Just a week after an AI disproved an 80-year-old conjecture and astonished mathematicians, another conjecture that had stood for half a century has fallen, inspired by the same techniques, but this time written entirely by humans. Last week, an unreleased AI model from OpenAI disproved an important conjecture first posed by Hungarian mathematician Paul Erdős, called the unit distance problem. The puzzle, which Erdős considered his "most striking contribution to geometry" and which many mathematicians had failed to unravel, concerns the number of similar-sized connections you can make between dots arranged on a flat surface. Erdős had set an upper ceiling on this number, which many experts had assumed was correct. But the AI model showed that this number could in fact be much larger, using an obscure trick from algebraic number theory to make complex structures with extremely high dimensions, which could then be used to arrange the dots in a very different arrangement than humans had considered.

Large language models (LLMs) exhibit in-context learning abilities which enable the same model to perform several tasks without any task-specific training. In contrast, traditional adaptation approaches, such as fine-tuning, modify the underlying models for each specific task. In-context learning, however, consistently underperforms task-specific tuning approaches even when presented with the same examples. While most existing approaches (e.g., prompt engineering) focus on the LLM's learned representations to patch this performance gap, our experiments actually reveal that LLM representations contain sufficient information to make good predictions. As such, we focus on the LLM's reasoning abilities and demonstrate that this performance gap exists due to their inability to perform simple probabilistic reasoning tasks. This raises an intriguing question: Are LLMs actually capable of learning how to reason in a task-agnostic manner? We answer this in the affirmative and, as a proof of concept, propose TART which generically improves an LLM's reasoning abilities using a synthetically trained reasoning module.

Are corpse flowers like'Pangy' dangerous? More information Adding us as a Preferred Source in Google by using this link indicates that you would like to see more of our content in Google News results. A blooming'Amorphophallus titanum,' also known as corpse flower, in Gunung Leuser National Park, North Sumatra Province, Indonesia in January 2025. Breakthroughs, discoveries, and DIY tips sent six days a week. What's big, rare, and smells like literal death?

The colorful explosion of flowers could last through June. Breakthroughs, discoveries, and DIY tips sent six days a week. The driest place on Earth could soon be awash in wildflowers. Death Valley National Park in California is expected to have the best bloom year since 2016. According to the National Park Service, many of their sprouts have not even flowered yet, so the fleeting beauty is just beginning.

However, using these 50B+ models requires high-end hardware, making them inaccessible to most researchers.

Why does chocolate turn white? No need to worry--some molecules just moved around. The white splotches on these pieces of chocolate are known as'chocolate bloom.' Breakthroughs, discoveries, and DIY tips sent six days a week. A few years ago, a small baker from the West Coast had a problem. A day or so after baking chocolate chip cookies, the chocolate chips would develop an unpleasant white haze.

Amateur mathematicians are using artificial intelligence chatbots to solve long-standing problems, in a move that has taken professionals by surprise. While the problems in question aren't the most advanced in the mathematical canon, the success of AI models in tackling them shows that their mathematical performance has passed a significant threshold, say researchers, and could fundamentally change the way we do mathematics. The questions being solved by AI originate from Hungarian mathematician Paul Erdős, who was famous for his ability to pose useful but difficult questions during a career that spanned over six decades. "The questions tended to be very simple, but very hard," says Thomas Bloom at the University of Manchester, UK. By his death in 1996, there were more than 1000 of these unsolved Erdős problems, spanning a wide range of mathematical disciplines, from combinatorics (the study of combinations) to number theory.

Large language models (LLMs) exhibit in-context learning abilities which enable the same model to perform several tasks without any task-specific training. In contrast, traditional adaptation approaches, such as fine-tuning, modify the underlying models for each specific task. In-context learning, however, consistently underperforms task-specific tuning approaches even when presented with the same examples. While most existing approaches (e.g., prompt engineering) focus on the LLM's learned representations to patch this performance gap, our experiments actually reveal that LLM representations contain sufficient information to make good predictions. As such, we focus on the LLM's reasoning abilities and demonstrate that this performance gap exists due to their inability to perform simple probabilistic reasoning tasks. This raises an intriguing question: Are LLMs actually capable of learning how to reason in a task-agnostic manner? We answer this in the affirmative and, as a proof of concept, propose TART which generically improves an LLM's reasoning abilities using a synthetically trained reasoning module.

Harmful algal blooms are a growing threat to inland water quality and public health worldwide, creating an urgent need for e fficient, accurate, and cost-e ff ective detection methods. This research introduces a high-performing methodology that integrates multiple open-source remote sensing data with advanced artificial intelligence models. Key data sources include Copernicus Sentinel-2 optical imagery, the Copernicus Digital Elevation Model (DEM), and NOAA's High-Resolution Rapid Refresh (HRRR) climate data, all e ffi ciently retrieved using platforms like Google Earth Engine (GEE) and Microsoft Planetary Computer (MPC). The NIR and two SWIR bands from Sentinel-2, the altitude from the elevation model, the temperature and wind from NOAA as well as the longitude and latitude were the most important features. The approach combines two types of machine learning models--tree-based models and a neural network--into an ensemble for classifying algal bloom severity. While the tree models performed strongly on their own, incorporating a neural network added robustness and demonstrated how deep learning models can e ff ectively use diverse remote sensing inputs. The method leverages high-resolution satellite imagery and AI-driven analysis to monitor algal blooms dynamically, and although initially developed for a NASA competition in the U.S., it shows potential for global application. Keywords: Machine learning; Inland Water; Algal Bloom; Remote Sensing; Data Fusion; Water Quality 1. Introduction Algal blooms are becoming the greatest inland water quality threat to public health and aquatic ecosystems that can degrade water quality to a greater extent than many chemicals (Brooks et al., 2016). Human nutrient loading and climate change (warming, altered rainfall) synergistically enhance cyanobacterial blooms in aquatic ecosystems (Paerl and Paul, 2012). Excessive nutrient loads in many cases comes from agricultural, industrial and other sources (Novotny, 2011). Phenology and trends of chlorophyll-a and cyanobacterial blooms are established (Matthews, 2014).

This paper explores the automatic classification of exam questions and learning outcomes according to Bloom's Taxonomy. A small dataset of 600 sentences labeled with six cognitive categories - Knowledge, Comprehension, Application, Analysis, Synthesis, and Evaluation - was processed using traditional machine learning (ML) models (Naive Bayes, Logistic Regression, Support Vector Machines), recurrent neural network architectures (LSTM, BiLSTM, GRU, BiGRU), transformer-based models (BERT and RoBERTa), and large language models (OpenAI, Gemini, Ollama, Anthropic). Each model was evaluated under different preprocessing and augmentation strategies (for example, synonym replacement, word embeddings, etc.). Among traditional ML approaches, Support Vector Machines (SVM) with data augmentation achieved the best overall performance, reaching 94 percent accuracy, recall, and F1 scores with minimal overfitting. In contrast, the RNN models and BERT suffered from severe overfitting, while RoBERTa initially overcame it but began to show signs as training progressed. Finally, zero-shot evaluations of large language models (LLMs) indicated that OpenAI and Gemini performed best among the tested LLMs, achieving approximately 0.72-0.73 accuracy and comparable F1 scores. These findings highlight the challenges of training complex deep models on limited data and underscore the value of careful data augmentation and simpler algorithms (such as augmented SVM) for Bloom's Taxonomy classification.