Archive for the ‘mathematics’ category

Dec 5, 2021

DeepMind’s AI helps untangle the mathematics of knots

Posted by in categories: mathematics, robotics/AI

Computer simulations and visualizations of knots and other objects have long helped mathematicians to look for patterns and develop their intuition, says Jeffrey Weeks, a mathematician based in Canton, New York, who has pioneered some of those techniques since the 1980s. But, he adds, “Getting the computer to seek out patterns takes the research process to a qualitatively different level.”

The authors say the approach, described in a paper in the 2 December issue of Nature1, could benefit other areas of maths that involve large data sets.

Dec 4, 2021

AI Is Discovering Patterns in Pure Mathematics That Have Never Been Seen Before

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

We can add suggesting and proving mathematical theorems to the long list of what artificial intelligence is capable of: Mathematicians and AI experts have teamed up to demonstrate how machine learning can open up new avenues to explore in the field.

While mathematicians have been using computers to discover patterns for decades, the increasing power of machine learning means that these networks can work through huge swathes of data and identify patterns that haven’t been spotted before.

In a newly published study, a research team used artificial intelligence systems developed by DeepMind, the same company that has been deploying AI to solve tricky biology problems and improve the accuracy of weather forecasts, to unknot some long-standing math problems.

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Dec 4, 2021

Pythagoras’ Revenge: Humans Didn’t Invent Mathematics, It’s What the Physical World Is Made Of

Posted by in categories: mathematics, particle physics, quantum physics, solar power, sustainability

Graphene consists of a planar structure, with carbon atoms connected in a hexagonal shape that resembles a beehive. When graphene is reduced to several nanometers (nm) in size, it becomes a graphene quantum dot that exhibits fluorescent and semiconductor properties. Graphene quantum dots can be used in various applications as a novel material, including display screens, solar cells, secondary batteries, bioimaging, lighting, photocatalysis, and sensors. Interest in graphene quantum dots is growing, because recent research has demonstrated that controlling the proportion of heteroatoms (such as nitrogen, sulfur, and phosphorous) within the carbon structures of certain materials enhances their optical, electrical, and catalytic properties.

Dec 1, 2021

Maths researchers hail breakthrough in applications of artificial intelligence

Posted by in categories: mathematics, robotics/AI

For the first time, computer scientists and mathematicians have used artificial intelligence to help prove or suggest new mathematical theorems in the complex fields of knot theory and representation theory.

The astonishing results have been published today in the pre-eminent scientific journal, Nature.

Professor Geordie Williamson is Director of the University of Sydney Mathematical Research Institute and one of the world’s foremost mathematicians. As a co-author of the paper, he applied the power of Deep Mind’s AI processes to explore conjectures in his field of speciality, representation theory.

Nov 30, 2021

Physics books of 2021

Posted by in categories: mathematics, particle physics

Explore 10 new works related to particle physics and astrophysics, plus a bonus book on math.

Nov 27, 2021

8 Intelligences: Are You a Jack of All Trades or a Master of One? | Howard Gardner | Big Think

Posted by in categories: business, education, ethics, internet, mathematics, media & arts, policy

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What does it mean when someone calls you smart or intelligent? According to developmental psychologist Howard Gardner, it could mean one of eight things. In this video interview, Dr. Gardner addresses his eight classifications for intelligence: writing, mathematics, music, spatial, kinesthetic, interpersonal, and intrapersonal.

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Nov 26, 2021

AI must have its own goals to be truly intelligent

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

There are synergies between the two kinds of intelligence. The brain serves the genes by improving the organism’s capability to survive and reproduce. In exchange, evolution favors genetic mutations that improve the brain’s innate and learning capacities for each species (this is why some animals are born with the ability to walk while others learn it weeks or months later).

At the same time, the brain comes with tradeoffs. Genes lose some of their control over the behavior of the organism when they relegate their duties to the brain. Sometimes, the brain can go chasing rewards that do not serve the self-replication of the genes (e.g., addiction, suicide). Also, the behavior learned by the brain does not pass on through genes (this is why you didn’t inherit your parents’ knowledge and had to learn language, math, and sports from scratch).

As Lee writes in Birth of Intelligence, “The fact that brain functions can be modified by experience implies that genes do not fully control the brain. However, this does not mean that the brain is completely free from genes, either. If the behaviors selected by the brain prevent the self-replication of its own genes, such brains would be eliminated during evolution. Thus, the brain interacts with the genes bidirectionally.”

Nov 25, 2021

Did Humans Invent Mathematics, or Is It a Fundamental Part of Existence?

Posted by in categories: mathematics, robotics/AI

Many people think that mathematics is a human invention. To this way of thinking, mathematics is like a language: it may describe real things in the world, but it doesn’t ‘exist’ outside the minds of the people who use it.

The idea of artificial intelligence overthrowing humankind has been talked about for many decades, and in January 2021, scientists delivered their verdict on whether we’d be able to control a high-level computer super-intelligence. The answer? Almost.

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Nov 24, 2021

Math may have caught up with Google’s quantum-supremacy claims

Posted by in categories: computing, mathematics, quantum physics

But, given the rapidly evolving quantum computing landscape, that may not matter.

Nov 23, 2021

The Mathematical Structure of Particle Collisions Comes Into View

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

And that’s where physicists are getting stuck.

Zooming in to that hidden center involves virtual particles — quantum fluctuations that subtly influence each interaction’s outcome. The fleeting existence of the quark pair above, like many virtual events, is represented by a Feynman diagram with a closed “loop.” Loops confound physicists — they’re black boxes that introduce additional layers of infinite scenarios. To tally the possibilities implied by a loop, theorists must turn to a summing operation known as an integral. These integrals take on monstrous proportions in multi-loop Feynman diagrams, which come into play as researchers march down the line and fold in more complicated virtual interactions.

Physicists have algorithms to compute the probabilities of no-loop and one-loop scenarios, but many two-loop collisions bring computers to their knees. This imposes a ceiling on predictive precision — and on how well physicists can understand what quantum theory says.

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