Samsung’s next big event could reveal foldables, smartwatches, and its first Android XR glasses.

While the rest of the world was watching the World Cup on Sunday evening, mathematician Levent Alpöge casually announced on X that he had used Anthropic’s Fable 5 to disprove the Jacobian conjecture.

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The Jacobian conjecture is a long-standing open problem in algebraic geometry that’s bedeviled highly accomplished mathematicians for almost 90 years. It was included in “Smale’s problems,” a list of unresolved math problems put forward by mathematician Stephen Smale in 1998.

But that proved no obstacle for Fable 5, Anthropic’s latest frontier AI model. (You may remember Fable 5 as the public version of Claude Mythos Preview, the AI model that Anthropic says has such advanced cybersecurity capabilities that it was too dangerous for public release.)

Alpöge is part of Harvard’s Society of Fellows, and his Linkedin profile notes an affiliation with Anthropic. We’ve reached out to Anthropic with questions about Alpöge’s work.

Meanwhile, for those of us who don’t understand polynomial functions from n-dimensional space, the question is: Does this represent a major breakthrough in artificial intelligence, or mathematics, or neither?

“This did not cause me to update my priors about what AI can and can’t do,” professor and mathematician Andrew Blumberg told Mashable. “This is exactly the kind of thing I would expect AI to be able to do. If there was a counterexample that was concise and easy to state that people haven’t found because it’s a pain to search through all this stuff, AI will find it.”

Blumberg, who has a joint appointment in mathematics and computer science at Columbia University, is involved in the First Proof project, an effort to test the capabilities of frontier large language models in solving research-level mathematics. So, it’s safe to say he understands mathematics and AI better than most of us.

‘You want to learn something from the answer’

Providing a counterexample to the Jacobian conjecture is still a significant achievement for AI in mathematics, Blumberg notes. But he also says there’s a big difference between providing a positive proof for a major math problem and providing a single counterexample that disproves it. Here’s the metaphor Blumberg used to explain.

“Suppose that Moses came down from the mountain with tablets, and on the tablet was written, ‘Cancer can be cured.’ Would you care? You don’t just want the answer to the question. You want to learn something from the answer. And the reason Smale thought this problem was important is because he thought that if we solved it, we would understand more things about the about the way nature is structured.”

In other words, Blumberg says, “this counterexample tells us essentially nothing. It’s just, you know, there are a lot of polynomials, and it’s hard for people to check them all, but it’s not hard for machines.”

The Jacobian conjecture isn’t the only math problem AI has tackled in recent months. OpenAI announced in May an “internal model” had disproved the Erdős unit distance conjecture, a central conjecture in discrete geometry.

However, in that case, the result was more productive, Blumberg says. That’s because OpenAI didn’t just provide a counterexample — but a disproof of the problem itself.

“The disproof there already has led to interesting things because experts in the area unpacked what was going on in the disproof and then used it to do other things,” Blumberg says.

And that’s not necessarily the case with the Jacobian conjecture counterexample, he adds — while conceding he’s not expert enough to see if there’s something special about the structure of the counterexample that we can learn from. “But it’s not in and of itself interesting.”

Disclosure: Ziff Davis, Mashable’s parent company, in April 2025 filed a lawsuit against OpenAI, alleging it infringed Ziff Davis copyrights in training and operating its AI systems.

You’ve waited long enough for Apple’s relaunch of Siri as an AI assistant, and now you can finally try out the Siri AI beta for iOS. But, psst, don’t tell anyone, but there’s even more Siri AI for you to try out with a secret Siri AI interface on Mac.

A Reddit user on the r/MacOSBeta subreddit has discovered a “hidden lightweight UI” for Siri AI in the macOS 27 Golden Gate beta. This feature basically provides users with an array of AI tools, presented in a pop-up menu whenever text is highlighted.

The Siri AI pop-up interface includes AI tools such as Rewrite, Proofread, “How does this sound?,” and “Edit with Siri.” There are also menu options for summarization and providing bullet points from the selected text.

Siri AI can also provide a selection of specific tools dependent on the context of what’s selected. For example, highlighting a phone number provides a pop-up to “Add to contacts” or when selecting an address the pop-up offers an “Open in Maps” option. There are tools for creating calendar events, composing messages and emails, and tracking flights and packages as well.

Why is the feature hidden? Well, as MacRumors points out, the Siri AI interface in macOS 27 developer beta 3 and public beta 1 is simply an unfinished product. Certain features don’t yet work how they’re supposed to. Some options don’t work at all. Clearly, Apple has yet to make it available because it’s simply not ready.

However, Reddit users say there is a way to turn the interface on in the macOS Golden Gate Beta. According to Redditor pdfu, if users running the macOS 27 beta simply need to open up the Terminal and input a few lines of code.

Please note: We do not recommend running terminal instructions or changing important OS files unless you fully understand what you’re doing. We have not tested these terminal instructions, so proceed at your own risk.

sudo mkdir -p /Library/Preferences/FeatureFlags/Domain && sudo defaults write /Library/Preferences/FeatureFlags/Domain/WritingTools LightweightUI_macOS -dict Enabled -bool true

After that, the Reddit threat instructs users to restart their computer and the Siri AI interface will be enabled.

If you’ve had enough of the unfinished interface, you can turn it back off by once again opening Terminal and the following input:

sudo defaults write /Library/Preferences/FeatureFlags/Domain/WritingTools LightweightUI_macOS -dict Enabled -bool false

It’s unclear if the Siri AI interface will launch with the official version of the new macOS. However, it’s certainly interesting to see Apple further brand its Siri AI relaunch as an all-in-one AI tool across the company’s products.

Samsung’s next big event could reveal foldables, smartwatches, and its first Android XR glasses.

While the rest of the world was watching the World Cup on Sunday evening, mathematician Levent Alpöge casually announced on X that he had used Anthropic’s Fable 5 to disprove the Jacobian conjecture.

This Tweet is currently unavailable. It might be loading or has been removed.

The Jacobian conjecture is a long-standing open problem in algebraic geometry that’s bedeviled highly accomplished mathematicians for almost 90 years. It was included in “Smale’s problems,” a list of unresolved math problems put forward by mathematician Stephen Smale in 1998.

But that proved no obstacle for Fable 5, Anthropic’s latest frontier AI model. (You may remember Fable 5 as the public version of Claude Mythos Preview, the AI model that Anthropic says has such advanced cybersecurity capabilities that it was too dangerous for public release.)

Alpöge is part of Harvard’s Society of Fellows, and his Linkedin profile notes an affiliation with Anthropic. We’ve reached out to Anthropic with questions about Alpöge’s work.

Meanwhile, for those of us who don’t understand polynomial functions from n-dimensional space, the question is: Does this represent a major breakthrough in artificial intelligence, or mathematics, or neither?

“This did not cause me to update my priors about what AI can and can’t do,” professor and mathematician Andrew Blumberg told Mashable. “This is exactly the kind of thing I would expect AI to be able to do. If there was a counterexample that was concise and easy to state that people haven’t found because it’s a pain to search through all this stuff, AI will find it.”

Blumberg, who has a joint appointment in mathematics and computer science at Columbia University, is involved in the First Proof project, an effort to test the capabilities of frontier large language models in solving research-level mathematics. So, it’s safe to say he understands mathematics and AI better than most of us.

‘You want to learn something from the answer’

Providing a counterexample to the Jacobian conjecture is still a significant achievement for AI in mathematics, Blumberg notes. But he also says there’s a big difference between providing a positive proof for a major math problem and providing a single counterexample that disproves it. Here’s the metaphor Blumberg used to explain.

“Suppose that Moses came down from the mountain with tablets, and on the tablet was written, ‘Cancer can be cured.’ Would you care? You don’t just want the answer to the question. You want to learn something from the answer. And the reason Smale thought this problem was important is because he thought that if we solved it, we would understand more things about the about the way nature is structured.”

In other words, Blumberg says, “this counterexample tells us essentially nothing. It’s just, you know, there are a lot of polynomials, and it’s hard for people to check them all, but it’s not hard for machines.”

The Jacobian conjecture isn’t the only math problem AI has tackled in recent months. OpenAI announced in May an “internal model” had disproved the Erdős unit distance conjecture, a central conjecture in discrete geometry.

However, in that case, the result was more productive, Blumberg says. That’s because OpenAI didn’t just provide a counterexample — but a disproof of the problem itself.

“The disproof there already has led to interesting things because experts in the area unpacked what was going on in the disproof and then used it to do other things,” Blumberg says.

And that’s not necessarily the case with the Jacobian conjecture counterexample, he adds — while conceding he’s not expert enough to see if there’s something special about the structure of the counterexample that we can learn from. “But it’s not in and of itself interesting.”

Disclosure: Ziff Davis, Mashable’s parent company, in April 2025 filed a lawsuit against OpenAI, alleging it infringed Ziff Davis copyrights in training and operating its AI systems.

You’ve waited long enough for Apple’s relaunch of Siri as an AI assistant, and now you can finally try out the Siri AI beta for iOS. But, psst, don’t tell anyone, but there’s even more Siri AI for you to try out with a secret Siri AI interface on Mac.

A Reddit user on the r/MacOSBeta subreddit has discovered a “hidden lightweight UI” for Siri AI in the macOS 27 Golden Gate beta. This feature basically provides users with an array of AI tools, presented in a pop-up menu whenever text is highlighted.

The Siri AI pop-up interface includes AI tools such as Rewrite, Proofread, “How does this sound?,” and “Edit with Siri.” There are also menu options for summarization and providing bullet points from the selected text.

Siri AI can also provide a selection of specific tools dependent on the context of what’s selected. For example, highlighting a phone number provides a pop-up to “Add to contacts” or when selecting an address the pop-up offers an “Open in Maps” option. There are tools for creating calendar events, composing messages and emails, and tracking flights and packages as well.

Why is the feature hidden? Well, as MacRumors points out, the Siri AI interface in macOS 27 developer beta 3 and public beta 1 is simply an unfinished product. Certain features don’t yet work how they’re supposed to. Some options don’t work at all. Clearly, Apple has yet to make it available because it’s simply not ready.

However, Reddit users say there is a way to turn the interface on in the macOS Golden Gate Beta. According to Redditor pdfu, if users running the macOS 27 beta simply need to open up the Terminal and input a few lines of code.

Please note: We do not recommend running terminal instructions or changing important OS files unless you fully understand what you’re doing. We have not tested these terminal instructions, so proceed at your own risk.

sudo mkdir -p /Library/Preferences/FeatureFlags/Domain && sudo defaults write /Library/Preferences/FeatureFlags/Domain/WritingTools LightweightUI_macOS -dict Enabled -bool true

After that, the Reddit threat instructs users to restart their computer and the Siri AI interface will be enabled.

If you’ve had enough of the unfinished interface, you can turn it back off by once again opening Terminal and the following input:

sudo defaults write /Library/Preferences/FeatureFlags/Domain/WritingTools LightweightUI_macOS -dict Enabled -bool false

It’s unclear if the Siri AI interface will launch with the official version of the new macOS. However, it’s certainly interesting to see Apple further brand its Siri AI relaunch as an all-in-one AI tool across the company’s products.