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Advancing mathematics research with AI-driven formal proof search

For decades, mathematicians have dreamed of a world where computers could do more than just crunch numbers—where they could actually think, reason, and help discover new truths. A major hurdle, however, has been the notorious “hallucination” problem of artificial intelligence: large language models (LLMs) are great at sounding confident, but they frequently make mathematical errors, making them unreliable for serious research.

Now, a groundbreaking study by researchers including Tsoukalas et al., published in Science, has shattered that barrier by combining the creative writing power of AI with the ruthless accuracy of a mathematical referee.

Their system—called AlphaProof Nexus—pioneers a new way of doing math by teaming up an AI with a specialized computer program called Lean is a “formal proof assistant,” a piece of software that acts as the ultimate skeptic. It doesn’t accept a mathematical proof unless every single logical step is airtight and verified by its strict compiler.

The endless loop of creativity and proof.

The magic of AlphaProof Nexus lies in its teamwork model:

1. The AI brainstorms: The large language model acts as the creative mathematician, generating ideas, strategies, and formal proofs in the Lean language.

2. The computer checks: The Lean compiler instantly tests the AI’s work. If there’s even a tiny flaw in the logic, it rejects it and points out why.

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Bonn researchers successfully rejuvenate human cells in a test tube

Researchers from the University Hospital of Bonn and the University of Bonn have succeeded in dramatically rejuvenating human cells in a test tube. To do so, they directly reprogrammed red blood cell precursors into stem cells from which neurons can be derived. During this process, the molecular clocks that indicate a cell’s age were reset. For example, blood cells from an 80-year-old were transformed into stem cells with a molecular age of less than 20 years. Since this rejuvenation process occurred very slowly, it is well-suited for a more detailed investigation of the underlying mechanisms. The results have been published in the journal Aging Cell.

The human body contains hundreds of different cell types. They all originate from the fertilized egg and therefore share the same genetic makeup. However, in the course of their development, they were committed to a specific fate: a skin cell cannot naturally become a liver cell, nor can a blood cell become a nerve cell.

Today, however, it is possible to reverse this determination in the laboratory. For example, nerve tissue can be grown from a skin cell, which may one day be used to treat neurodegenerative diseases. To achieve this reprogramming, researchers use a cocktail of various transcription factors. These factors cause the cell to read different genetic instructions and thus embark on a different developmental path.

Engineers at NASA’s Johnson Space Center modeled a Mars propellant plant turning Martian air and buried ice into 300 metric tons of methane and oxygen, and power generation was 59 percent of its landed mass

Mars propellant plant modeled at NASA Johnson would turn Martian air and buried ice into 300 metric tons of methane and oxygen in one Martian year

Hybrid quantum computer observes foundational quantum effect in a new setting

Physicists in the Department of Physics at the University of Oxford have used a hybrid quantum computer, made up of qubits and quantum oscillators, to observe the Aharonov–Bohm effect in a quantum simulation. The effect is a quantum phenomenon in which a particle can acquire a measurable phase by traveling around a magnetic flux, even though it never passes through a region where a magnetic field is present.

The result demonstrates how hybrid quantum systems can be used to simulate interactions between matter and gauge fields that become increasingly difficult to model on classical computers. The paper has been published in Nature Physics.

Remember Orkut? Its founder wants to bring it back

In a post on X on Thursday, Orkut Büyükkökten, the founder of the eponymous social network, urged users to visit Orkut.com and add their names in support of bringing it back, as well as invite others to join.

Orkut first debuted in 2004 as a side project by Büyükkökten, 51, while he was at Google. The social network went on to become hugely popular in India and Brazil but later lost ground to Facebook. Google eventually shut it down in September 2014, shifting its focus to other platforms, including Google+ and YouTube.

In a letter published on Orkut.com, Büyükkökten criticized how social media has evolved over the past two decades, particularly the growing influence of algorithms and AI-generated content. “Artificial intelligence is extraordinary technology, but it’s dissolving the one premise that made social networking special and worth building: that there was a person on the other side,” he wrote.

The Steel Was Never Real

7 review: how falling walls between science, bodies, and AI are changing everything.

https://youtu.be/tNXNZLZI7Us](https://youtu.be/tNXNZLZI7Us)

*Oct 10, 2026 • S7 E75 • 50:52*

What if the walls between the sciences were never real? 🗄️🔥

After 75 deep dives, Heliox found a hidden pattern: the best answers live in the overlap between disciplines.

In “The Steel Was Never Real,” you’ll hear:

• How a Bayesian model revealed that two identical heart attacks can have completely different biological causes.

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Ultrathin mesh harvests energy from human heart cells to generate electricity

A team of engineers led by the University of Massachusetts Amherst has designed an ultrathin, flexible mesh that seamlessly integrates electronics with human cells to provide a continuous, reliable, powerful electrical supply. The study, published in Science Advances, provides a potential solution to one of the most difficult problems in wearable and implantable electronics: how to get rid of batteries.

“Humans have long dreamed of a future where certain electronics can augment our abilities,” says Jun Yao, associate professor in UMass Amherst’s Riccio College of Engineering and the paper’s senior author. One can think of famous examples from science fiction’s cyborgs, but there are also plenty of everyday examples that have nothing to do with Star Trek: pacemakers and implantable defibrillators, for example, or deep brain stimulators, cochlear implants and various health monitors. Every one of these needs a power source.

Unfortunately, batteries—the dominant power source—are bulky and eventually run out of juice, and making them smaller and more flexible reduces the charge they can store.

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