Top Mathematics discussions
NishMath - #mathematics
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@Martin Escardo
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References:
The Aperiodical
, denisegaskins.com
Recent activity on Mathstodon, the mathematics-focused corner of Mastodon, has sparked discussions across a variety of mathematical topics. Users such as MartinEscardo and Ddrake have been active, contributing to the vibrant exchange of ideas within the community. The Aperiodical, a website dedicated to recreational mathematics, has also been a key source of content, highlighting events like the "Big Internet Math-Off" competitions from previous years and teasing the upcoming "Big Internet Math-Off 2024." Denise Gaskins' "Playful Math for the Summer" blog post was shared, showcasing engaging math resources and games.
These online platforms provide a space for mathematicians and enthusiasts to share insights, puzzles, and announcements. One example is a post from Ngons highlighting a tiling pattern involving dodecagon rings, squares, and triangles, which can be connected to form a Koch snowflake, demonstrating the intersection of geometry, fractals, and math art. Another post referenced an issue of Double Maths First Thing by Colin, who discusses his mission to the moon and spreading joy for math. In addition to sharing interesting mathematical concepts, some Mastodon users are addressing platform-specific issues. MartinEscardo proposed a feature request aimed at improving the reply system, suggesting that users should have more control over who is notified in a thread to avoid irrelevant notifications. The Mathstodon community continues to be a hub for mathematical exploration, resource sharing, and discussions on improving the online experience for its members. Recommended read:
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@Trebor
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Trebor
Recent discussions in theoretical computer science and programming have touched upon diverse topics, ranging from type theory for SDG (Sustainable Development Goals) to the complexities encountered in programming. One thread explored the characteristics a type theory for SDG should possess, suggesting it should include a judgmentally commutative ring, possibly a Q-algebra, where neutral forms of type R are polynomials with other neutral forms as indeterminates. Participants believe such a system would have decidable typechecking.
A common sentiment shared among programmers, particularly those using languages with dependent types like Rust, is the initial hurdle of satisfying the compiler's requirements. Some have described the experience as an engaging puzzle that can involve spending considerable time to prove the validity of their code. The discussion also addressed the subjective nature of "complexity" in programming, suggesting it is a term often used to dismiss unfamiliar concepts rather than a concrete measure of inherent difficulty. In related news, Microsoft’s Krysta Svore has announced geometric error-correcting codes as a potential advancement toward practical quantum computing. These codes utilize high-dimensional geometry to enhance performance, potentially leading to more efficient encoding and logical operations with fewer qubits. The approach builds on topological error correction, employing a mathematical method called Hermite normal form to reshape the grid, resulting in substantial reductions in qubit count and faster logical clock speeds. This geometric reshaping results in substantial reductions in qubit count. In one notable case, they achieved six logical qubits using just 96 physical qubits, which is a 16-to-1 ratio that would mark a significant improvement over standard two-dimensional codes. Recommended read:
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@martinescardo.github.io
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ellipticnews.wordpress.com
The mathematics community is buzzing with activity, including upcoming online events and ongoing discussions about research methodologies. A significant event to watch for is the online celebration marking the 40th anniversary of Elliptic Curve Cryptography (ECC) on August 11, 2025. This event will commemorate the foundational work of Victor Miller and Neal Koblitz in 1985. It is anticipated to be a very important event for those in the cryptography community and to those who work with elliptic curves.
The ECC celebration will feature personal reflections from Miller and Koblitz, alongside lectures by Dan Boneh and Kristin Lauter, who will explore ECC's broad impact on cryptography and its unforeseen applications. The history of ECC is used as a good example of how fundamental research can lead to unexpected and practical outcomes. This serves as a good way to promote blue skies research. In other news, mathematicians are actively discussing the use of formal methods in their research. One Mathstodon user described using LaTeX and Agda in TypeTopology for writing papers and formalizing mathematical remarks. They found that formalizing remarks in a paper could reveal errors in thinking and improve results, even in meta-mathematical methodology. This shows how computational tools are increasingly being used to verify and explore mathematical ideas, highlighting the practical utility of pure math skills in applied contexts. Recommended read:
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MAA@maa.org
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maa.org
The Mathematical Association of America (MAA) has announced the recipients of the 2025 awards for expository mathematical writing in MAA publications. The awards recognize outstanding contributions to mathematical literature. Jordan S. Ellenberg was awarded the Chauvenet Prize for his work "Geometry, Inference, Complexity, and Democracy," which appeared in the Bulletin (New Series) of the American Mathematical Society. Ellenberg's work explores the challenge of fairly dividing democratic polities into legislative districts, demonstrating the practical application of mathematics to societal issues. Ismar Volíc of Wellesley College, received the Euler Book Prize for his book "Making Democracy Count: How Mathematics Improves Voting, Electoral Maps, and Representation," which brings complex topics, such as voting theory, apportionment, gerrymandering, and the Electoral College, to life.
Awarded individuals are reciving either the Chauvenet Prize, the Euler Book Prize, the Daniel Solow Author’s Award, the George Pólya Awards, the Paul R. Halmos–Lester R. Ford Awards, the Trevor Evans Award, or the Carl B. Allendoerfer Awards. Ellenberg's article, drawn from his 2020 Current Events Bulletin lecture, showcases how mathematical approaches can measure fairness in democratic processes. Volíc's book makes complex topics accessible to readers, highlighting the crucial role of mathematics in collective decision-making, and providing essential insights without political bias. Both works exemplify clear and engaging writing, effectively communicating intricate mathematical ideas to a wider audience. As summer approaches, Denise Gaskins is offering discounts on her math game books at the Playful Math Store. This presents an opportunity for families and educators to enhance mathematical learning through playful activities. Gaskins' "Math You Can Play" series offers math games sorted by topics traditionally taught at various age levels, with teaching tips and advice aimed at parents and teachers. Her new series, "Tabletop Math Games Collection," also covers the same mathematical topics. These books are designed for direct use by players of all ages, making them ideal for spontaneous math play. These books are available in both physical and digital formats, providing flexibility for use in math centers, homeschool co-op classes, or at home. Recommended read:
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@www.quantamagazine.org
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Recent breakthroughs have significantly advanced the "Core of Fermat's Last Theorem," a concept deeply rooted in number theory. Four mathematicians have extended the key insight behind Fermat's Last Theorem, which states there are no three positive integers that, when raised to a power greater than two, can be added together to equal another number raised to the same power. Their work involves applying this concept to other mathematical objects, notably elliptic curves. This extension represents a major step towards building a "grand unified theory" of mathematics, a long-sought goal in the field.
This achievement builds upon the groundwork laid by Andrew Wiles's famous 1994 proof of Fermat's Last Theorem. Wiles, with assistance from Richard Taylor, demonstrated that elliptic curves and modular forms, seemingly distinct mathematical entities, are interconnected. This discovery revealed a surprising "modularity," where these realms mirror each other in a distorted way. Mathematicians can now leverage this connection, translating problems about elliptic curves into the language of modular forms, solving them, and then applying the results back to the original problem. This new research goes beyond elliptic curves, extending the modularity connection to more complicated mathematical objects. This breakthrough defies previous expectations that such extensions would be impossible. The Langlands program, a set of conjectures aiming to develop a grand unified theory of mathematics, hinges on such correspondences. The team's success provides strong support for the Langlands program and opens new avenues for solving previously intractable problems in various areas of mathematics, solidifying the power and reach of the "Core of Fermat's Last Theorem." Recommended read:
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@www.ams.org
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www.ams.org
The American Mathematical Society (AMS) has announced the allocation of $1 million in Backstop Grants, designed to provide crucial support to the mathematical community. This initiative is a response to recent federal funding cuts that have significantly impacted societies, institutes, and departments engaged in mathematical research and activities. The grants aim to ensure the continuation of essential projects, conferences, and other scholarly pursuits within the mathematical sciences.
The AMS Backstop Grants will be administered through a streamlined and transparent application process, emphasizing equitable support for a wide range of activities and mathematicians. As an initial step, the AMS is providing a grant to the Association for Women in Mathematics (AWM) to support its 2025 Research Symposium. Organizations that have been affected by funding reductions are encouraged to inquire about potential support from the AMS. The move comes as the U.S. National Science Foundation (NSF) has faced substantial budget constraints, with spending on basic sciences reduced by 50% or more in 2025. Similar cuts are projected for the coming year, leading to widespread disruption within the academic research ecosystem. This situation has resulted in laboratories suspending operations, graduate students facing uncertainty about completing their degrees, and early-career faculty losing critical grants. Recommended read:
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@docslib.org
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nLab
The Kazhdan-Lusztig correspondence, a significant concept in representation theory, is gaining increased attention. This correspondence establishes an equivalence between representation categories of quantum groups and affine Lie algebras. Recent research explores its applications in areas like logarithmic conformal field theory (CFT), particularly concerning the representation category of the triplet W-algebra. The Kazhdan-Lusztig correspondence has also been investigated in relation to vertex algebras, further solidifying its importance across different mathematical and physical domains.
Dennis Gaitsgory was awarded the Breakthrough Prize in Mathematics for his broad contributions to the field, including work closely related to representation theory and the geometric Langlands program. His recognition highlights the impact of representation theory on other areas of mathematics. Further research is focusing on exploring tensor structures arising from affine Lie algebras and building on Kazhdan and Lusztig's foundational work in the area. Recent work has also explored the Kazhdan-Lusztig correspondence at a positive level using Arkhipov-Gaitsgory duality for affine Lie algebras. A functor is defined which sends objects in the DG category of G(O)-equivariant positive level affine Lie algebra modules to objects in the DG category of modules over Lusztig’s quantum group at a root of unity. Researchers are actively working to prove that the semi-infinite cohomology functor for positive level modules factors through the Kazhdan-Lusztig functor at positive level and the quantum group cohomology functor with respect to the positive part of Lusztig’s quantum group. Recommended read:
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@www.the-independent.com
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The election of Pope Leo XIV, formerly known as Robert Francis Prevost, has sparked significant reactions, particularly within American political circles. Prevost, who holds a mathematics degree from Villanova University, marks a unique instance of a Pope with a strong background in mathematics. His election on May 8, 2025, following the death of Pope Francis, is considered a historic moment. Prevost's background includes serving as a missionary in Peru and later as Prefect of the Dicastery for Bishops.
Adding fuel to the fire, former President Donald Trump has weighed in with controversial suggestions, including the annexation of Vatican City by the United States. Trump, referring to Pope Leo XIV being from Chicago, quipped, "If the Pope's American, the Vatican is American." He proposed designating the Vatican as the 51st state, envisioning a "perfect merger of church and state," while also adding that he might look to repeal some of the commandments, stating that "everything is on the table.” The former president's comments have ignited further discussion, turning the papal election into a geopolitical talking point. The election has also drawn strong reactions from conservative media and figures. Laura Loomer has criticized the new Pope as "anti-Trump, anti-MAGA, pro-open Borders, and a total Marxist," echoing sentiments of a "woke Marxist Pope." Evangelical leaders are reportedly divided, with some seeing the election as a "divine realignment of power" and others reminding Trump that Catholicism is technically not Protestant. Fox News has even launched a series titled "Was the Vatican Always Ours?", highlighting the polarized views surrounding the new American Pope. Recommended read:
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Tom Bridges@blogs.surrey.ac.uk
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References:
phys.org
, www.sciencedaily.com
Recent mathematical explorations have focused on a variety of intriguing number patterns and historical mathematical context. One notable discovery comes from UNSW Sydney mathematician Norman Wildberger, who has revealed a new algebraic solution to higher polynomial equations, a problem considered unsolvable since the 19th century. Polynomials are equations with variables raised to powers, and while solutions for lower-degree polynomials are well-known, a general method for those of degree five or higher has remained elusive. Wildberger's method, detailed in a publication with computer scientist Dr. Dean Rubine in The American Mathematical Monthly, uses novel number sequences to "reopen a previously closed book in mathematics history."
Wildberger's approach challenges the traditional use of radicals, which often involve irrational numbers. Irrational numbers, with their infinite, non-repeating decimal expansions, are seen by Wildberger as problematic. He argues that assuming their existence in formulas implies treating infinite decimals as complete objects, an assumption he rejects. His solution involves discarding irrational numbers, a move that may redefine how certain algebraic problems are approached. Critics may find the claims overstated, as one commentary notes the article never specifies what "algebra's oldest problem" actually is, but indicates that solving it requires discarding irrational numbers. In addition to advancements in solving polynomial equations, mathematicians continue to explore other number sequences, such as Recamán’s sequence, a favorite of N. J. A. Sloane, founder of the Online Encyclopedia of Integer Sequences. The sequence starts at 0, and each subsequent number is derived by moving forward or backward a specific number of steps from the previous number, based on certain conditions. Recamán’s sequence can be visualized using circular arcs and even represented as music, associating each number with a note on the chromatic scale, showcasing the diverse ways in which mathematical concepts can be explored and interpreted. Recommended read:
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@sciencedaily.com
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Dan Drake ?
, phys.org
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A mathematician from UNSW Sydney has reportedly solved one of algebra's oldest and most challenging problems: finding a general algebraic solution for higher polynomial equations. These equations, which involve a variable raised to powers, are fundamental in mathematics and science, with broad applications ranging from describing planetary movement to writing computer programs. While solutions for lower-degree polynomials (up to degree four) have been known for centuries, a general method for solving equations of degree five or higher had remained elusive, until now.
Professor Norman Wildberger, along with computer scientist Dr. Dean Rubine, developed a new approach using novel number sequences to tackle this problem. Their solution, recently published in The American Mathematical Monthly journal, challenges established mathematical assumptions and potentially "reopens a previously closed book in mathematics history," according to Professor Wildberger. The breakthrough centers around rethinking the use of radicals (roots of numbers) in classical formulas, traditionally used to solve lower-order polynomials. Wildberger argues that radicals, often representing irrational numbers with infinite, non-repeating decimal expansions, introduce incompleteness into calculations. He claims that since these irrational numbers can never be fully calculated, assuming their 'existence' in a formula is problematic. This perspective led him to develop an alternative method based on number sequences, potentially offering a purely algebraic solution to higher-degree polynomial equations, bypassing the limitations of traditional radical-based approaches. Recommended read:
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@quantumcomputingreport.com
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Metadata
, Quantum Computing Report
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Universities worldwide are engaging in a diverse range of mathematics-related activities, from exploring quantum communication to using origami for hands-on learning. Heriot-Watt University in Edinburgh recently inaugurated a £2.5 million ($3.3 million USD) Optical Ground Station (HOGS) to foster advancements in satellite-based quantum-secure communication. This facility, equipped with a 70-cm precision telescope, aims to conduct quantum key distribution (QKD) experiments with satellites, monitor space debris, and test high-speed optical communications for next-generation networks. The project is a significant step in the UK's ambition to establish a quantum-secure internet, offering a unique platform for industry and academia to collaborate on secure communications across various sectors.
HOGS is connected to Heriot-Watt’s quantum labs via dark fibre, enabling real-time simulation and validation of optical quantum networks. This infrastructure will serve as a valuable R&D platform for secure communications in financial services, healthcare, and critical infrastructure, aiming to mitigate the UK's estimated £27 billion annual cost of cybercrime. The university also intends to expand Scotland’s space economy and workforce through partnerships and STEM programs, emphasizing the educational outreach aspect of the new facility. The Integrated Quantum Networks (IQN) Hub also considers the station part of Heriot-Watt's role as a leader in the development of quantum-secure communications. Meanwhile, ETH Zürich is promoting practical mathematics through its goMATH funding program, exemplified by the Origami Challenge. ETH students visited schools to introduce origami mathematics in a fun and engaging way, encouraging pupils to create geometric origami artworks from paper without using glue. This initiative aims to make mathematics more accessible and enjoyable for young students. At the TLA+ Community Event in Hamilton, Ontario, discussions revolved around integrating TLA+ into tooling for fuzzers, trace validators, and compilers, emphasizing its evolving role beyond just specifications. Attendees observed that TLA+ is increasingly being used to build bridges from models to real-world applications. Recommended read:
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Katie Steckles@The Aperiodical
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The Aperiodical
, D-MATH News
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The Carnival of Mathematics, a monthly gathering of mathematical blog posts, continues to connect the global math community. For over a decade, this event has been hosted by various math bloggers, showcasing a wide range of mathematical topics, from recreational puzzles to advanced research. It serves as a valuable resource for mathematicians and enthusiasts alike, offering a way to stay informed about current trends and innovative ideas within the field.
The latest edition, Carnival of Maths 239, is now available at Reflections and Tangents, featuring blog posts from April 2025. This edition, like its predecessors, aims to broaden the accessibility of diverse mathematical discussions to a larger audience. Readers can expect to find explorations of topics like origami mathematics, as well as discussions of mathematical concepts relevant to daily life. Besides the Carnival of Mathematics, other events are taking place within the math community. An Origami Challenge was undertaken in schools by ETH students, who visited schools and taught about origami and its relationship to the mathematical world, and a simple way to generate random points on a sphere was recently highlighted. These varied activities showcase the dynamic and engaging nature of mathematics and its diverse applications. Recommended read:
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@phys.org
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A mathematician from UNSW Sydney has made a significant breakthrough in addressing a longstanding problem in algebra: solving higher polynomial equations. Honorary Professor Norman Wildberger has developed a novel method that utilizes intriguing number sequences to tackle equations where variables are raised to the power of five or higher, a challenge that has eluded mathematicians for centuries. The findings are outlined in a recent publication co-authored with computer scientist Dr. Dean Rubine, and could lead to advancements in various mathematical disciplines. This new approach has the potential to reshape mathematical problem-solving techniques.
Professor Wildberger's approach challenges traditional methods that rely on radicals, which often represent irrational numbers—decimals that extend infinitely without repeating. He argues that these irrational numbers introduce imprecision, and that a real answer to a polynomial equation can never be completely calculated because it would need an infinite amount of work. The mathematician suggests this solution "reopens a previously closed book in mathematics history." Prior to this discovery, French mathematician Évariste Galois demonstrated in 1832 that it's impossible to resolve higher polynomial equations with a general formula, such as the quadratic formula. Approximate solutions for higher-degree polynomials have been used, but are not pure algebra. Wildberger's radical rejection has lead to a new method for solving this decades old problem. Recommended read:
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@exercism.org
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jcarroll.com.au
Modulo arithmetic is being explored as a technique for rotation, inspired by a post from Greg Egan on Mastodon. Jonathan Carroll implemented Egan's formula in various languages. The formula, rot(n, j, k) = (n * 10^k) mod (10^j-1), efficiently rotates a j-digit number n by k digits. Carroll highlighted the importance of understanding fundamental operators across different languages while implementing this seemingly simple mathematical concept.
This exploration is beneficial for fortifying knowledge of basic functionalities in different programming languages. As Carroll wrote in his blog, implementing this simple math "means I’ll be working with some basic functionality and I believe it’s very important to have that locked in comfortably." Carroll demonstrated the implementation in R, utilizing the power operator '^' and the modulo operator '%%'. He also showed how to determine the number of digits in a number using the 'nchar()' function, showcasing practical application of these operators. The R implementation allows for the cyclic rotation of digits within a number. While R doesn't have a built-in function for this specific purpose, Carroll demonstrated the usage of his '{vec}' package for a similar ring-buffer effect on vectors. This involved using modulo on the indices to achieve the desired rotation. The formula subtracts (10^j-1) times the leftmost k digits of n*10^k, removing them from the left and adding them to the right. Recommended read:
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@sciencedaily.com
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www.sciencedaily.com
Researchers are employing advanced mathematical techniques to tackle complex problems in diverse fields. A recent study highlights the application of the hinge function in fluvial geomorphology, providing a solution for predicting bedload sediment transport in rivers. Additionally, mathematicians have used mathematical modeling to unravel the mystery behind the striped patterns of "broken" tulips, a phenomenon that has puzzled scientists for centuries. These examples demonstrate the power of mathematical methods in understanding and predicting phenomena across various scientific disciplines.
A team at Washington State University has developed a new forecasting model that helps businesses predict customer demand more accurately, even when key data is missing. This model, published in Production and Operations Management, uses a mathematical modeling method to estimate customer interest beyond just completed transactions and traditional forecasting techniques. By analyzing real-world sales data, the model provides a clearer view of how many customers considered a purchase but ultimately did not buy due to factors like pricing or timing. The researchers utilized a computational technique called the sequential minorization-maximization algorithm to improve forecasting accuracy. Furthermore, researchers at the University of Alberta have solved a centuries-old floral mystery by using a mathematical model to explain how striped tulips get their distinctive pattern. The study, published in Nature Communications Biology, reveals that the tulip-breaking virus inhibits the production of anthocyanins, the pigments that give tulips their vibrant colors. The mathematical model incorporates two key mechanisms—the substrate-activator mechanism and Wolpert's positional information mechanism—to simulate the interaction between the virus, pigment production, and cellular resources within the plant, ultimately creating the striped pattern. Recommended read:
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@Math Blog
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Math Blog
, denisegaskins.com
Mathematical concepts and their applications are gaining increased attention, with recent explorations into diverse areas. A blog post discusses the fundamental differences between mathematical and statistical reasoning, using the example of predicting days with the fewest noninduced births. Researchers are also delving into methods for eliminating parameters in parametric equations. A podcast delves into the philosophy of mathematics and set theory, examining the nature of mathematics itself.
The article "Eliminating the Parameter in Parametric Equations" provides a guide for expressing relationships between variables `x` and `y` when they are defined in terms of a parameter `t`. It explains the process of removing the parameter to obtain a direct equation between `x` and `y`, showcasing examples and solutions. Furthermore, there is a discussion on Charlotte Mason's approach to mathematics using living books as a method of teaching. Python's dominance in AI and machine learning is a significant development. An article explores the factors behind this, highlighting Python's readability, extensive libraries like NumPy, Pandas, Scikit-learn, TensorFlow, and PyTorch, and the role of AI hype in its rise. The Church of Logic podcast also featured a discussion with Joel David Hamkins on the philosophy of mathematics and set theory, particularly exploring differing perspectives on the nature of mathematics. Recommended read:
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@www.quantamagazine.org
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Recent advancements in mathematics and physics are pushing the boundaries of our understanding of the universe. A decades-old bet between mathematicians Noga Alon and Peter Sarnak regarding the nature of optimal expander graphs has recently been settled, with both mathematicians being proven wrong. This involved tapping into a crucial phenomenon in physics and pushing it to its limits, demonstrating the interconnectedness of mathematics and physics. Also, Researchers have successfully modeled how 'broken' tulips get their stripes, solving a centuries-old floral mystery. The mathematical model explains that the tulip-breaking virus inhibits the production of anthocyanins, leading to the distinctive striped pattern.
Efforts are underway to bridge the gap between quantum mechanics and general relativity, with researchers exploring the possibility of creating quantum gravity in the lab. Monika Schleier-Smith at Stanford University is leading this effort by using laser-cooled atoms to explore whether gravity could emerge from quantum entanglement. NASA is also contributing to this field by developing the first space-based quantum gravity gradiometer. This gradiometer will use ultra-cold rubidium atoms to detect gravitational anomalies with high precision from orbit, with potential applications in water resource management and subsurface geology. Further progress is being made in language model development. Researchers are exploring methods to sidestep language in order to improve how language models work with mathematics. By allowing these models to operate directly in mathematical spaces, they aim to enhance efficiency and reasoning capabilities. This research highlights the potential for artificial intelligence systems to benefit from thinking independently of language, paving the way for more advanced and effective AI applications. Recommended read:
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Miranda Martinengo@Istituto Grothendieck
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Recent developments in the mathematics community showcase notable achievements and career advancements. Ryuya Hora, a doctoral scholar from the University of Tokyo specializing in topos theory and automata theory applications, has been appointed Research Associate of the Centre for Topos Theory and its Applications (CTTA). He is scheduled to collaborate with Olivia Caramello and other researchers at the Centre in Paris between April and June 2025. His appointment signifies a valuable addition to the field, with opportunities to follow his work, including his talk at the "Toposes in Mondovì" conference.
Cesare Tronci has been promoted to Professor of Mathematics at the University of Surrey, effective April 1, 2025. This promotion acknowledges his contributions to the field, and further information about his research can be found on his website. Also at the University of Surrey, Jessica Furber has successfully defended her PhD thesis, "Mathematical Analysis of Fine-Scale Badger Movement Data," marking the completion of her doctoral studies. Her external examiner was Prof Yuliya Kyrychko from Sussex, and the internal examiner was Dr Joaquin Prada from the Vet School, Surrey. In related news, the Mathematics Division at Stellenbosch University in South Africa is seeking a new permanent appointee at the Lecturer or Senior Lecturer level, with consideration potentially given to other levels under specific circumstances. While preference will be given to candidates working in number theory or a related area, applications from those in other areas of mathematics will also be considered. The deadline for applications is April 30, 2025, with detailed information available in the official advertisement. Recommended read:
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