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 β€’ 373 implied HN points β€’ 26 May 23
🚌 Education Mathematics Teaching Learning Abstract
  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.

Edge colourings and Archimedean lattices

A Piece of the Pi: mathematics explained β€’ 24 implied HN points β€’ 18 Feb 24
πŸ”¬ Science Mathematics Graphs Symmetry
  1. Edge colorings of graphs are not just recreational, but have practical applications in quantum technology.
  2. Graphs can be colored either by edges or by vertices, with different requirements for each coloring approach.
  3. Vizing's Theorem states that a graph can be edge colored with either the maximum degree or the maximum degree plus one colors.

Introducing QF Cities

Quantum Formalism β€’ 39 implied HN points β€’ 20 Jan 24
🚌 Education Mathematics Community Building
  1. QF Cities is an initiative by Quantum Formalism to create local hubs for learning math and quantum information science.
  2. They are looking for volunteers to run QF programs in their cities and require proof of at least ten participants to request sponsorship.
  3. The timelines for the QF Cities program include an application deadline of March 22 and a kickstart date of June 21.

GM Shaders Mini: Imagination

GM Shaders Mini Tuts β€’ 157 implied HN points β€’ 02 Sep 23
πŸ•Ή Technology Graphics Programming Mathematics Algorithms Tutorials
  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.
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A formal language for first-order predicate logic

Infinitely More β€’ 15 implied HN points β€’ 02 Mar 24
🚌 Education Mathematics Logic Philosophy Semantics
  1. A formal language for first-order predicate logic involves understanding the basic syntax, terms, variables, and structure interpretations.
  2. Signatures in structures specify the elements like relations, functions, and constants in a mathematical structure, detailing their features and meanings.
  3. Mathematics uses a wide array of first-order structures to study various concepts like orders, graphs, groups, and more, unifying different mathematical investigations.

The surreal numbers

Infinitely More β€’ 41 implied HN points β€’ 06 Jan 24
πŸ”¬ Science Mathematics Numbers Recursion
  1. The surreal numbers unify various number systems into one comprehensive system.
  2. Surreal numbers are generated through a recursive process of completion and ordering.
  3. The surreal number generation rule involves separating existing numbers into lower and upper sets to create new numbers.

Lattices

Infinitely More β€’ 33 implied HN points β€’ 17 Jan 24
πŸ”¬ Science Mathematics
  1. A lattice is an order relation where every pair of elements has a least upper bound and a greatest lower bound.
  2. In lattices, the join of two elements is the larger of them and the meet is the smaller of them.
  3. Every linear order, set of positive integers, Boolean algebra, and field of sets can be considered lattices.

Distinguishing mathematical structures by their theories

Infinitely More β€’ 15 implied HN points β€’ 24 Feb 24
πŸ”¬ Science Mathematics Logic
  1. With first-order logic, subtle features can help distinguish mathematical structures from similar alternatives.
  2. Different mathematical structures can be differentiated by how symbols are interpreted in each structure, revealing unique properties.
  3. Finding statements in the language of orders that are true in one structure and false in others can help distinguish mathematical structures.

Strong Students Aren't Always Ready for More

Pershmail β€’ 137 implied HN points β€’ 07 Aug 23
🚌 Education Mathematics Teaching Learning Child development Curriculum
  1. Strong students may not always be ready for more challenging material.
  2. Mathematics education is not a one-size-fits-all journey, some students have specific areas of interest and may not be ready for broader mathematical growth.
  3. Kids may have peaks of interest in specific mathematical topics, and that's completely normal, parents should be aware of this and educator should offer real challenges to help them grow.

A very royal function

Logging the World β€’ 199 implied HN points β€’ 04 May 23
πŸ’Ύ History Mathematics Contributions
  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.

Corridor numbers, Fibonacci numbers, and Pascal’s triangle

A Piece of the Pi: mathematics explained β€’ 12 implied HN points β€’ 25 Feb 24
πŸ”¬ Science Mathematics Geometry Chess
  1. Corridor numbers count ways to take diagonal steps down a corridor with fixed width. The numbers in each box form Fibonacci numbers when summed vertically.
  2. Fibonacci sequence is generated by summing the previous two terms. In the context of corridor numbers, Fibonacci numbers represent different routes to specific boxes.
  3. Pascal's triangle has rows starting and ending with 1, where each entry is the sum of two nearest entries from the row above. Circular Pascal arrays relate to corridor numbers and can produce Fibonacci numbers when subtracting specific entries.

Math for kids outside of the Calculus Sequence

Kids Who Love Math β€’ 111 HN points β€’ 07 Aug 23
🚌 Education Mathematics Learning Teaching Resources
  1. There's a clear path from arithmetic to calculus in math education, but kids who advance too quickly may face challenges in a traditional school setting.
  2. Instead of just accelerating through the math curriculum, consider enrichment to explore topics outside the typical sequence like statistics, probability, and mathematical finance.
  3. Parents can support their kids in exploring enrichment math by learning alongside them, finding tutors or math circles, and utilizing resources like books and educational videos.

An algebra of orders

Infinitely More β€’ 17 implied HN points β€’ 04 Feb 24
πŸ”¬ Science Mathematics Algebra Operations
  1. There is a rich algebra of orders involving operations like addition and multiplication.
  2. The disjoint sum operation creates a combined order without interactions between the two parts.
  3. The ordered sum operation combines two orders by placing one above the other, creating new orders with distinct properties.

Chaos train and monkey madnessβ€”fun with quantifiers

Infinitely More β€’ 12 implied HN points β€’ 19 Feb 24
🚌 Education Logic Language Mathematics Semantics Exercises
  1. First-order predicate logic provides a formal language and semantics capable of expressing fine distinctions and shades of meaning.
  2. Understanding quantifiers, such as βˆƒ and βˆ€, is crucial in first-order logic as they allow one to make statements like 'there is an x such that Ο†' or 'every x has property Ο†.'
  3. Engaging in logic puzzles and practice can help in developing a deeper comprehension of first-order logic concepts and their applications.

Math Problems

The Better Letter β€’ 157 implied HN points β€’ 17 Mar 23
πŸ”¬ Science Mathematics Probability Sports Psychology Economics
  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.

The edge of reason

Logging the World β€’ 219 implied HN points β€’ 28 Dec 22
πŸ”¬ Science Mathematics Models Analogies Limitations Uncertainty
  1. When adding numbers, there are basic properties like getting another number, having a special zero that doesn't change sums, and having partners that return to zero when added.
  2. Mathematicians use abstraction to find essential properties, like in groups, to study various systems efficiently and effectively.
  3. Seeking historical analogies in current events can be misleading; it's important to understand the limitations of models and not be overconfident in applying mathematical rules to real-world situations.

WELCOME!

Silicon Reckoner β€’ 117 implied HN points β€’ 03 Jul 23
πŸ”¬ Science Mathematics AI Technology Research Ideology
  1. There has been a surge in newsletter subscriptions after being mentioned in a New York Times article.
  2. There are concerns about the relationship between AI, mathematics, and industries like tech and defense.
  3. Articles in the newsletter cover topics such as the conflict between mathematics and computing, the goals of mathematics, and AI's impact on mathematical reasoning.

What's on your mind?

Kids Who Love Math β€’ 83 implied HN points β€’ 16 Aug 23
🚌 Education Mathematics Learning
  1. The author is curious about your thoughts and questions related to teaching math to kids
  2. The author shares information about their kids' math education and current activities
  3. The author is open to sharing book highlights and is interested in knowing if you'd like to read about them

Math for Software Engineering[Math Mondays]

Technology Made Simple β€’ 139 implied HN points β€’ 21 Mar 23
πŸ•Ή Technology Mathematics Software Engineering Data Analysis Algorithms Machine Learning
  1. Linear Algebra is crucial for software engineers, especially for operations involving vector and matrix operations. Understanding the basics is key for most developers.
  2. Probability and Statistics play a significant role in analyzing data, and even non-AI professionals can benefit from grasping concepts like causal inference. Focus on foundational principles before diving deeper.
  3. Calculus, though important, may not be essential for all software engineers. Studying up to Calc-2 is generally adequate, as it appears in various other topics.

Applications of induction

Infinitely More β€’ 5 implied HN points β€’ 13 Mar 24
🚌 Education Mathematics Games Numbers
  1. Induction is about the impossibility of minimal counterexamples, and it comes in various forms like common induction and strong induction.
  2. Flexible use of induction is key - choose the valid form that best fits your proof.
  3. Differentiate between examples and proofs - examples can provide insight but don't prove universal statements.

The countable random graph

Infinitely More β€’ 10 implied HN points β€’ 10 Feb 24
πŸ”¬ Science Mathematics Graph Theory
  1. A countable random graph is a graph where you flip a coin to decide the edges between vertices in an infinite set, and the result is the same graph almost every time.
  2. Graph theory is a complex subject with beautiful theorems, and different notions of graphs exist, such as directed graphs and simple graphs.
  3. In mathematics, there are variations in graph definitions, such as allowing reflexivity or multiple edges, but in simpler contexts, graphs are typically referred to as simple graphs.

Review of "Mathematica" by David Bessis

Silicon Reckoner β€’ 117 implied HN points β€’ 09 Mar 23
πŸ“š Literature Mathematics Books Authors Philosophy Metaphor
  1. The book 'Mathematica' by David Bessis emphasizes the idea that everyone is already an accomplished mathematician, promoting awakening and emancipation from misconceptions about math.
  2. Mathematics is viewed as a sensual and carnal experience by mathematicians like Bill Thurston, focusing on understanding over logical reasoning.
  3. The concept of 'elephantitude' in the book highlights the importance of human understanding in mathematics, contrasting with the focus on reasoning in technology like deep learning.

2x2 games will change your life

Wyclif's Dust β€’ 7 HN points β€’ 24 Feb 24
🚌 Education Game Theory Mathematics Social Sciences Economics Theory
  1. Mathematics can change the way you think by showing how words correspond to underlying structures.
  2. 2x2 games, like the Prisoner's Dilemma, are simple models that offer powerful insights into cooperation, trade, and decision-making.
  3. Understanding game theory, particularly 2x2 games, can help in analyzing real-world scenarios such as economics, politics, and social interactions.

Christmas chocolates, plus UK COVID data, week starting 5th December 2022

Logging the World β€’ 159 implied HN points β€’ 08 Dec 22
πŸ₯ Health & Wellness Covid data Mathematics
  1. The author discusses using mathematical and statistical concepts to understand real-world situations, including analyzing Christmas chocolates.
  2. The UK COVID data from late 2022 shows a notable increase in hospital admissions, but the rate of growth is not as alarming as in previous waves.
  3. Various data plots highlight slow increases in COVID cases and hospital admissions, indicating a less rapid growth compared to past variant-driven waves.

Mathematical induction

Infinitely More β€’ 10 implied HN points β€’ 30 Jan 24
🚌 Education Mathematics Proofs
  1. Mathematical induction is a fundamental principle in mathematics, used to prove many fundamental facts in arithmetic and number theory.
  2. The common induction principle states that if a set of natural numbers contains 0 and whenever n is in the set, n+1 is also in the set, then every natural number is in the set.
  3. Strong induction allows the induction step to use multiple smaller numbers to prove a statement, and can be proven from the least-number principle.

Do Large Language Models have a "Reasoning Gap"?

The Irregular Voice β€’ 2 HN points β€’ 01 Apr 24
πŸ•Ή Technology AI Data Machine Learning Experiments Mathematics
  1. Large Language Models (LLMs) may not always exhibit true reasoning abilities, with a potential reliance on memorization instead of learning general techniques.
  2. Synthetic data generation systems like MATH() can be used to explore the reasoning capabilities of LLMs, but may introduce biases if not carefully analyzed and corrected for errors.
  3. Fine-tuning LLMs on specific problem areas can reveal insights into their reasoning abilities, but challenges with longer solutions and complex problem sets may impact performance.

The Network Effect- The phenomenon enabling trillion dollar social media industry [Math Mondays]

Technology Made Simple β€’ 79 implied HN points β€’ 20 Jun 23
πŸ•Ή Technology Mathematics Business Social media Software Engineering
  1. The Network Effect refers to a concept where the value of a product/service increases as more people use it, making the network more valuable for each participant.
  2. The power of the Network Effect can be understood mathematically; as more individuals join a network, the connections exponentially increase, making the system more useful for outsiders.
  3. Businesses/systems built around the Network Effect are powerful due to factors like increased value with more users, a growing network, and the ability to reshape industries and drive innovation.

New words #5

Mutual Information β€’ 39 implied HN points β€’ 22 Sep 23
🚌 Education Language Science Mathematics Medicine History
  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.