Mathematicians have described a new class of shape that characterizes forms commonly found in nature — from the chambers in the iconic spiral shell of the nautilus to the way in which seeds pack into plants.
‘Soft cells’ — shapes with rounded corners and pointed tips that fit together on a plane — feature in onions, molluscs and more.
With only 6.6B activate parameters, GRIN MoE achieves exceptionally good performance across a diverse set of tasks, particularly in coding and mathematics tasks.
Microsoft releases GRIN😁 MoE
GRadient-INformed MoE
Scientists from the U.S. Department of Energy’s (DOE) Brookhaven National Laboratory have shown that a type of qubit whose architecture is more amenable to mass production can perform comparably to qubits currently dominating the field. With a series of mathematical analyses, the scientists have provided a roadmap for simpler qubit fabrication that enables robust and reliable manufacturing of these quantum computer building blocks.
In 1971, English mathematical physicist and Nobel-prize winner Roger Penrose proposed how energy could be extracted from a rotating black hole. He argued that this could be done by building a harness around the black hole’s accretion disk, where infalling matter is accelerated to close to the speed of light, triggering the release of energy in multiple wavelengths.
Since then, multiple researchers have suggested that advanced civilizations could use this method (the Penrose Process) to power their civilization and that this represents a technosignature we should be on the lookout for.
Examples include John M. Smart’s Transcension Hypothesis, a proposed resolution to the Fermi Paradox where he suggested advanced intelligence may migrate to the region surrounding black holes to take advantage of the energy available.
Mathematician Bernhard Riemann was born #OTD in 1826.
Bernhard Riemann was another mathematical giant hailing from northern Germany. Poor, shy, sickly and devoutly religious, the young Riemann constantly amazed his teachers and exhibited exceptional mathematical skills (such as fantastic mental calculation abilities) from an early age, but suffered from timidity and a fear of speaking in public. He was, however, given free rein of the school library by an astute teacher, where he devoured mathematical texts by Legendre and others, and gradually groomed himself into an excellent mathematician. He also continued to study the Bible intensively, and at one point even tried to prove mathematically the correctness of the Book of Genesis.
Although he started studying philology and theology in order to become a priest and help with his family’s finances, Riemann’s father eventually managed to gather enough money to send him to study mathematics at the renowned University of Göttingen in 1846, where he first met, and attended the lectures of, Carl Friedrich Gauss. Indeed, he was one of the very few who benefited from the support and patronage of Gauss, and he gradually worked his way up the University’s hierarchy to become a professor and, eventually, head of the mathematics department at Göttingen.
Enjoy the videos and music you love, upload original content, and share it all with friends, family, and the world on YouTube.
Australian physicists resolve time travel paradox, showing it could be possible according to einstein’s theory.
Australian physicists have demonstrated that time travel could be theoretically possible by resolving the classic grandfather paradox. By aligning Einstein’s theory of general relativity with classical dynamics, researchers at the University of Queensland showed that time travel scenarios, such as altering past events, can coexist without resulting in logical inconsistencies. They used a model involving the coronavirus pandemic to illustrate how events would adjust themselves to avoid paradoxes. This research suggests that time travel, while complex, does not inherently create contradictions and could be feasible according to current mathematical models.
After reading the article, a Reddit user named Harry gained more than 524 upvotes with this comment: Isn’t the problem with time travel that it is also space travel? The earth isn’t in the same spot now as it was when you first started reading my comment, the earth travels very fast in space so wouldn’t you also have to find out where in space the earth was in 1950 (chose random date) in order to physically travel there? And how could we know where in physical space the earth was in 1950?
Some big claims here: https://openai.com/index/learning-to-reason-with-llms/
OpenAI o1 ranks in the 89th percentile on competitive programming questions (Codeforces), places among the top 500 students in the US in a qualifier for the USA Math Olympiad (AIME), and exceeds human PhD-level accuracy on…
We are introducing OpenAI o1, a new large language model trained with reinforcement learning to perform complex reasoning. o1 thinks before it answers—it can produce a long internal chain of thought before responding to the user.
Several fields of mathematics have developed in total isolation, using their own “undecipherable” coded languages. In a new study published in Proceedings of the National Academy of Sciences, Tamás Hausel, professor of mathematics at the Institute of Science and Technology Austria (ISTA), presents “big algebras,” a two-way mathematical ‘dictionary’ between symmetry, algebra, and geometry, that could strengthen the connection between the distant worlds of quantum physics and number theory.
ChatGPT creator OpenAI on Thursday released a new series of artificial intelligence models designed to spend more time thinking—in hopes that generative AI chatbots provide more accurate and beneficial responses.
The new models, known as OpenAI o1-Preview, are designed to tackle complex tasks and solve more challenging problems in science, coding and mathematics, something that earlier models have been criticized for failing to provide consistently.
Unlike their predecessors, these models have been trained to refine their thinking processes, try different methods and recognize mistakes, before they deploy a final answer.
