Apr 14, 2026 09:33 PM
(This post was last modified: Apr 14, 2026 09:40 PM by C C.)
The AI revolution in math has arrived
https://www.quantamagazine.org/the-ai-re...-20260413/
EXCERPT: Mathematicians who had dismissed AI models as too error-prone to be useful started playing around with them. Those early adopters found, to their surprise, not only that the models were good at puzzles, but that they could help break genuinely new ground. Soon, mathematicians were using AI to discover and prove new results, accomplishing in a day what would have once taken them weeks or months. “2025 was the year when AI really started being useful for many different tasks,” said Terence Tao, a prominent mathematician at the University of California, Los Angeles.
While no single new result is a world-beating breakthrough, some of them are on par with discoveries published in professional mathematical journals. In some cases, algorithms formulate a conjecture, prove it, and verify the proof with minimal human intervention. In others, extensive chats with large language models such as ChatGPT, Claude, or Gemini lead to novel proof strategies.
“This guy’s got a shovel. This guy’s got a pickax. Together we can bore a tunnel,” Tao said. There’s “a lot of throwing things at the wall to see what sticks.”
Though Tao is perhaps the most prominent exponent of AI’s utility in mathematics, others agree. Even by solving easy problems, said Daniel Litt (opens a new tab)of the University of Toronto, AI “is changing how mathematics is done.”
Soon, “it will look and feel altogether different from the way mathematics was traditionally done,” Tao said. Where before mathematicians studied one problem at a time, “with these tools you can solve thousands of problems at once and start doing statistical studies.” Though nobody I spoke with thinks AI will replace mathematicians, Tao added that “there are a lot of institutional changes, cultural changes, we will have to make.” (MORE - missing details)
Does gravity follow the rules of quantum mechanics?
https://www.eurekalert.org/news-releases/1123987
INTRO: In quantum physics, objects can exist in multiple states at the same time—a phenomenon known as quantum superposition, where a particle does not have a single definite value of position or momentum until it is measured. A major open question is whether gravity, one of the fundamental forces, also follows the quantum rule.
One way to examine this is through gravity-induced entanglement, in which two objects that interact only via gravity become quantum mechanically linked. Now, researchers led by Professor Kazuhiro Yamamoto at the Faculty of Science and Quantum and Spacetime Research Institute, Kyushu University, have proposed a way to enhance the quantum superposition of a mirror's position in systems in which two mirrors interact via gravity, thereby making the resulting entanglement signal easier to detect.
Their findings, published in the journal Physical Review Research on April 13, 2026, represent a crucial step toward experimentally testing whether gravity is fundamentally quantum.
Gravity-induced entanglement suggests that if gravity follows the quantum mechanics, then two objects interacting only through gravity should become entangled. This is a natural prediction of the quantum nature of gravity. Detecting this effect, however, is challenging as gravity is weak at small scales.
One way to make such effects observable is to carefully control relatively large objects so that they are in the quantum regime. This is achieved by cooling the large objects near their lowest-energy state, called the quantum ground state, not only through cryogenic cooling but also through an optimal filtering technique. At this point, random thermal motion is minimized. In this state, quantum behavior becomes easier to detect. The object's position and momentum are then governed by the Heisenberg uncertainty principle, which states that neither property can be known with perfect precision.
Using this approach, the research team including Ryotaro Fukuzumi, Kosei Hatakeyama, Daisuke Miki, along with their colleagues from Kyushu University, Japan, and the California Institute of Technology, USA, have proposed a method to enhance gravity-induced entanglement by creating a momentum-squeezed state in movable mirrors... (MORE - details, no ads)
https://www.quantamagazine.org/the-ai-re...-20260413/
EXCERPT: Mathematicians who had dismissed AI models as too error-prone to be useful started playing around with them. Those early adopters found, to their surprise, not only that the models were good at puzzles, but that they could help break genuinely new ground. Soon, mathematicians were using AI to discover and prove new results, accomplishing in a day what would have once taken them weeks or months. “2025 was the year when AI really started being useful for many different tasks,” said Terence Tao, a prominent mathematician at the University of California, Los Angeles.
While no single new result is a world-beating breakthrough, some of them are on par with discoveries published in professional mathematical journals. In some cases, algorithms formulate a conjecture, prove it, and verify the proof with minimal human intervention. In others, extensive chats with large language models such as ChatGPT, Claude, or Gemini lead to novel proof strategies.
“This guy’s got a shovel. This guy’s got a pickax. Together we can bore a tunnel,” Tao said. There’s “a lot of throwing things at the wall to see what sticks.”
Though Tao is perhaps the most prominent exponent of AI’s utility in mathematics, others agree. Even by solving easy problems, said Daniel Litt (opens a new tab)of the University of Toronto, AI “is changing how mathematics is done.”
Soon, “it will look and feel altogether different from the way mathematics was traditionally done,” Tao said. Where before mathematicians studied one problem at a time, “with these tools you can solve thousands of problems at once and start doing statistical studies.” Though nobody I spoke with thinks AI will replace mathematicians, Tao added that “there are a lot of institutional changes, cultural changes, we will have to make.” (MORE - missing details)
Does gravity follow the rules of quantum mechanics?
https://www.eurekalert.org/news-releases/1123987
INTRO: In quantum physics, objects can exist in multiple states at the same time—a phenomenon known as quantum superposition, where a particle does not have a single definite value of position or momentum until it is measured. A major open question is whether gravity, one of the fundamental forces, also follows the quantum rule.
One way to examine this is through gravity-induced entanglement, in which two objects that interact only via gravity become quantum mechanically linked. Now, researchers led by Professor Kazuhiro Yamamoto at the Faculty of Science and Quantum and Spacetime Research Institute, Kyushu University, have proposed a way to enhance the quantum superposition of a mirror's position in systems in which two mirrors interact via gravity, thereby making the resulting entanglement signal easier to detect.
Their findings, published in the journal Physical Review Research on April 13, 2026, represent a crucial step toward experimentally testing whether gravity is fundamentally quantum.
Gravity-induced entanglement suggests that if gravity follows the quantum mechanics, then two objects interacting only through gravity should become entangled. This is a natural prediction of the quantum nature of gravity. Detecting this effect, however, is challenging as gravity is weak at small scales.
One way to make such effects observable is to carefully control relatively large objects so that they are in the quantum regime. This is achieved by cooling the large objects near their lowest-energy state, called the quantum ground state, not only through cryogenic cooling but also through an optimal filtering technique. At this point, random thermal motion is minimized. In this state, quantum behavior becomes easier to detect. The object's position and momentum are then governed by the Heisenberg uncertainty principle, which states that neither property can be known with perfect precision.
Using this approach, the research team including Ryotaro Fukuzumi, Kosei Hatakeyama, Daisuke Miki, along with their colleagues from Kyushu University, Japan, and the California Institute of Technology, USA, have proposed a method to enhance gravity-induced entanglement by creating a momentum-squeezed state in movable mirrors... (MORE - details, no ads)