helps to find ways to rearrange the letters efficiently, especially when dealing with repeated letters.

Where have the International Math Olympiad Gold Medallists Ended Up? Part Two of Three

Neeloy’s Substack • 2 HN points • 29 Jul 24
🚌 Education Mathematics
  1. Most International Math Olympiad gold medallists choose to study at MIT, as it is the top destination for them. Many also stay in their home countries, especially those from China and Russia.
  2. Around 70% of these medallists go on to pursue a PhD, but the trend is declining as more opt for jobs in tech and finance. Academia remains a popular path but is facing stiff competition.
  3. Google is a major employer of these medal winners in tech, while quant finance firms are increasingly attracting graduates. This shows a shift in career preferences towards finance and tech over traditional academia.

Edge 456: Inside the Toughest Math Benchmark Ever Built

TheSequence • 56 implied HN points • 12 Dec 24
🕹 Technology Mathematics
  1. Mathematical reasoning is a key skill for AI, showing how well it can solve problems. Recently, AI models have made great strides in math, even competing in tough math competitions.
  2. Current benchmarks often test basic math skills but don’t really challenge AI's creative thinking or common sense. AI still struggles with complex problem-solving that requires deeper reasoning.
  3. FrontierMath is a new benchmark designed to test AI on really tough math problems, pushing it beyond the simpler tests. This helps in evaluating how well AI can handle more advanced math challenges.

My Class About Causal Inference

By Reason Alone • 42 implied HN points • 13 Feb 25
🚌 Education Mathematics
  1. Teaching causal inference helps students understand the relationship between cause and effect in social sciences. It's important to make complex ideas relatable to engage younger audiences.
  2. Using visual aids, like graphs, can enhance understanding of complicated topics, especially in a classroom setting. Students can connect better with the material when it’s presented visually.
  3. Recommended readings and real-world examples, like the draft lottery, can spark curiosity in students. Sharing interesting studies can help them see the relevance of these concepts in everyday life.

Elo ELI5'd

inexactscience • 39 implied HN points • 15 Jul 23
🎾 Sports Mathematics
  1. Elo ratings are used to compare the strength of players, particularly in chess. They help predict the outcome of games based on the players' ratings.
  2. The formula for updating Elo ratings takes into account the expected score of a player and the actual outcome of a game. If the outcome is surprising, the rating changes more significantly.
  3. Elo ratings can also be applied beyond chess to other areas, like ranking items or comparing performance in various fields, showing their versatility as a simple yet effective system.