Latest news with #mathematics
Daily Mail
a day ago
- Entertainment
- Daily Mail
Blueprints by Marcus Du Sautoy: Every artist is actually just a good mathematician
Blueprints by Marcus Du Sautoy (Fourth Estate £22, 304pp) The pairing of art and mathematics, as Marcus Du Sautoy writes on the first page of his absorbing new book, would seem for many 'synonymous with chalk and cheese. A contradiction in terms.' Maths inhabits a realm of cold logic; the arts, one of emotional expression. Yet Du Sautoy will have none of this. Maths has its own aesthetic. He quotes approvingly the mathematician G.H. Hardy, who once wrote that, 'Beauty is the first test: there is no permanent place in this world for ugly mathematics.' Recent research has shown that, when mathematicians encounter maths they consider beautiful, a part of their brain lights up. It's the same part activated in non-mathematicians looking at art or listening to music that they appreciate. Du Sautoy contends that the fundamental structures underpinning artistic creativity are mathematical. He calls them blueprints. Artists may not always know it but they are 'secret mathematicians'. The strong connections between music and maths have frequently been acknowledged. Two of the greatest classical composers were obsessed by numbers. According to Du Sautoy, Mozart's opera The Magic Flute is 'dripping with maths'. The repeated use of groups of three in the story is only the most obvious of many numerical patterns the composer employed. J.S. Bach had his own obsession – with the number 14 – and wove it everywhere into his music. However, it is not just music that is shaped by mathematics. So too are other arts. In architecture, the villas designed in the 16th century by Andrea Palladio have been described as 'frozen music'. They could equally be called 'frozen mathematics', since they make ingenious use of geometric theory. In the 20th century, the tower block known as L'Unite d'Habitation, designed by the Swiss-French architect Le Corbusier, has measurements based on a sequence of numbers he devised. Each number in the sequence is the sum of the two previous numbers. This is familiar to mathematicians, who know it as the Fibonacci sequence. Du Sautoy finds his blueprints wherever he looks in creative endeavour. In the visual arts, he notes that the abstract works of Jackson Pollock were examples of an important mathematical structure only identified properly in the 20th century. Pollock was painting 'fractals', a word describing a geometric pattern that arbitrarily repeats – it was not coined until two decades after the artist's death. Recently, a group of supposed Pollock canvases were shown to be fakes because they were not fractals. In literature, Du Sautoy explores the hidden games Shakespeare played with numbers. Blueprints is not always an easy read for non-mathematicians. But it's a constantly surprising one in its determination to show us that works of art we love are 'often pieces of mathematics in disguise'.
Gizmodo
2 days ago
- General
- Gizmodo
A Brief History of Our Obsession With Prime Numbers—and Where the Hunt Goes Next
A shard of smooth bone etched with irregular marks dating back 20,000 years puzzled archaeologists until they noticed something unique – the etchings, lines like tally marks, may have represented prime numbers. Similarly, a clay tablet from 1800 B.C.E. inscribed with Babylonian numbers describes a number system built on prime numbers. As the Ishango bone, the Plimpton 322 tablet and other artifacts throughout history display, prime numbers have fascinated and captivated people throughout history. Today, prime numbers and their properties are studied in number theory, a branch of mathematics and active area of research today. A history of prime numbers Informally, a positive counting number larger than one is prime if that number of dots can be arranged only into a rectangular array with one column or one row. For example, 11 is a prime number since 11 dots form only rectangular arrays of sizes 1 by 11 and 11 by 1. Conversely, 12 is not prime since you can use 12 dots to make an array of 3 by 4 dots, with multiple rows and multiple columns. Math textbooks define a prime number as a whole number greater than one whose only positive divisors are only 1 and itself. Math historian Peter S. Rudman suggests that Greek mathematicians were likely the first to understand the concept of prime numbers, around 500 B.C.E. Around 300 B.C.E., the Greek mathematician and logician Euler proved that there are infinitely many prime numbers. Euler began by assuming that there is a finite number of primes. Then he came up with a prime that was not on the original list to create a contradiction. Since a fundamental principle of mathematics is being logically consistent with no contradictions, Euler then concluded that his original assumption must be false. So, there are infinitely many primes. The argument established the existence of infinitely many primes, however it was not particularly constructive. Euler had no efficient method to list all the primes in an ascending list. In the middle ages, Arab mathematicians advanced the Greeks' theory of prime numbers, referred to as hasam numbers during this time. The Persian mathematician Kamal al-Din al-Farisi formulated the fundamental theorem of arithmetic, which states that any positive integer larger than one can be expressed uniquely as a product of primes. From this view, prime numbers are the basic building blocks for constructing any positive whole number using multiplication – akin to atoms combining to make molecules in chemistry. Prime numbers can be sorted into different types. In 1202, Leonardo Fibonacci introduced in his book 'Liber Abaci: Book of Calculation' prime numbers of the form (2p – 1) where p is also prime. Today, primes in this form are called Mersenne primes after the French monk Marin Mersenne. Many of the largest known primes follow this format. Several early mathematicians believed that a number of the form (2p – 1) is prime whenever p is prime. But in 1536, mathematician Hudalricus Regius noticed that 11 is prime but not (211 – 1), which equals 2047. The number 2047 can be expressed as 11 times 89, disproving the conjecture. While not always true, number theorists realized that the (2p – 1) shortcut often produces primes and gives a systematic way to search for large primes. The search for large primes The number (2p – 1) is much larger relative to the value of p and provides opportunities to identify large primes. When the number (2p – 1) becomes sufficiently large, it is much harder to check whether (2p – 1) is prime – that is, if (2p – 1) dots can be arranged only into a rectangular array with one column or one row. Fortunately, Édouard Lucas developed a prime number test in 1878, later proved by Derrick Henry Lehmer in 1930. Their work resulted in an efficient algorithm for evaluating potential Mersenne primes. Using this algorithm with hand computations on paper, Lucas showed in 1876 that the 39-digit number (2127 – 1) equals 170,141,183,460,469,231,731,687,303,715,884,105,727, and that value is prime. Also known as M127, this number remains the largest prime verified by hand computations. It held the record for largest known prime for 75 years. Researchers began using computers in the 1950s, and the pace of discovering new large primes increased. In 1952, Raphael M. Robinson identified five new Mersenne primes using a Standard Western Automatic Computer to carry out the Lucas-Lehmer prime number tests. As computers improved, the list of Mersenne primes grew, especially with the Cray supercomputer's arrival in 1964. Although there are infinitely many primes, researchers are unsure how many fit the type (2p – 1) and are Mersenne primes. By the early 1980s, researchers had accumulated enough data to confidently believe that infinitely many Mersenne primes exist. They could even guess how often these prime numbers appear, on average. Mathematicians have not found proof so far, but new data continues to support these guesses. George Woltman, a computer scientist, founded the Great Internet Mersenne Prime Search, or GIMPS, in 1996. Through this collaborative program, anyone can download freely available software from the GIMPS website to search for Mersenne prime numbers on their personal computers. The website contains specific instructions on how to participate. GIMPS has now identified 18 Mersenne primes, primarily on personal computers using Intel chips. The program averages a new discovery about every one to two years. The largest known prime Luke Durant, a retired programmer, discovered the current record for the largest known prime, (2136,279,841 – 1), in October 2024. Referred to as M136279841, this 41,024,320-digit number was the 52nd Mersenne prime identified and was found by running GIMPS on a publicly available cloud-based computing network. This network used Nvidia chips and ran across 17 countries and 24 data centers. These advanced chips provide faster computing by handling thousands of calculations simultaneously. The result is shorter run times for algorithms such as prime number testing. The Electronic Frontier Foundation is a civil liberty group that offers cash prizes for identifying large primes. It awarded prizes in 2000 and 2009 for the first verified 1 million-digit and 10 million-digit prime numbers. Large prime number enthusiasts' next two challenges are to identify the first 100 million-digit and 1 billion-digit primes. EFF prizes of US$150,000 and $250,000, respectively, await the first successful individual or group. Eight of the 10 largest known prime numbers are Mersenne primes, so GIMPS and cloud computing are poised to play a prominent role in the search for record-breaking large prime numbers. Large prime numbers have a vital role in many encryption methods in cybersecurity, so every internet user stands to benefit from the search for large prime numbers. These searches help keep digital communications and sensitive information safe. Jeremiah Bartz, Associate Professor of Mathematics, University of North Dakota. This article is republished from The Conversation under a Creative Commons license. Read the original article.
Associated Press
3 days ago
- Business
- Associated Press
Elephant Learning Donates $450,000 in Mathematics Education Resources to Schools Across India
05/30/2025, Los Angeles, California // PRODIGY: Feature Story // Elephant Learning has announced an initiative to donate $450,000 worth of mathematics learning resources to schools across India. This donation comes as part of a strategic partnership with an online LaTeX and Rich Text collaborative writing and publishing platform. With the goal of redefining how the subject is taught and understood in the classroom, this donation aims to equip schools with access to Elephant Learning's adaptive mathematics platform and educator support materials. 'Mathematics isn't just about getting the right answer. It's about understanding the problem you're trying to solve,' says Dr. Aditya Nagrath, founder of Elephant Learning. 'This donation is about giving students in India an opportunity to experience mathematics as a language, as a way of thinking, and not just a subject in school.' Essentially, Elephant Learnings intends to plant seeds that will grow into confidence, curiosity, and competence by providing schools and parents with access to tools that nurture true comprehension. This move aligns with Elephant Learning's broader mission. It was developed to address the issue regarding students memorizing procedures without understanding the concepts behind them. This superficial approach to mathematics education created learning gaps that compounded over time, making advanced concepts like algebra inaccessible. To solve this, Elephant Learning created an adaptive learning platform tailored for K–8 students that zeroes in on conceptual comprehension. The platform presents mathematical ideas through gamified, puzzle-like activities. This donation to Indian schools is a milestone in Elephant Learning's growth. It signifies a commitment to educational transformation on a global scale. Moreover, it reflects an ambition to challenge entrenched norms in Indian education, particularly the rote memorization methods that dominate mathematics classrooms. 'Many students encounter multiplication or division on the board before ever experiencing what those operations actually mean,' says Nagrath. 'It's like teaching a child to spell a word before they know what it means. Our system is designed to ensure that every student has that foundational experience, whether through the grocery store with a parent or with a virtual activity on our platform before they step into the classroom. Once they understand the idea, memorization becomes meaningful and useful.' The program being rolled out in India is a tailored version of Elephant Learning's core platform. This means it's designed for school-wide implementation. While the student experience remains personalized and adaptive, the school version includes expanded support for teachers. Resources such as detailed teacher guides, curriculum-aligned scope and sequence documentation, and classroom tools are included to facilitate smooth integration into existing instruction. The platform will be deployed using a scalable licensing model, with schools purchasing access based on student count and using anonymized IDs for data privacy. This donation is only the beginning of Elephant Learning's vision. The company hopes to establish a foothold in institutions that are open to adopting international best practices in education and that can lead the shift toward conceptual learning in the region. While this first phase targets international curriculum and higher-fee schools, the long-term goal is to make the platform accessible to a broader range of institutions, including public schools and those in underserved areas. Media Contact Name: Raymark Barroga Email: [email protected] Source published by Submit Press Release >> Elephant Learning Donates $450,000 in Mathematics Education Resources to Schools Across India
South China Morning Post
3 days ago
- Science
- South China Morning Post
Peking University dropout cracks IUT – the ‘alien's language' that can upend mathematics
Zhou Zhongpeng, a 28-year-old Peking University doctoral dropout turned tech engineer , has deciphered one of mathematics' most cryptic frontiers dubbed the 'alien's language' for its impenetrable 2,000-page framework and extraterrestrial-like notation. Advertisement Japanese professor Shinichi Mochizuki's Inter-universal Teichmueller Theory (IUT) has baffled experts since its 2012 debut as a proposed proof for the ABC conjecture , a Holy Grail problem with radical implications for number theory. Armed with late-night study sessions and a discarded academic career, Zhou's breakthrough may have transformed the ABC conjecture from conceptual abstraction to computationally usable tool. The feat, achieved during weekends between gruelling 14-hour shifts as a Beijing algorithm engineer, not only revives Mochizuki's controversial theory but threatens to eclipse Andrew Wiles' famed 1995 proof of Fermat's Last Theorem in scope. 'His results are infinitely stronger than Wiles,' declared Professor Ivan Fesenko, a leading IUT authority who now mentors Zhou at Westlake University. Advertisement Kyoto University mathematician Shinichi published a 500-page paper claiming to prove the ABC conjecture in 2012.
CTV News
5 days ago
- Entertainment
- CTV News
Math magician brings mind-bending tricks to Nova Scotia
Mikael Taieb brought his mathematical magic to Halifax this week. When he was nine years old, Mikael Taieb was trying to solve a Rubik's Cube. His math teacher eventually showed him a solution, which set him down a path that eventually led to Canada's Got Talent. 'He really helped me build my confidence,' Taieb said. Taieb, a Rubik's Cube artist and math magician, is hoping to impart that confidence onto future generations with his touring shows. He recently performed at LeMarchant-St. Thomas Elementary in Halifax, leading a workshop and a showcase. 'The goal of the workshop is to demonstrate how spectacular mathematics can be,' he said. 'The brain is a muscle. Working with math and the Rubik's Cube brings self confidence. 'It helps you to feel better about yourself and get some direct result of what you can do.' Taieb's math skills landed him a spot in season four of Canada's Got Talent. 'It was an amazing experience and amazing exposure to bring art and math to the biggest stage of the country,' he said. Taieb is hopeful his performances encourage people to explore the world of mathematics. 'Math can be for anyone, for any brain,' he said. 'It can be very fun. Everyone is capable of amazing things.' Mikael Taieb Mikael Taieb brought his mathematical magic to Halifax this week. For more Nova Scotia news, visit our dedicated provincial page
