The hottest Mathematics Substack posts right now

And their main takeaways
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Top Science Topics

How We Set Math Class up to Fail

Mathworlds • 373 implied HN points • 26 May 23
🚌 Education Mathematics
  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.

2.6 Isaac Newton

Fields & Energy • 199 implied HN points • 24 Jan 24
🔬 Science Mathematics
  1. Isaac Newton built his laws of motion and gravitation on the earlier work of scientists like Galileo and Kepler. This helped him connect how things move on Earth with how planets move in space.
  2. Newton discovered that gravity acts in a certain way: the force gets weaker as you move further away from an object. He showed this through thinking about how an apple falls and how the moon orbits the Earth.
  3. To explain the gravitational pull of larger bodies, Newton used advanced math concepts, making his ideas more accurate. He proved that the gravity of a round object is the same as if all its mass was concentrated in one point at its center.

International Gender Disparities in Math

Heterodox STEM • 135 implied HN points • 17 Aug 25
🚌 Education Mathematics
  1. Boys generally perform better than girls in high-level math, but the difference is small. At the lower end, girls often do just as well or better.
  2. Socioeconomic status and nationality have a bigger impact on math performance than gender does. Countries with more resources often show better overall math scores.
  3. Equal representation of genders in math isn't necessary or realistic. Focusing on improving math education and training for all students is more important than pushing for gender parity.

Against Mathiness

The Honest Broker Newsletter • 1364 implied HN points • 02 Jan 24
🔬 Science Mathematics
  1. Mathiness can allow for academic politics to masquerade as science.
  2. Good empirical research can eventually win out in truth battles, even if it takes time.
  3. It's possible to distinguish between good policy research and mathiness, despite potential professional benefits and political challenges.

So... what is the lottery ticket hypothesis [Math Mondays]

Technology Made Simple • 159 implied HN points • 05 Feb 24
🕹 Technology Mathematics
  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.
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Replay: Putting the "M" in STEM

The Bell Ringer • 59 implied HN points • 17 May 24
🚌 Education Mathematics
  1. Math is an important part of STEM education and needs more focus. It's often overlooked, but it is essential for understanding science and technology.
  2. Encouraging students in math can help close the achievement gap. When students feel supported in math, they tend to perform better overall.
  3. There are resources and strategies available to help improve math learning. Schools and educators can use various tools to make math more engaging for students.

Turing's Work on the Riemann Hypothesis

Cantor's Paradise • 379 implied HN points • 24 Jan 25
🔬 Science Mathematics
  1. Alan Turing is famous for his work in computer science and cryptography, but he also made important contributions to number theory, specifically the Riemann hypothesis.
  2. The Riemann hypothesis centers on a mathematical function which helps in understanding the distribution of prime numbers, and it remains unproven after over 160 years.
  3. Turing created special computers to help calculate values related to the Riemann hypothesis, showing his deep interest in the question of prime numbers and mathematical truth.

Square waves, or non-elephant biology

lcamtuf’s thing • 2040 implied HN points • 18 Apr 23
🔬 Science Mathematics
  1. Analyzing electronic circuits with square wave signals is more complex than with sine waves.
  2. Square waves can be approximated as a sum of sine waves at the fundamental frequency and odd multiples.
  3. Understanding the behavior of square waves and their harmonics is essential for circuit design and noise suppression.

The CAP Theorem of Clustering: Why Every Algorithm Must Sacrifice Something

Confessions of a Code Addict • 529 implied HN points • 29 Oct 24
🕹 Technology Mathematics
  1. Clustering algorithms can never be perfect and always require trade-offs. You can't have everything, so you have to choose what matters most for your project.
  2. There are three key properties that clustering should ideally have: scale-invariance, richness, and consistency, but no algorithm can achieve all three simultaneously.
  3. Understanding these sacrifices helps in making better decisions when using clustering methods. Knowing what to prioritize can lead to more effective data analysis.

How To Fix Math(s) Education

Insight Axis • 276 implied HN points • 11 Sep 23
🚌 Education Mathematics
  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.

2.2 Early & Medieval Physics

Fields & Energy • 179 implied HN points • 27 Dec 23
💾 History Mathematics
  1. The Ptolemaic model explained how planets move in terms of circles and smaller orbits called epicycles. This model was clever, even though it was eventually replaced by simpler ideas in science.
  2. During the Middle Ages, many people thought that science was stuck, but some scholars made important contributions and kept the spirit of experimentation alive, especially figures like Albertus Magnus and Roger Bacon.
  3. The study of more complex shapes, like conic sections, was overlooked for a long time. Eventually, scholars at places like Oxford started to explore motion more deeply and share their findings across Europe.

The poetry of Steiner systems

A Piece of the Pi: mathematics explained • 42 implied HN points • 14 Nov 25
🎭️ Culture Mathematics
  1. A Steiner triple system is made up of a set and its unique 3-element subsets, called blocks. Each pair of elements only appears together in one block.
  2. Kirkman's Schoolgirl Problem is about scheduling walks for girls so each pair walks together just once. This problem is an example of how Steiner systems can solve real-life scenarios.
  3. Resolving Steiner systems allows for structured arrangements that can be creatively used, like constructing poetry, where each block represents a line and unique keyword pairs are included in an organized way.

The Origins of Deutsche Physik (1910s)

Cantor's Paradise • 363 implied HN points • 06 Jan 25
🔬 Science Mathematics
  1. The conflict in the physics community during the 1910s was largely about differing views on science and the influence of World War I. German physicists felt pressure to defend national pride while dealing with the rise of theoretical physics led by figures like Einstein.
  2. There was a significant clash between experimentalists and theorists, with older physicists struggling to accept new ideas. Many were uncomfortable with Einstein's theories because they felt too abstract and removed from traditional experimental methods.
  3. As political tensions grew, the conflict transformed into overt anti-Semitism, particularly targeting Einstein. Some physicists expressed nationalistic and racial ideologies, which later aligned with the Nazi agenda.

1.4 What’s the Benefit of This New Model?

Fields & Energy • 199 implied HN points • 22 Nov 23
🔬 Science Mathematics
  1. This new model helps us understand how antennas and electromagnetic radiation work better. It shows how waves and fields can create visible effects, like standing waves, which we see in everyday life.
  2. The theory offers answers to old physics puzzles like wave-particle duality. Instead of seeing particles and waves as opposites, they work together as two different things.
  3. It provides solutions to tricky problems in electromagnetism, like radiation reaction and vacuum energy. The model suggests that radiation comes from the applied fields, not just from accelerating charges.

Science giveth and science taketh away

Razib Khan's Unsupervised Learning • 366 implied HN points • 17 Dec 24
🔬 Science Mathematics
  1. Science has advanced a lot since Darwin's time, but we often miss the wonder and excitement that comes with these discoveries. It seems like people today are less amazed by scientific progress than they used to be.
  2. Darwin proposed that evolution happens through natural selection, but he didn’t fully explain how traits are passed down. Later scientists combined genetics with evolution to better understand how traits vary across generations.
  3. Today, understanding evolution requires recognizing four main forces: mutation, migration, selection, and drift. These forces shape the genetic diversity that fuels evolution.

The Making of a Gene Circuit

Asimov Press • 290 implied HN points • 16 Feb 25
🔬 Science Mathematics
  1. The repressilator is a simple gene circuit that helps scientists understand how to control living cells. It's made of three genes that work together in a loop to create a rhythmic 'on-off' signal.
  2. Michael Elowitz and his team proved that you could design circuits in living cells, which opened the door to synthetic biology. This means we can now program cells to perform specific tasks.
  3. Modern advancements have built on the repressilator, allowing us to create complex gene circuits that can mimic computing processes inside cells. This shows how biology can become a tool for engineering and technology.

In defense of curiosity driven research

Heterodox STEM • 120 implied HN points • 16 Jul 25
🔬 Science Mathematics
  1. Curiosity-driven research is essential for advancing science and understanding complex theories. It helps discover fundamental truths that may not have immediate practical applications.
  2. Recent funding cuts to foundational research, especially in STEM fields, can harm the growth and competitiveness of scientific knowledge in the U.S. These cuts prioritize immediate economic gains over long-term scientific exploration.
  3. Mathematics plays a crucial role in science and technology, influencing discoveries and innovations that impact everyday life. A strong focus on mathematical ideas can lead to transformative advances in various fields.

The surreal line is topologically compact!

Infinitely More • 25 implied HN points • 28 Nov 25
🔬 Science Mathematics
  1. Compactness in mathematics means that a set can be covered by a limited number of open sets, making it easier to work with. This concept is important in various areas of math like topology and analysis.
  2. The surreal numbers initially seem to lack compactness compared to real numbers, showing that many of the typical properties may not apply directly.
  3. However, by looking at the surreal numbers from a different perspective, we can discover surprising instances of compactness that we didn't expect.

The Human Use of Human Beings

Life in the 21st Century • 137 implied HN points • 09 Jan 24
🔬 Science Mathematics
  1. Norbert Wiener emphasized the importance of feedback for learning in technology and society.
  2. Wiener warned against the negative impacts of allowing militarism to lead technological development.
  3. Wiener's critique highlights the need to value technology based on its benefit to human beings, not just for its own sake.

How a Convertible Note Converts During Priced Round (e.g- Series A, B) ? | 2008-09 Global Startup Ecoystem & More

Venture Curator • 219 implied HN points • 10 Jul 23
💼 Business Mathematics
  1. Convertible notes convert in three ways: Pre-money Method, Percentage Ownership Method, Dollars Invested Method, catering to different preferences of founders and investors.
  2. Key parameters to consider in evaluating a convertible note include Discount Rate, Valuation Cap, Interest Rate, and Maturity Date, which affect the conversion process during priced rounds like Series A or B.
  3. Understanding the math behind the conversion of convertible notes during priced rounds involves calculations based on factors like pre-money valuation, discount rates, and valuation caps, influencing the final ownership percentages.

How to Measure Molecules

Asimov Press • 367 implied HN points • 17 Nov 24
🔬 Science Mathematics
  1. In the late 19th century, Lord Rayleigh measured the size of a single molecule using simple materials like oil and water. This clever experiment showed how basic observations can lead to important scientific discoveries.
  2. Benjamin Franklin also made significant observations about oil on water in the 18th century, but he didn't calculate the size of molecules. His work laid the groundwork for future scientists like Rayleigh.
  3. Rayleigh's experiment demonstrated that you don’t always need complex tools to make groundbreaking discoveries. Even simple experiments can provide valuable insights that inspire later research.

The Sequence Opinion #754: Generalist vs. Specialist: Which School Will Win in Mathematical AI

TheSequence • 35 implied HN points • 13 Nov 25
🕹 Technology Mathematics
  1. Generalist AI models can handle a wide range of math problems and can even score well on exams, but they struggle with creating new math concepts.
  2. Specialist AI models focus on specific math tasks and provide precise answers, but they have limits in flexibility and scope.
  3. Choosing between generalist and specialist models depends on the math task at hand, as each has its own strengths and weaknesses.

Beeping Booping Busy Beavers

Bram’s Thoughts • 157 implied HN points • 24 Nov 23
🔬 Science Mathematics
  1. Busy Beaver numbers are a classic example of a noncomputable function.
  2. Beeping Busy Beaver numbers grow faster by making states emit 'beeps'.
  3. Beeping Booping Busy Beaver is a new concept that involves beeps and boops in its output interpretation.

A very royal function

Logging the World • 199 implied HN points • 04 May 23
💾 History Mathematics
  1. Many royals in history have played a significant role in supporting and patronizing mathematics, creating environments where mathematicians could thrive and contribute to important work.
  2. Royal figures like Ptolemy I Soter and King Charles XII of Sweden had direct connections to mathematics, either through patronage or making contributions to the subject themselves.
  3. Monarchs like Queen Victoria and al-Mu'taman of Zaragoza have interesting mathematical connections and stories associated with them, showcasing how math and royalty intersected in various ways throughout history.

Four ways of thinking

Logging the World • 199 implied HN points • 28 Sep 23
🔬 Science Mathematics
  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.

Accessing the Bonus Content in Your Curriculum

Mathworlds • 196 implied HN points • 18 May 23
🚌 Education Mathematics
  1. Teachers find ways to access bonus content in the curriculum, going beyond what's expected.
  2. Good curriculum lets teachers offer bonus content to students through ingenuity and pedagogy.
  3. In engaging classrooms, students' ideas and thinking become the focus, essentially becoming the curriculum.

The Sequence Opinion #694: From Proof Engines to Polymaths: How AI Conquered the International Math Olympiad

TheSequence • 91 implied HN points • 30 Jul 25
🕹 Technology Mathematics
  1. AI has advanced significantly, now able to solve complex math problems at an Olympiad level. This shows how much smarter and capable AI has become.
  2. Recent competition results indicate that general AI models can perform creative problem-solving, moving beyond just following rules.
  3. The evolution of AI from specialized models to general-purpose ones highlights the rapid growth in technology and its potential applications.

Philosophy is the mathematics of language

Wood From Eden • 816 implied HN points • 23 Dec 23
📖 Philosophy Mathematics
  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.

The surreal line is topologically disconnected—or is it?

Infinitely More • 25 implied HN points • 15 Nov 25
📖 Philosophy Mathematics
  1. The surreal line can be seen as disconnected based on one way of thinking about connectedness. It's like having gaps that separate parts of a line.
  2. On another hand, if we consider how sets and classes differ, the surreal line appears connected. This means when viewed differently, those gaps can seem to vanish.
  3. Understanding these ideas helps explain why the surreal numbers are unique and fascinating, showing how different perspectives can change our view of mathematics.

(Ad-free Video) What's New in Science With Sabine and Lawrence | Fusion Dark Matter, String Theory in Biology, and Rapid Evolution

Critical Mass • 3 implied HN points • 13 Feb 26
🔬 Science Mathematics
  1. Future fusion reactors might produce axion-like particles through neutron–lithium reactions in their shielding, offering a new way to search for very light, weakly interacting dark-matter candidates.
  2. Quantum interference has been observed with clusters of thousands of atoms, pushing the boundary of everyday quantum effects and reigniting debate about whether wavefunction collapse is a real physical process.
  3. Cross-disciplinary methods are yielding surprises: string-theory math and AI are being applied to biological and mathematical problems, evidence suggests life rebounded faster after the Chicxulub impact, and some tumors can hijack nerve signaling to suppress local immunity.

Foundations of Physical Theory: Function of Models

Fields & Energy • 3 HN points • 02 Sep 24
🔬 Science Mathematics
  1. Models in physics help us understand complex ideas by simplifying them into more relatable forms. They allow us to reason about things we can't observe directly.
  2. It's important to consider the medium through which forces act, rather than just thinking of actions at a distance. This helps explain phenomena like electricity and magnetism more clearly.
  3. Using analogies can be helpful in learning new concepts, but we must be careful not to confuse them with the actual properties of the things we are studying.

About "artificial intuition"

Silicon Reckoner • 98 implied HN points • 11 Jan 24
🔬 Science Mathematics
  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.

Math Problems

The Better Letter • 157 implied HN points • 17 Mar 23
🔬 Science Mathematics
  1. Unlikely events happen more often than we realize, influencing outcomes in sports, investments, and life.
  2. Probability plays a significant role in determining outcomes, such as in coin tosses, NCAA brackets, and market predictions.
  3. Randomness, noise, and unpredictability are intrinsic to life, affecting decision-making and the way we perceive events.

GM Shaders Mini: Imagination

GM Shaders Mini Tuts • 157 implied HN points • 02 Sep 23
🕹 Technology Mathematics
  1. When working with shaders, think in terms of vector fields to direct the flow and create gradients.
  2. Consider the acceptable input domains and the output ranges of your functions to prevent errors and unexpected results.
  3. Utilize periodic functions for repetition, sine and cosine for waves and rotations, dot product as a ruler, and exponentiation for adjusting brightness levels.