Archive for the ‘mathematics’ category: Page 21

Jul 12, 2023

Claude 2: We are pleased to announce Claude 2, our new model

Posted by in categories: business, education, mathematics

We are pleased to announce Claude 2, our new model. Claude 2 has improved performance, longer responses, and can be accessed via API as well as a new public-facing beta website, We have heard from our users that Claude is easy to converse with, clearly explains its thinking, is less likely to produce harmful outputs, and has a longer memory. We have made improvements from our previous models on coding, math, and reasoning. For example, our latest model scored 76.5% on the multiple choice section of the Bar exam, up from 73.0% with Claude 1.3. When compared to college students applying to graduate school, Claude 2 scores above the 90th percentile on the GRE reading and writing exams, and similarly to the median applicant on quantitative reasoning.

Think of Claude as a friendly, enthusiastic colleague or personal assistant who can be instructed in natural language to help you with many tasks. The Claude 2 API for businesses is being offered for the same price as Claude 1.3. Additionally, anyone in the US and UK can start using our beta chat experience today.

Continue reading “Claude 2: We are pleased to announce Claude 2, our new model” »

Jul 11, 2023

Claude 2.0, Anthropic’s Latest ChatGPT Rival, Is Here — And This Time, You Can Try It

Posted by in categories: business, mathematics, robotics/AI

AI startup Anthropic has released its next major model – and this time, you can see for yourself how it compares to other AI standouts such as OpenAI’s ChatGPT or Inflection’s Pi. Anthropic announced on Tuesday that it’s released Claude 2, a large-language model that the company said showed improvement across several key benchmarks that include coding, math and reasoning skills, while producing fewer harmful answers.

Claude 2 is more widely available in its second major iteration. Anthropic launched a new beta-test website for general users to register in the U.S. and U.K. – – while opening up the new model to businesses by API at the same price they paid for Anthropic’s previous,… More.

New model Claude 2.0 is better at coding, math and reasoning, CEO Dario Amodei said. Unlike its predecessor, it’s available for general consumer use.

Continue reading “Claude 2.0, Anthropic’s Latest ChatGPT Rival, Is Here — And This Time, You Can Try It” »

Jul 6, 2023

European researchers design a rubber block that can count to ten

Posted by in categories: computing, mathematics, quantum physics

Physicist Lennard Kwakernaak finds the “complexity of simple things” intriguing, and it is a tough ask to make an inanimate object count.

A collaboration between researchers at Leiden University and AMOLF in Amsterdam has yielded a new metamaterial, a rubber block that can count. The researchers are calling it a Beam Counter and it is pretty nifty.

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Jul 6, 2023

Elusive Ninth Dedekind Number Discovered: Unlocking a Decades-Old Mystery of Mathematics

Posted by in categories: mathematics, supercomputing

Scientists from the Universities of Paderborn and Leuven solve long-known problem in mathematics.

Making history with 42 digits: Scientists at Paderborn University and KU Leuven have unlocked a decades-old mystery of mathematics with the so-called ninth Dedekind number. Experts worldwide have been searching for the value since 1991. The Paderborn scientists arrived at the exact sequence of numbers with the help of the Noctua supercomputer located there. The results will be presented in September at the International Workshop on Boolean Functions and their Applications (BFA) in Norway.

What started as a master’s thesis project by Lennart Van Hirtum, then a computer science student at KU Leuven and now a research associate at the University of Paderborn, has become a huge success. The scientists join an illustrious group with their work: Earlier numbers in the series were found by mathematician Richard Dedekind himself when he defined the problem in 1,897, and later by greats of early computer science such as Randolph Church and Morgan Ward. “For 32 years, the calculation of D was an open challenge, and it was questionable whether it would ever be possible to calculate this number at all,” Van Hirtum says.

Jul 5, 2023

From Atoms to Materials: Algorithmic breakthrough unlocks path to sustainable technologies

Posted by in categories: chemistry, computing, information science, mathematics, particle physics, sustainability

New research by the University of Liverpool could signal a step change in the quest to design the new materials that are needed to meet the challenge of net zero and a sustainable future.

Published in the journal Nature, Liverpool researchers have shown that a mathematical algorithm can guarantee to predict the structure of any material just based on knowledge of the atoms that make it up.

Developed by an interdisciplinary team of researchers from the University of Liverpool’s Departments of Chemistry and Computer Science, the algorithm systematically evaluates entire sets of possible structures at once, rather than considering them one at a time, to accelerate identification of the correct solution.

Jul 3, 2023

A.I. Is Coming for Mathematics, Too

Posted by in categories: mathematics, robotics/AI

For thousands of years, mathematicians have adapted to the latest advances in logic and reasoning. Are they ready for artificial intelligence?

Jul 2, 2023

We’re on the brink of the biggest changes to computing’s DNA and it’s not just quantum that’s coming

Posted by in categories: biotech/medical, computing, mathematics, quantum physics

Computers are built around logic: performing mathematical operations using circuits. Logic is built around things such as Adders—not the snake; the basic circuit that adds together two numbers. This is as true of today’s microprocessors as all those going back to the very beginning of computing history. You could go back to an abacus and find that, at some fundamental level, it does the same thing as your shiny gaming PC. It’s just much, much less capable.

Nowadays, processors can do a lot of mathematical calculations using any number of complex circuits in a single clock. And a lot more than just add two numbers together, too. But to get to your shiny new gaming CPU, there has been a process of iterating on the classical computers that came before, going back centuries.

Jul 2, 2023

Cosmological models are built on a simple, century-old idea, but new observations demand a radical rethink

Posted by in categories: mathematics, space

Our ideas about the universe are based on a century-old simplification known as the cosmological principle. It suggests that when averaged on large scales, the Cosmos is homogeneous and matter is distributed evenly throughout.

This allows a mathematical description of space-time that simplifies the application of Einstein’s general theory of relativity to the universe as a whole.

Our are based on this assumption. But as new telescopes, both on Earth and in space, deliver ever more precise images, and astronomers discover massive objects such as the giant arc of quasars, this foundation is increasingly challenged.

Jun 30, 2023

Decoding Nuclear Matter: A Two-Dimensional Solution Unveils Neutron Star Secrets

Posted by in categories: information science, mathematics, nuclear energy, particle physics, space

Scientists at Brookhaven National Laboratory have used two-dimensional condensed matter physics to understand the quark interactions in neutron stars, simplifying the study of these densest cosmic entities. This work helps to describe low-energy excitations in dense nuclear matter and could unveil new phenomena in extreme densities, propelling advancements in the study of neutron stars and comparisons with heavy-ion collisions.

Understanding the behavior of nuclear matter—including the quarks and gluons that make up the protons and neutrons of atomic nuclei—is extremely complicated. This is particularly true in our world, which is three dimensional. Mathematical techniques from condensed matter physics that consider interactions in just one spatial dimension (plus time) greatly simplify the challenge. Using this two-dimensional approach, scientists solved the complex equations that describe how low-energy excitations ripple through a system of dense nuclear matter. This work indicates that the center of neutron stars, where such dense nuclear matter exists in nature, may be described by an unexpected form.

Jun 28, 2023

Mathematicians Discover The Ninth Dedekind Number, After 32 Years of Searching

Posted by in categories: mathematics, supercomputing

Undeterred after three decades of looking, and with some assistance from a supercomputer, mathematicians have finally discovered a new example of a special integer called a Dedekind number.

Only the ninth of its kind, or D, it is calculated to equal 286 386 577 668 298 411 128 469 151 667 598 498 812 366, if you’re updating your own records. This 42 digit monster follows the 23-digit D discovered in 1991.

Grasping the concept of a Dedekind number is difficult for non-mathematicians, let alone working it out. In fact, the calculations involved are so complex and involve such huge numbers, it wasn’t certain that D would ever be discovered.

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