Top Mathematics discussions
NishMath - #mathematics
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@techcrunch.com - 90d
OpenAI has launched its new 'o1' model, representing a significant advancement in AI capabilities. The model is available to Plus and Team users and is part of the '12 Days of OpenAI' series, which aims to improve the accessibility and interactivity of AI tools. The o1 model boasts enhanced reasoning capabilities and is faster and more powerful than its predecessors, with notable improvements in math, coding, and now also includes image processing. Internal tests show a 34% reduction in major errors compared to the o1-preview model, making it more reliable for various tasks.
The 'o1' model is now accessible through a new 'Pro' plan, named ChatGPT Pro, which is priced at $200 per month. This premium subscription grants users access to the advanced features of the 'o1' model, as well as a voice module and improved answers to complex queries. Some reviewers have noted that while the model is about 11% better in coding compared to the standard version, the cost may be prohibitive for some users when compared to other alternatives, with the pro version costing 10 times the regular subscription. Despite this, the o1 pro mode is expected to be useful in fields like math, physics, and medicine. Recommended read:
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A-Maths@Maths on Medium - 90d
A series of Medium articles offer accessible explanations of diverse mathematical concepts and their real-world applications. Topics covered include solving various types of equations, from basic algebraic problems to more advanced exponential equations relevant to data science. One article provides a step-by-step guide to understanding and solving equations, emphasizing the importance of this skill across numerous fields like finance and programming. Another article tackles the frequency illusion, also known as the Baader-Meinhof phenomenon, explaining the cognitive bias behind why we notice things more frequently after becoming newly aware of them.
Furthermore, the collection explores the significant relationship between mathematics and coding, illustrating how mathematical principles underpin fundamental concepts in computer science such as algorithms, data structures, and computational complexity. The articles also include practical applications, like using exponential equations in data science and demonstrating the use of linear regression in predictive analytics. A selection of math puzzles with answers is also provided, offering engaging challenges for readers to test and hone their problem-solving skills. Recommended read:
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@techcrunch.com - 27d
DeepMind's artificial intelligence, AlphaGeometry2, has achieved a remarkable feat by solving 84% of the geometry problems from the International Mathematical Olympiad (IMO) over the past 25 years. This performance surpasses the average gold medalist in the prestigious competition for gifted high school students. The AI's success highlights the growing capabilities of AI in handling sophisticated mathematical tasks.
AlphaGeometry2 represents an upgraded system from DeepMind, incorporating advancements such as the integration of Google's Gemini large language model and the ability to reason by manipulating geometric objects. This neuro-symbolic system combines a specialized language model with abstract reasoning coded by humans, enabling it to generate rigorous proofs and avoid common AI pitfalls like hallucinations. This could potentially impact fields that heavily rely on mathematical expertise. Recommended read:
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vishnupriyan@Verdict - 10d
Google's AI mathematics system, known as AlphaGeometry2 (AG2), has surpassed the problem-solving capabilities of International Mathematical Olympiad (IMO) gold medalists in solving complex geometry problems. This second-generation system combines a language model with a symbolic engine, enabling it to solve 84% of IMO geometry problems, compared to the 81.8% solved by human gold medalists. Developed by Google DeepMind, AG2 can engage in both pattern matching and creative problem-solving, marking a significant advancement in AI's ability to mimic human reasoning in mathematics.
This achievement comes shortly after Microsoft released its own advanced AI math reasoning system, rStar-Math, highlighting the growing competition in the AI math domain. While rStar-Math uses smaller language models to solve a broader range of problems, AG2 focuses on advanced geometry problems using a hybrid reasoning model. The improvements in AG2 represent a 30% performance increase over the original AlphaGeometry, particularly in visual reasoning and logic, essential for solving complex geometry challenges. Recommended read:
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Tom Bridges@blogs.surrey.ac.uk - 15d
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The London Mathematical Society has awarded Polina Vytnova a Research in Pairs grant, dated February 14th. The grant will enable Vytnova to host Victor Kleptsyn, a CNRS Researcher from the University of Rennes, at the University of Surrey. Together, they will collaborate on a joint research project focusing on the "Arithmetic of Cantor sets."
Also, Terry Tao has announced a collaboration with Grant Sanderson of 3blue1brown, along with Tanya Klowden, to produce a two-part video about the history of the cosmic distance ladder. This project builds upon a previous public lecture by Tao and is related to their forthcoming book. The first part of the video is already available, with Sanderson currently editing the second part. Recommended read:
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@artsci.washington.edu - 25d
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Recent News
, artsci.washington.edu
University of Washington professors Xiaodong Xu, Cynthia Vinzant, and Shayan Oveis Gharan have been honored by the National Academy of Sciences (NAS) for their outstanding research achievements. The NAS awards program has been recognizing outstanding achievement in the physical, biological, and social sciences since 1866. The annual awards ceremony will honor the major contributions made by 20 researchers.
Xu received the NAS Award for Scientific Discovery for his experimental observation of the fractional quantum anomalous Hall effect. This award, presented every two years, recognizes an accomplishment or discovery in basic research within the previous five years that is expected to have a significant impact on astronomy, biochemistry, biophysics, chemistry, materials science, or physics. Xu's research explores new quantum phenomena in layered two-dimensional materials and engineered quantum systems. Vinzant and Oveis Gharan, along with Nima Anari and Kuikui Liu, will receive the Michael and Sheila Held Prize for breakthrough work advancing the theory of matroids and mixing rates of Markov chains. The Michael and Sheila Held Prize is presented annually to honor outstanding, innovative, creative, and influential research in the areas of combinatorial and discrete optimization, or related parts of computer science, such as the design and analysis of algorithms and complexity theory. This $100,000 prize is intended to recognize recent work. Recommended read:
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@Department of mathematics - 4d
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www.ams.org
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The American Mathematical Society (AMS) is actively advocating for mathematics, particularly concerning the National Science Foundation (NSF). The AMS has started a page to coordinate support for professional mathematics, focusing on executive orders impacting the NSF. Recently, the NSF has seen significant changes, including the firing of 168 employees, which raises concerns about the potential impact on quantum funding and artificial intelligence research. These layoffs, occurring in response to a presidential executive order aimed at reducing the federal workforce, have affected both probationary employees and part-time experts in physics-related fields.
The AMS provides tools for the mathematical community to engage with government representatives, ensuring that the voices of mathematicians are heard in policy discussions. The AMS also actively supports mathematics on a global stage, as demonstrated by the US team earning third place at the 2025 Romanian Master of Mathematics, a challenging international high school mathematics competition, with team members earning individual awards. Penn State also rose in the NSF Higher Education Research and Development rankings. The AMS is dedicated to advancing research and connecting the diverse global mathematical community through publications, meetings and conferences, MathSciNet, professional services, advocacy, and awareness programs. Recommended read:
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@medium.com - 58d
The year 2025 is gaining attention not just for marking a new year but also for its unique mathematical properties. It's a perfect square, specifically 45 squared (45 x 45 = 2025). This means it can be represented as a square shape with 45 units on each side. Perfect square years are not common, with the last one being 1936 and the next one not until 2116, making 2025 mathematically special and a rare occurrence. Beyond being a perfect square 2025 also has other interesting traits that are being noted.
Another unusual property of 2025 is that it's linked to the concept of Kaprekar numbers, with 45 fitting the criteria. When 2025 is split into 20 and 25, their sum is 45. Furthermore, 2025 can be expressed as the sum of the cubes of all single-digit numbers from one to nine, and is also a sum of three squares, 40², 20², and 5². The number also happens to be the product of squares, and the sum of two consecutive triangular numbers. These properties highlight the complex and intriguing nature of the number 2025 within mathematical theory. Recommended read:
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@Thony Christie - 12d
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Pat'sBlog
Several blogs and articles delve into the historical development and conceptual understanding of mathematics. One area of focus includes the cosmic distance ladder, a method for measuring distances to astronomical objects. This is explored in a blog post discussing a video featuring commentary and corrections to the topic, referencing a collaboration between Grant Sanderson and others. This content clarifies inaccuracies and omissions present in the video, offering valuable insights for viewers.
Mathematical history is further enriched by discussions on geometric vanishes, the history of the factorial function, and mathematical induction. Geometric vanishes, often presented as puzzles, date back to the 16th century. One blog explores their history, referencing examples from the Renaissance era. A blog post and external links also explore the evolution of factorial notation and the concept of mathematical induction, explaining how it works like dominoes, cascading through a series of logical steps to prove mathematical statements. Recommended read:
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@uk.bookshop.org - 20d
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Now Appearing
, www.brianclegg.net
Popular science author Brian Clegg is offering a bonus puzzle related to his book, "Conundrum," a collection of 200 puzzles and ciphers. Participants who solve the puzzle will be entered into a draw for a free signed copy of the book. The puzzle requires solvers to combine different elements, with the solution needing to be submitted via a form on the Conundrum Book Site by the end of February 28, 2025.
Solving the bonus puzzle involves interpreting clues such as "Passing under the seventh Duke, take the date of the crocodile, add the psalm number and divide by the verse to get the answer." Hints are available on the website for those needing assistance. "Conundrum" challenges readers with general knowledge and lateral thinking skills across various subjects. More information about the book, including purchase options and a Facebook page, can be found on Brian Clegg's website. Recommended read:
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@medium.com - 49d
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medium.com
, medium.com
Recent explorations in probability, statistics, and data analysis have highlighted the significance of the z-score as a tool for understanding data distribution. The z-score, a standard way of comparing data points across different distributions, helps identify outliers and make data-driven decisions. This statistical method is crucial for understanding how unusual or typical a particular data point is in relation to the average and is a fundamental element in making sound inferences from data. Researchers are emphasizing the importance of mastering these fundamentals for anyone involved in data science or analytical fields.
The study of distributions plays a key role in both probability and generalized function theories. Understanding how these distributions are related enhances our insights into patterns and randomness in the natural world. The normal distribution, often represented by a bell curve, illustrates how many phenomena tend to cluster around an average, with rarer events falling at the extremes. Moreover, the essential mathmatics behind these theories, including descriptive statistics, basic probability, inferential statistics, and regression analysis, form the heart and soul of data science, allowing data scientists to analyze and make sense of raw data. Recommended read:
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@raindrops - 76d
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babycharmander.tumblr.com
, kingoftartesoss.tumblr.com
A recent online debate has highlighted the ambiguities present in seemingly straightforward mathematical expressions. The equation "8/2*(2+2)" has sparked controversy, with some arguing the correct answer is 1, while others insist it is 16. This disagreement stems from differing interpretations of the order of operations, specifically how multiplication and division are handled when both are present without parenthesis to determine which should be actioned first, with some proceeding left to right after solving the parenthesis and others assuming the 2(4) is a single term.
This has led to arguments about the correct application of PEMDAS (Parenthesis, Exponents, Multiplication, Division, Addition, Subtraction), often taught in schools. Some mathematicians have pointed out that multiplication and division are in fact the same operation, and the same goes for addition and subtraction, suggesting that operations should be resolved in order. The debate underscores the critical importance of clear and unambiguous mathematical notation, with some advocating for the use of fractions to avoid confusion when both division and multiplication are present. Recommended read:
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