The hottest Mathematics Substack posts right now

And their main takeaways
Category
Top Science Topics

Lecture 7 Invitation

Quantum Formalism • 0 implied HN points • 28 Oct 20
🚌 Education Mathematics
  1. The lecture will cover core topics such as Vector Space Isomorphisms, Product of Operators, and Invertible Operators.
  2. Participants are encouraged to attend live sessions to ask questions and keep up with the increasing level of abstraction.
  3. The upcoming session will introduce complex matrices and move towards working with Hilbert spaces.

Lecture 05

Quantum Formalism • 0 implied HN points • 16 Oct 20
🚌 Education Mathematics
  1. Key concepts in the session included linear independence
  2. The lecture covered the topic of bases (Hamel)
  3. The importance of dimensions in complex vector spaces was emphasized

Lecture #04

Quantum Formalism • 0 implied HN points • 09 Oct 20
🚌 Education Mathematics
  1. Introduction to complex vector spaces was covered in this live session.
  2. Key concepts included Additive Groups Axioms, Field Axioms, and Complex Vector Space Axioms.
  3. Various topics like Linear Subspaces, Linear Combinations, and Dirac Notation were also discussed.

Newcomers Invitation to Lecture #4

Quantum Formalism • 0 implied HN points • 05 Oct 20
🚌 Education Mathematics
  1. New subscribers are warmly welcomed to attend a live session on complex vector spaces by following specific steps.
  2. To attend, new subscribers need to fill out a Google form for verification and should cover basics about rings and fields from the previous session.
  3. The Zaiku Group team expresses gratitude to the newcomers and provides guidance for joining future sessions.

Lecture #03

Quantum Formalism • 0 implied HN points • 02 Oct 20
🚌 Education Mathematics
  1. The lecture covered topics like rings, fields, and complex vector spaces.
  2. Specific topics included Ring Axioms, Integral Domains, and the 2x2 Complex Matrix Ring.
  3. An update was made to a slide regarding commutators in the session.
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Group Commutator Warning + Chat Community Volunteers

Quantum Formalism • 0 implied HN points • 27 Sep 20
🚌 Education Mathematics
  1. When computing the commutator, be cautious of existing software packages using a different formula than the group commutator defined in the lecture.
  2. Consider having community volunteers help moderate lectures to ensure smooth discussions and aid in clarifying concepts for others.
  3. Participants volunteering in the community will receive rewards such as a special badge and priority selection as hosts for fireside chats with industry and academia guests.

Lecture #2: A Brief Introduction to Group Theory

Quantum Formalism • 0 implied HN points • 26 Sep 20
🚌 Education Mathematics
  1. The lecture provided a basic introduction to Group Theory, catering to those unfamiliar with the subject and uncomfortable with mathematical abstraction.
  2. The session covered important group-theoretic concepts like Binary Operations on Sets and Group Theory Axioms.
  3. The upcoming Matrix Groups section will delve into more complex topics like GL(2, C) Commutator.

Last chance to register for live lecture #2!

Quantum Formalism • 0 implied HN points • 24 Sep 20
🚌 Education Mathematics
  1. The live lecture features abstract algebra and requires knowledge of complex numbers for participation.
  2. It is important to watch or attend the previous lecture to understand set theoretic conventions for the upcoming session.
  3. The Zaiku Group team advises viewers to make sure they are prepared and up to speed on the necessary materials for the live lecture.

Mathematical Abstraction Survey

Quantum Formalism • 0 implied HN points • 12 Sep 20
🔬 Science Mathematics
  1. A pre-lecture survey on mathematical abstraction is available to help adjust content and approach for the upcoming live session.
  2. Those attending the live session can look forward to it happening next Friday.
  3. For those not able to attend, there is the option to subscribe to the YouTube channel where the live session recording will be uploaded.

Influential Mathematicians:  Évariste Galois

Quantum Formalism • 0 implied HN points • 08 Sep 20
🔬 Science Mathematics
  1. Evarist Galois developed Galois Theory, revolutionizing abstract algebra, despite facing personal struggles and tragedy in his life.
  2. Group Theory, inspired by Galois' work, plays a crucial role in quantum formalism, with concepts like unitary operators forming a group structure.
  3. Although Galois didn't directly contribute to quantum formalism, his mathematical legacy continues to influence and shape modern mathematical frameworks.

Influential Mathematicians: Frigyes Riesz

Quantum Formalism • 0 implied HN points • 15 Jul 20
🔬 Science Mathematics
  1. Frigyes Riesz was a significant mathematician who made key contributions to functional analysis and operator theory, impacting areas like physics and Hilbert spaces.
  2. His work, including the Riesz-Fischer theorem, influenced the development of quantum theory, showing the unitary equivalence of different quantum theories.
  3. Riesz is known for foundational work in Functional Analysis, which is crucial for the mathematical formalism of quantum mechanics, and concepts like Dirac's bracket notation make sense thanks to Riesz representation theorem.

Influential Mathematicians: Emmy Amalie Noether

Quantum Formalism • 0 implied HN points • 29 Jun 20
🔬 Science Mathematics
  1. Emmy Noether, despite facing discrimination as a woman in academia, made significant contributions to mathematics and physics.
  2. Noether's work in invariant theory and abstract algebra, along with her collaborations, influenced the development of advanced algebraic tools used in treating quantum formalism.
  3. Noether played a mentorship role in shaping the career of another influential female mathematician, Grete Hermann, who made important contributions to the foundations of quantum mechanics.

Influential Mathematicians: David Hilbert

Quantum Formalism • 0 implied HN points • 11 Jun 20
🔬 Science Mathematics
  1. David Hilbert's contributions to geometry and axiomatic methods influenced mathematics and physics significantly.
  2. Though Hilbert didn't directly work on quantum mechanics, his foundational work on integral equations paved the way for the development of quantum formalism.
  3. Hilbert's interest in applying axiomatic methods to physics led to his famous 'Sixth Problem,' advocating for treating physics with mathematical axioms.

There's Math Behind Dobble

tbg/public • 0 implied HN points • 16 Mar 24
🔬 Science Mathematics
  1. Dobble game uses math with 55 cards having a single common symbol when paired.
  2. Having fewer symbols affects deck size in the game, leading to balanced card distribution.
  3. Dobble's structure is related to finite projective planes, creating a symmetrical large deck.

Issues with MATH()

The Irregular Voice • 0 implied HN points • 01 Apr 24
🔬 Science Mathematics
  1. Some math problems in the MATH() dataset have incorrect answers marked during evaluation, possibly due to bugs in question generation or solution calculation code.
  2. Certain math problems in the MATH() dataset are overly complex, requiring lengthy computations or involving very large numbers, making them challenging for un-augmented language models.
  3. The MATH() dataset includes math problems with arithmetic or factorization involving extremely large numbers, which may not accurately test a language model's mathematical reasoning ability.

A history of elliptic curves in tweets

Thái | Hacker | Kỹ sư tin tặc • 0 implied HN points • 04 Sep 20
💾 History Mathematics
  1. The history of elliptic curves dates back to the work of prominent mathematicians like Kepler, Newton, and Leibniz, who laid the foundation for further exploration.
  2. Various mathematicians such as Bernoulli, Liouville, and Legendre made significant contributions to understanding elliptic integrals and functions, paving the way for further advancements in mathematics.
  3. Elliptic curves have not only played a crucial role in mathematics but also in modern cryptography, where figures like Diffie-Hellman and NSA have explored their encryption capabilities.

On studying mathematics

Thái | Hacker | Kỹ sư tin tặc • 0 implied HN points • 20 Aug 19
🚌 Education Mathematics
  1. Studying math is essential for various fields, as it offers a unique competitive advantage and is necessary for understanding complex systems and solving real-world problems.
  2. Math is not just about calculations, it's about beauty and joy. It allows you to explore the wonders of the universe and engage in mental games that have intrigued brilliant minds for centuries.
  3. Despite common negative experiences with math education, anyone can learn math and discover its beauty. Approach it with an open mind, and you might find yourself amazed by its elegance and power.

Giải trí^H^H^Htoán cuối tuần

Thái | Hacker | Kỹ sư tin tặc • 0 implied HN points • 06 Jun 16
🔬 Science Mathematics
  1. The author recalls enjoying solving math problems as a child but never had one published, reminiscing about a math professor who is now a professor in the US
  2. The author recently discovered a math test and attempted to solve a problem involving finding integer solutions and another that required rearranging numbers in a specific way, providing multiple solutions
  3. The author shares a strategy for rearranging numbers to satisfy a given condition, showcasing a step-by-step approach to solve the problem and inviting readers to explore different methods

Diffie & Hellman win the Nobel prize of computer science, yay!

Thái | Hacker | Kỹ sư tin tặc • 0 implied HN points • 02 Mar 16
🕹 Technology Mathematics
  1. Diffie & Hellman won the Nobel prize in computer science for their groundbreaking work in cryptography.
  2. Their invention of Diffie-Hellman is a crucial component of internet security, used when connecting to major platforms like Google and Facebook.
  3. Despite its complexity, the math trick behind Diffie-Hellman is surprisingly simple and has remained unsolved for over 40 years.

$(-1)^2$

Thái | Hacker | Kỹ sư tin tặc • 0 implied HN points • 10 Jan 16
🔬 Science Mathematics
  1. Imaginary numbers like $i$ are not real because there isn't a real number whose square is -1, pushing the boundaries of mathematical concepts beyond reality.
  2. The rule stating that multiplying two negative numbers results in a positive number, like $(-1) * (-1) = +1$, is a construct by mathematicians to maintain consistency in arithmetic.
  3. Mathematicians create and manipulate rules in pure math to explore interesting results and sometimes stumble upon practical applications, demonstrating the power of abstraction in mathematics.

$i^i$

Thái | Hacker | Kỹ sư tin tặc • 0 implied HN points • 10 Jan 16
🔬 Science Mathematics
  1. The imaginary number $i$ has a square of $-1$ and when raised to the power of $i$, it yields approximately 0.2, an unexpected real number result.
  2. Euler's identity is a beautiful and seemingly magical equation that involves $e$, $i$, $ extit{ extbf{ extgreek{π}}}$, $0$, and $1$, which are all fundamental mathematical constants.
  3. Leonhard Euler, a prolific mathematician, produced an incredible amount of work under challenging circumstances, with impressive achievements and contributions to mathematics.

Đường đến Galois

Thái | Hacker | Kỹ sư tin tặc • 0 implied HN points • 04 Nov 15
🔬 Science Mathematics
  1. When working with polynomial equations with complex roots, Galois theory provides a powerful tool to understand and solve them.
  2. Field extensions, such as adding roots of numbers to the rational field, play a key role in finding all roots of a polynomial.
  3. Galois theory reveals the importance of group theory in understanding the symmetries and roots of polynomial equations.

Từ đại số đến Bitcoin: 26, Fermat và tôi

Thái | Hacker | Kỹ sư tin tặc • 0 implied HN points • 15 Jul 14
🔬 Science Mathematics
  1. 26 is a unique natural number sandwiched between a square and a cube, a discovery by Fermat, a notable French mathematician.
  2. Euler's proof on Fermat's equation $y^2 = x^3 - 2$ showcases the power of abstract algebra and group theory in solving complex mathematical problems.
  3. Understanding algebraic structures like groups, rings, and unique factorization plays a crucial role in various fields, from cryptography to machine learning.

Google End-To-End

Thái | Hacker | Kỹ sư tin tặc • 0 implied HN points • 08 Jun 14
🕹 Technology Mathematics
  1. The creation of the End-To-End email encryption program involved significant effort and collaboration, highlighting the importance of teamwork in large software projects.
  2. Working on projects like encryption libraries can lead to gaining a wealth of new knowledge and skills through the experience.
  3. Understanding mathematical concepts like elliptic curve cryptography and number theory is crucial for creating secure encryption systems.

Từ đại số đến bitcoin

Thái | Hacker | Kỹ sư tin tặc • 0 implied HN points • 19 Dec 13
🕹 Technology Mathematics
  1. The concept of digital currency evolved from early versions like creating symbolic money during childhood games.
  2. Digital signatures like RSA and blind signatures by Chaum helped ensure anonymity and prevent double-spending in electronic transactions.
  3. DigiCash, founded by Chaum, aimed to make digital currency a payment tool but faced challenges due to dependence on banks and lack of competition with credit cards.

Thử nghiệm MathJax

Thái | Hacker | Kỹ sư tin tặc • 0 implied HN points • 26 Sep 13
🔬 Science Mathematics
  1. The author discovered MathJax as a way to write mathematical formulas on the web, finding it visually appealing on Chrome in Linux.
  2. MathJax seemed to not work on Chrome in Android, prompting the author to wonder about its functionality on other platforms and browsers.
  3. The post includes mathematical formulas like Cauchy-Schwarz inequality, Fermat's little theorem, and Euler's beautiful identity, showcasing the use and testing of MathJax for such expressions.

Phép chia dài

Thái | Hacker | Kỹ sư tin tặc • 0 implied HN points • 23 Sep 13
🚌 Education Mathematics
  1. Estimating the first digit of the quotient in long division can help reduce the number of calculations needed.
  2. Understanding Knuth's Long Division algorithm can aid in efficiently performing arithmetic operations on large integers.
  3. Choosing a smart value for the base when dividing large numbers can lead to more accurate estimations and fewer operations required.

Solutions manual for NTB - 3.3. Basic integer arithmetic

Thái | Hacker | Kỹ sư tin tặc • 0 implied HN points • 26 Jul 09
🚌 Education Mathematics
  1. The algorithm in Exercise 3.31 can efficiently determine if a given integer is a perfect power and compute its pair in a short amount of time.
  2. In the algorithm from the previous exercise, a more careful implementation can significantly reduce the total running time by decreasing the time each loop iteration takes.
  3. It is possible to convert between base-10 representation and the internal representation of an integer efficiently and quickly as shown in Exercise 3.32.

Solutions manual for NTB - 1.1 Divisibility and primality

Thái | Hacker | Kỹ sư tin tặc • 0 implied HN points • 07 Jul 09
🚌 Education Mathematics
  1. Check for divisibility between two numbers by comparing their multiples with another common multiple, often using integers.
  2. Composite integers have prime divisors that are less than or equal to the square root of the composite integer.
  3. The number of multiples of a given integer within a specified interval can be calculated using floor functions and division.

Solutions manual for "A computational introduction to number theory and algebra"

Thái | Hacker | Kỹ sư tin tặc • 0 implied HN points • 07 Jul 09
🚌 Education Mathematics
  1. The book "A computational introduction to number theory and algebra" is recommended as an excellent resource for those interested in number theory, algebra, and cryptography, particularly from a computer science perspective.
  2. The book emphasizes computational aspects, presents algorithms, and discusses complexity analysis, making it a valuable resource for cryptography applications.
  3. The author has created a solutions manual for some chapters of the book, focusing on exercises related to basic properties of integers, congruences, and computing with large integers.

Eric Weinstein Members' Q&A

The Bigger Picture • 0 implied HN points • 30 Apr 20
🎙 Podcasts Mathematics
  1. In the Q&A, Eric Weinstein discusses various topics, including the failures of the governing class during the current crisis.
  2. He also shares his passion for mathematics with Rebel Wisdom members.
  3. To access the full post, readers can start a 7-day free trial of The Bigger Picture.

On Humans And Our Love of Data

The Digital Anthropologist • 0 implied HN points • 16 Sep 23
🔬 Science Mathematics
  1. Our brains love patterns, math, and language to comprehend the world and shape realities.
  2. Humans have a deep-rooted history of creating, analyzing, and utilizing data for various purposes throughout civilizations.
  3. Data, when transformed into information and knowledge, holds significant value and potential for enhancing human evolution and species advancement.

Deep-Tech Newsletter | August 2022.

Deep-Tech Newsletter • 0 implied HN points • 08 Aug 22
🕹 Technology Mathematics
  1. Researchers successfully attacked the SIKE encryption algorithm using classical methods, raising questions about other potential vulnerabilities in post-quantum cryptography.
  2. Understanding advanced mathematics is crucial for analyzing and implementing secure cryptographic standards.
  3. Zaiku Group is launching a community course on Measure Theory and Functional Analysis, valuable for those interested in quantum information and related fields.

Deep-Tech Newsletter | July 2022

Deep-Tech Newsletter • 0 implied HN points • 14 Jul 22
🕹 Technology Mathematics
  1. NIST announced post-quantum cryptography standards, setting a foundation for a transition to secure systems resistant to quantum computer attacks in the future.
  2. Zaiku Group initiated a mentorship program for young mathematicians to transition from academia to industry, offering resources, mentorship, and work placements.
  3. Zaiku Group is sponsoring the LOGML Summer School, emphasizing the synergy between modern Geometry and Machine Learning.

Deep-Tech Newsletter | October 2021

Deep-Tech Newsletter • 0 implied HN points • 22 Oct 21
🕹 Technology Mathematics
  1. The quantum computing industry is still in early stages, needing high-risk R&D investment with a long-term return on investment timeline of 15-20 years, potentially conflicting with traditional VC investment cycles.
  2. Rigetti's $1.5bn SPAC could lead to more SPACs by companies with similar qubit technologies, and there might be a shift for quantum software companies to join the trend.
  3. The Quantum Formalism Community focuses on teaching advanced mathematics to STEM professionals, aiming to bridge academia and industry, offering opportunities like Industry Career Fellowship and a Deep-Tech Incubator.

Deep-Tech Newsletter #03 | July 2021

Deep-Tech Newsletter • 0 implied HN points • 14 Jul 21
🕹 Technology Mathematics
  1. Topology is a modern branch of pure mathematics with applications in Topological Data Analysis and Topological Quantum Computation.
  2. The crash course on Topology is suitable for individuals with a background in university-level mathematics like Calculus and Real Analysis.
  3. The Zaiku Group is planning a quantum fellowship program for top students who graduate from their courses.