Top Mathematics discussions
NishMath - #general
|
@primes.utm.edu
//
This week saw a flurry of mathematical activity, highlighted by the 238th Carnival of Mathematics, organized by Aperiodical. The carnival showcases a variety of submissions and mathematical art, focusing on the number 238 itself. Noteworthy facts about 238 include that it is 2 × 7 × 17, the sum of the first 13 primes, and a "triprime". The carnival also encourages exploration beyond pure mathematics, with community members contributing insights linking the number to uranium isotopes, birth minutes, and even hexadecimal representations. It also shines a light on #MathArtMarch, with examples of crochet, coding, and painting from around the world.
Continuing the daily exploration of numbers, several interesting facts and events were highlighted for April 6th, 7th, 8th and 10th. The number 96, the 96th day of the year, was examined for its unique properties, such as being the smallest number expressible as the difference of two squares in four different ways. Events like Euler's first paper on partitions (April 7th, 1741) and Al-Biruni's observation of a solar eclipse in 1019 were also noted, linking mathematical concepts to historical contexts. Also, the number 97 has been noted as the 97th day of the year, where 97 is the largest prime that we can ever find that is less than the sum of square of its digits. In recreational mathematics, a "Salute" game for reinforcing multiplication and division was featured, emphasizing the inverse relationship between these operations. Additionally, the concept of "truncatable primes" was explored through a game where players create strings of prime numbers by adding digits to either end of a number. The number 91 was discussed as the 91st day of the year where 10 n + 91 and 10 n + 93 are twin primes for n = 1, 2, 3 and 4. Finally, highlighting mathematics beyond academia, James Abram Garfield, a former Congressman and mathematician, was mentioned for his original proof of the Pythagorean Theorem, illustrating the interdisciplinary nature of mathematics.
Share:
References :
Classification:
Terence Tao@What's new
//
Terence Tao has recently uploaded a paper to the arXiv titled "Decomposing a factorial into large factors." The paper explores a mathematical quantity, denoted as t(N), which represents the largest value such that N! can be factorized into t(N) factors, with each factor being at least N. This concept, initially introduced by Erdös, delves into how equitably a factorial can be split into its constituent factors.
Erdös initially conjectured that an upper bound on t(N) was asymptotically sharp, implying that factorials could be split into factors of nearly uniform size for large N. However, a purported proof by Erdös, Selfridge, and Straus was lost, leading to the assertion becoming a conjecture. The paper establishes bounds on t(N), recovering a previously lost result. Further conjectures were made by Guy and Selfridge, exploring whether relationships held true for all values of N. On March 30th, mathematical enthusiasts celebrated facts related to the number 89. Eighty-nine is a Fibonacci prime, and patterns emerge when finding it's reciprocal. Also, the number 89 can be obtained by a summation of the first 5 integers to the power of the first 5 Fibonacci numbers. 89 is also related to Armstrong numbers, which are numbers that are the sum of their digits raised to the number of digits in the number.
Share:
References :
Classification:
@The Cryptography Caffe? ?
//
The UK's National Cyber Security Centre (NCSC) has released a roadmap for transitioning to post-quantum cryptography (PQC), establishing key dates for organizations to assess risks, define strategies, and fully transition by 2035. This initiative aims to mitigate the future threat of quantum computers, which could potentially break today's widely used encryption methods. The NCSC’s guidance recognizes that PQC migration is a complex and lengthy process requiring significant planning and investment.
By 2028, organizations are expected to complete a discovery phase, identifying systems and services reliant on cryptography that need upgrades, and draft a migration plan. High-priority migration activities should be completed by 2031, with infrastructure prepared for a full transition. The NCSC emphasizes that these steps are essential for addressing quantum threats and improving overall cyber resilience. Ali El Kaafarani, CEO of PQShield, noted that these timelines give clear instructions to protect the UK’s digital future. Researchers have also introduced ZKPyTorch, a compiler that integrates ML frameworks with ZKP engines to simplify the development of zero-knowledge machine learning (ZKML). ZKPyTorch automates the translation of ML operations into optimized ZKP circuits and improves proof generation efficiency. Through case studies, ZKPyTorch successfully converted VGG-16 and Llama-3 models into ZKP-compatible circuits.
Share:
References :
Classification:
|
Blogs
|