The hottest Mathematics Substack posts right now

And their main takeaways
Category
Top Science Topics

Why are neural networks so powerful?

The Palindrome β€’ 1 implied HN point β€’ 11 Sep 23
πŸ”¬ Science Mathematics
  1. Neural networks are powerful due to their ability to closely approximate almost any function.
  2. Machine learning involves finding a function that approximates the relationship between data points and their ground truth.
  3. Approximation theory seeks to find a simple function close enough to a complex one by determining the right function family and precise approximation within that family.

SiΓͺu hacker

ThΓ‘i | Hacker | Kα»Ή sΖ° tin tαΊ·c β€’ 19 implied HN points β€’ 17 May 11
πŸ•Ή Technology Mathematics
  1. Software like MPlayer, Google Chrome, and VLC all use the FFmpeg library, which is also likely used in other devices like TVs and phones.
  2. Technologies such as Xen, VirtualBox, and Linux Kernel-based Virtual Machine utilize QEmu, with even cloud computing services like Amazon EC2 running on Xen.
  3. The International Obfuscated C Code Contest (IOCCC) showcases creative and complex C code snippets, with past winners achieving incredible feats like calculating massive prime numbers and building self-compiling compilers in minimal bytes.

120 Years of Game-Changing Genius: Celebrating John von Neumann's Birth

Phoenix Substack β€’ 1 HN point β€’ 13 Mar 23
πŸ•Ή Technology Mathematics
  1. John von Neumann was a brilliant mathematician and polymath who contributed significantly to various fields.
  2. Automated Moving Target Defense (AMTD) in cybersecurity involves constantly changing the system's attack surface to deter attackers.
  3. The minimax theorem from John von Neumann's game theories suggests that defenders should choose MTD strategies that minimize the maximum possible loss.
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Linear regression and the least squares problem

The Palindrome β€’ 0 implied HN points β€’ 12 Dec 23
πŸ”¬ Science Mathematics
  1. Linear regression can be optimized by hand, especially for single variable models where the loss function is simple.
  2. Gradient descent for linear regression can be like using a cannonball to shoot a sparrow, due to the simplicity of the loss function.
  3. Premium subscribers of The Palindrome can access exclusive content and chapters of 'Mathematics of Machine Learning' for an in-depth education.

Introduction to the Photon Lines Blog

Photon-Lines Substack β€’ 0 implied HN points β€’ 07 Jun 23
πŸ•Ή Technology Mathematics
  1. The blog focuses on providing visual and intuitive guides for understanding complex topics.
  2. The community is open to followers interested in software design, mathematics, physics, economics, business, and more.
  3. Content includes explanations on various complex subjects, insights into the universe, and book summaries.

Small follow-ons

Bram’s Thoughts β€’ 0 implied HN points β€’ 07 Dec 23
πŸ”¬ Science Mathematics
  1. Fermat's Last Theorem is a level 1 question that an ordinary Busy Beaver can answer.
  2. The Twin Primes Conjecture is a level 2 question requiring a level 2 Busy Beaver with access to a level 1 Busy Beaver oracle.
  3. Level 3 questions are more difficult and less common in mathematics compared to level 2 questions.

Is AlphaGeometry a dead end?

Silicon Reckoner β€’ 0 implied HN points β€’ 30 Jan 24
πŸ”¬ Science Mathematics
  1. AlphaGeometry uses AI to synthesize theorems and proofs in geometry.
  2. The environmental impact of training AI models for mathematics is a growing concern.
  3. Uncertain if AlphaGeometry will lead to significant advancements beyond standardized geometry.

More first order systems

Only Wonder Knows β€’ 0 implied HN points β€’ 24 Nov 23
πŸ”¬ Science Mathematics
  1. Linear time-invariant systems are characterized by impulse or step response and frequency response.
  2. Measurement of systems is done using step response and response to sinusoids of different frequencies.
  3. First order systems are characterized by gain at zero frequency and either time constant or corner frequency.

Wednesday Curiosity Links

Grist Potentia β€’ 0 implied HN points β€’ 07 Feb 24
πŸ”¬ Science Mathematics
  1. Today in history, G. H. Hardy was born - a famous mathematician known for his work in number theory.
  2. Genes may not be the complete blueprint for life as previously thought.
  3. Noise pollution is a significant environmental concern that needs attention.

Tuesday Curiosity Links

Grist Potentia β€’ 0 implied HN points β€’ 30 Jan 24
πŸ”¬ Science Mathematics
  1. Douglas Engelbart, a pioneer in computer technology, created the computer mouse and more innovations in human-computer interaction.
  2. Lessons from history's top R&D labs offer valuable insights for innovation.
  3. Implementing a 4-day workweek and cutting employee salaries by 20% helped a CEO save their company from layoffs.

Book Review: β€œThe Great Mental Models, Volume 3: Systems and Mathematics” by Farnam Street 4/5

Poczwardowski Notes β€’ 0 implied HN points β€’ 20 Oct 23
🚌 Education Mathematics
  1. Exploring topics like system thinking and mathematics can help us understand the world better, even if they are not commonly taught in schools.
  2. The book does a great job of explaining complex concepts like feedback loops and bottlenecks in systems, making them easier to comprehend and apply in real life.
  3. Understanding systems and mathematics not only enhances our knowledge of the world but also improves our decision-making process as a bonus.

Aaron Lee Master Framework Philosophic Foundations & Explanation Document

Autodidact Obsessions β€’ 0 implied HN points β€’ 17 Feb 24
πŸ“– Philosophy Mathematics
  1. The Aaron Lee Master Framework integrates various logical systems to understand language dynamics, emphasizing the contextual nature of meaning.
  2. Key components like Non-Monotonic Logic and Fuzzy Logic help in adjusting beliefs based on new information and dealing with gradations in meaning, respectively.
  3. The Framework's philosophical and logical foundations aim to provide a comprehensive model for the complexities of language and semantics by elucidating the emergence of meaning through interactions and context.

Polymath Engineer Weekly #83

Polymath Engineer Weekly β€’ 0 implied HN points β€’ 27 Feb 24
πŸ•Ή Technology Mathematics
  1. Deliberate practice is crucial for improvement. Practicing mindlessly can hinder progress by reinforcing existing habits instead of enhancing them.
  2. Understanding different programming paradigms like supervision trees in Erlang can be beneficial for managing state and processes effectively.
  3. The Black-Scholes/Merton equation, originating from physics, revolutionized finance with trillions of dollars at stake, showcasing the impact of cross-disciplinary knowledge.

Linear regression in multiple variables

The Palindrome β€’ 0 implied HN points β€’ 05 Mar 24
πŸ”¬ Science Mathematics
  1. Real datasets often have multiple features, going beyond a single variable. Understanding how to handle multiple variables is crucial in machine learning.
  2. Linear regression can be generalized to handle multiple variables by using a regression coefficient vector and a bias term.
  3. The parameters of a multivariable linear regression model help define a d-dimensional plane, providing a way to map feature vectors to target values in a straightforward manner.

Probabilistic Risk Assessment (PRA) 's growing popularity with regulators & industries - A behind the scenes view

Beyond Harm β€’ 0 implied HN points β€’ 06 Mar 24
πŸ”¬ Science Mathematics
  1. Probabilistic Risk Assessment (PRA) predicts the 'frequency' of industrial accidents, but this can be misleading as it does not reveal how soon the next accident might occur.
  2. PRA has limitations due to its optimistic bias, which leads to under-predicting accident rates because it ignores important factors like climate change and technology wear-out.
  3. An alternative to PRA would be using Prescriptive Protection Design Requirements, which have been historically successful in ensuring safety without relying on probability mathematics.

Mathematical Tools of Quantum Mechanics

Quantum Formalism β€’ 0 implied HN points β€’ 26 Oct 23
πŸ”¬ Science Mathematics
  1. Live lecture series on Hilbert spaces & Operators is open to everyone interested in quantum information science.
  2. Sessions will be held on Fridays at 4pm UK time; replays available on YouTube for those unable to attend live.
  3. Zaiku Group offers a chance to delve into quantum information science through a mathematical lens.

Differential Equations Review

Quantum Formalism β€’ 0 implied HN points β€’ 08 Sep 23
🚌 Education Mathematics
  1. The course on quantum hardware has prerequisite lectures on differential equations available on YouTube.
  2. There are just one or two more reviews on differential equations before delving into the quantum lectures.
  3. Late admission for the course is still possible through the Course Admission Form for those with limited mathematical background.

QF Community Microgrants

Quantum Formalism β€’ 0 implied HN points β€’ 27 May 23
πŸ’Ό Business Mathematics
  1. Applications for quantumformalism.com open-source microgrant scheme are now available on a rolling basis, allowing anyone to apply for $5k - $10k to develop open-source ideas
  2. The microgrant program seeks to fund bold ideas with strong mathematical aspects, providing PhD-level mathematicians as mentors, and is not interested in supporting incremental improvements to existing projects
  3. Proposals in specific technical themes and industries aligned with their interests have potential for longer-term funding/collaboration opportunities with the company

QF Learning Management System Exploration

Quantum Formalism β€’ 0 implied HN points β€’ 15 May 23
πŸ•Ή Technology Mathematics
  1. There is a plan to run more mathematics courses and applied topics relevant to mathematical courses to enhance the QF learning experience.
  2. The team is considering implementing a learning management system to provide QF learners with access to all courses in one place for a better asynchronous learning experience.
  3. A survey has been launched to gather feedback on the necessity of a learning management system and to explore open-source systems for customization and hosting.

Community update | March 13

Quantum Formalism β€’ 0 implied HN points β€’ 13 Mar 23
🚌 Education Mathematics
  1. A Category theory course tutorial was held, and the replay is now available on YouTube.
  2. There are plans to invite a guest speaker to discuss applying Category theory in Machine Learning after lecture six.
  3. The Measure Theory & Functional Analysis course will continue in April, focusing on infinite dimensional Hilbert spaces.

Lecture 1: Categories, Functors, & Naturality

Quantum Formalism β€’ 0 implied HN points β€’ 07 Mar 23
🚌 Education Mathematics
  1. Category theory is important in various fields like functional programming, formal verification, machine learning, and quantum information science.
  2. Connecting with experts like Brian Hepler can provide valuable insights and opportunities in mathematical research.
  3. The course emphasizes sharing knowledge and encouraging more people to learn the language of Category theory.

Category theory Mini-course

Quantum Formalism β€’ 0 implied HN points β€’ 24 Feb 23
🚌 Education Mathematics
  1. A six-lecture mini-course on Category theory is starting on March 6 to provide a solid basic understanding of categories.
  2. Registration is open for the mini-course session on Crowdcast, and the YouTube recording will be available if you can't attend live.
  3. There is a Discord channel dedicated to the Category theory course for further discussion and engagement.

Hello 2023!

Quantum Formalism β€’ 0 implied HN points β€’ 10 Jan 23
πŸ”¬ Science Mathematics
  1. The course will cover Measure Theory, Functional Analysis, and delve into infinite-dimensional Hilbert spaces.
  2. A crash course on Category Theory is planned, focusing on topics like Functors, Adjoint Functors, and its applications in various mathematical areas.
  3. A Quantum computing PoC microgrant scheme will be initiated, offering grants and mentorship to work on projects related to advanced mathematical topics.

Bring on 2023!

Quantum Formalism β€’ 0 implied HN points β€’ 19 Dec 22
🚌 Education Mathematics
  1. 2022 has been a fantastic year for the QF community, driving enthusiasm for abstract mathematical topics relevant to quantum computing.
  2. A course on Measure Theory & Functional Analysis (MTFA) is ongoing, beneficial for those interested in Continuous Variable Quantum Information and Machine Learning.
  3. QF plans to launch an open source quantum computing proof of concept microgrant program with a narrow focus on specific areas like classical-to-quantum data encoding.

Group theory 2022 course wrap up!

Quantum Formalism β€’ 0 implied HN points β€’ 13 Dec 22
🚌 Education Mathematics
  1. Certificates of completion were offered to regular attendees of the group theory course who have a baseline knowledge from certain lectures, preparing them for the next course on Lie Groups & Representations.
  2. The upcoming course on Lie Groups & Representations starting in January 2023 does not require completion of the previous crash courses, but having some baseline knowledge in certain areas is recommended for better understanding.
  3. After the Lie Groups & Representations course, there will be a virtual mini school focusing on practical applications such as quantum error correction, classical machine learning, and quantum machine learning.

Group theory study session today!

Quantum Formalism β€’ 0 implied HN points β€’ 18 Nov 22
🚌 Education Mathematics
  1. Group theory study session focusing on real matrix groups like O(n) and SO(n). These are examples of Lie groups.
  2. Upcoming group theory lectures will cover complex matrix groups: U(n) and SU(n), also Lie groups.
  3. A basic introduction to representation theory will be provided after wrapping up the group theory crash course.

Group theory session 18 invitation

Quantum Formalism β€’ 0 implied HN points β€’ 11 Nov 22
🚌 Education Mathematics
  1. Live group theory session 18 covers real matrix group topics and delves into complex groups next.
  2. Register for the session at the provided link or catch the replay on YouTube if you can't make it.
  3. The session promises to be informative and engaging for Quantum Formalists.

Group theory course update.

Quantum Formalism β€’ 0 implied HN points β€’ 17 Oct 22
🚌 Education Mathematics
  1. Learn about the application of group theory in Origami Modular Design from a talk by Bob Miller.
  2. Explore Representation Theory for Geometric Quantum Machine Learning in the upcoming Lie Groups & Representations course.
  3. Discover the lectures on Measure Theory & Functional Analysis available on YouTube, covering topics like real analysis, sigma algebras, measures, and Borel Measures.

Measure Theory and Functional Analysis

Quantum Formalism β€’ 0 implied HN points β€’ 19 Sep 22
🚌 Education Mathematics
  1. The MTFA course lectures have moved to a biweekly release format, so now they will be released every two weeks.
  2. Attend the webinar 'An Optimal Entanglement Distribution Policy for a Quantum Switch' happening on Monday, September 26, by registering at the provided link.
  3. The Quantum Formalism community offers various resources like a YouTube playlist, GitHub repository for homework and solutions, Discord channel, and a LinkedIn page.

Friday community updates.

Quantum Formalism β€’ 0 implied HN points β€’ 09 Sep 22
🚌 Education Mathematics
  1. Friday community updates include group theory live sessions covering various topics like cosets, index of subgroups, normal subgroups, and quotient groups.
  2. The upcoming Module II will focus on Lie Groups, Lie Algebras & Representations, following prerequisites like a crash course on Topology & Differential Geometry.
  3. Measure Theory & Functional Analysis Course offers valuable content on real analysis, Riemann's integration theory, sigma algebras, and solutions to assignments.

Topology review (suggestion)

Quantum Formalism β€’ 0 implied HN points β€’ 03 Sep 22
🚌 Education Mathematics
  1. Understanding the abstract definition of a topology on a set can help in comprehending sigma algebras, which can be generated from existing topologies like Borel sigma Algebras.
  2. MTFA offers a YouTube Playlist for reference: https://www.youtube.com/playlist?list=PL6N_Y7ao_aHtdzh1tgonK08g0Nx8Owjps.
  3. Joining the Discord channel provided allows participation in discussions and questions to the speakers, as well as checking out the QF LinkedIn page for more information.

Taking on OpenAI

Experiments with NLP and GPT-3 β€’ 0 implied HN points β€’ 11 Jun 23
πŸ•Ή Technology Mathematics
  1. Sama believes building foundational models to compete with OpenAI's ChatGPT is hopeless without significant investment.
  2. The current approach depends heavily on data and compute resources, which OpenAI has in abundance.
  3. The author plans to build foundational models using the KESieve algorithm, focus on math, involve students, and avoid traditional funding methods.