TECH

The new artificial intelligence war may be decided by something other than intelligence

Historically, most technological breakthroughs do not fundamentally affect the risk of conflict. There have been notable exceptions. The invention of printing helped fuel the social and religious upheavals in Europe that later contributed to the outbreak of the Thirty Years’ War in 1618. By contrast, nuclear weapons have significantly dampened the risk of great power war since World War II.

Because advanced artificial intelligence (AI) could create far-reaching social, economic, and military disruptions, it could be another exceptional technology with important implications for international security (Kissinger, Schmidt, and Mundie 2024). Analysts need to seriously consider the possibility that AI may cause changes in the international security landscape that could lead to the outbreak of wars that would not otherwise happen (Mitre and Predd 2025).

Drawing on decades of research about what conditions make wars more or less likely throughout history, we examine six hypotheses about how AI might increase the potential for major interstate war (Van Evera 1994). The hypotheses reflect different ways that AI’s effects on militaries, economies, and societies might undermine international stability, with a focus on the pathways that appear most plausible and concerning. We evaluate these hypotheses by identifying what key conditions are needed for them to be valid and then assessing the likelihood that those conditions will align in ways that would make conflict more likely.

Exploring the consequences of advanced artificial intelligence that is much more sophisticated than what exists today, the analysis assumes that AI could eventually become capable of reliably matching human performance across a wide range of cognitive tasks, which some technologists refer to as “artificial general intelligence” (Kahl 2025).

Overall, the risk that AI will directly trigger a major war appears low, especially if governments take steps to manage the technology’s use. But AI could create destabilizing shifts in the balance of power or negatively influence human strategic judgment in ways that fuel misperceptions. Fortunately, prudent government policies can help limit these risks.

For years, the race for leadership in artificial intelligence was measured almost exclusively by one question: which company created the most powerful model? That logic remains important, but a second metric is emerging that could completely change the game. Cheaper models are achieving results close to those of the most advanced systems while operating at much higher speeds and lower costs. For those developing AI agents, this difference could be decisive.

Google highlighted this shift with Gemini 3.8 Flash, introduced as its most advanced general-purpose model to date. The tool was developed specifically for programming, multi-step reasoning, and agentic tasks—scenarios where the AI ​​must use tools, verify results, and correct its own errors.

The promotional price is $0.75 per million input tokens and $3.75 per million output tokens. This rate applies through the end of 2026, after which the prices will double the following year.

The most interesting aspect, however, emerges when price and performance are analyzed together. On Artificial Analysis’s Intelligence Index, Gemini 3.8 Flash scores 59 points in high-level reasoning, placing it close to the configurations of much more expensive models.

Its speed is also noteworthy. The system reaches approximately 327 tokens per second—more than four times the median recorded among reasoning models evaluated by the platform.

There is, however, a caveat: the new Gemini uses about 30% more output tokens than its predecessor and may make more tool calls. Consequently, while the price per token remains low, the effective cost per task has risen by about 40%.

Just when it seemed Google had found a particularly aggressive balance between price and capability, Meta unveiled Muse Spark 1.3.

The model was designed for programming and long-running tasks, particularly those requiring the management of tools, files, and multiple instructions within a single context. In the "xhigh" configuration, Muse Spark 1.3 scores 61 points on the Intelligence Index—two points higher than Gemini 3.8 Flash. The "max" variant, currently limited in availability, reaches 62 points.

The cost is also competitive: $1.25 per million input tokens and $4.25 per million output tokens. According to Artificial Analysis, each task analyzed costs approximately $0.55—slightly less than Google's model.

Meta also claims that the new system uses about 20% fewer tool calls and 25% fewer tokens than the previous generation.

This doesn't automatically make Muse Spark the best model. Gemini, for instance, boasts nearly double the generation speed. Furthermore, no single benchmark can replicate every real-world use case.

Even so, the results highlight something important: the gap between cost-effective models and cutting-edge systems is narrowing rapidly.

The shift that might unsettle OpenAI and Anthropic... This is where the competition gets interesting. For a simple query, the price difference between models might seem negligible. But autonomous agents operate differently.

An AI tasked with coding an application, analyzing hundreds of documents, or conducting extensive research might make dozens of tool calls and consume millions of tokens. In that scenario, small price differences are no longer small.

More expensive models from OpenAI and Anthropic can cost several times more per million tokens. In certain comparisons, Gemini 3.8 Flash costs up to 13 times less per token while maintaining performance levels relatively close to the competition in some evaluations.

This doesn't mean Google or Meta have definitively overtaken the leaders in artificial intelligence. That isn't the point.

To compete, they may not even need to create the smartest model on the planet. It is enough to offer an AI capable of performing nearly the same tasks, with sufficient speed and at a fraction of the price.

In the era of autonomous agents, that detail could be huge. A difference of just a few points on a benchmark may matter less than the number of tasks a company can execute within the same budget.

The next great battle in artificial intelligence, therefore, may not be decided solely by who has the smartest model. The winner could be the one that delivers enough intelligence to get the job done—while spending far less to do so.

mundophone

 

TECH

Machine learning tool could speed up fire safety assessments for steel beams

The numerous advantages of steel in construction, such as strength-to-weight ratio, ease of construction, etc., have made steel structures widely used in various industries. However, when compared to concrete, in the case of fire incidence, steel beams can experience significant deformation, compromising their structural integrity and posing serious risks to life and property. For this reason, an efficient approach to measuring and evaluating the deformation of steel beams when subjected to fire is essential for accurately quantifying fire-induced damage, which will consequently facilitate efficient decision-making (process). Historical fire incidents around the world, such as the World Trade Center (2001) and the Grenfell Tower (2017) have underscored the vulnerability of steel structures to fire. According to a statistical report on fire accidents around the world, over seven million fire accidents took place all over the world causing about seventy thousand casualties. With the increase of structural fire knowledge, considerations for fire resistance are incorporated into standards. 

These considerations are traditionally based on standard experiments conducted on individual structural members subjected to predetermined boundary conditions and structural loading. This practice, despite being accepted by engineering practitioners and academicians, has certain limitations. A typical example is the seven large-scale fire tests (BS 8414‐1) commissioned by the UK government following the Grenfell event to determine the combinations of insulation and aluminium composite material (ACM) cladding that could be safely used. According to the method, it is required that the test be stopped when flames are observed higher than the test. 

Thus, this method cannot be used to examine all façade fire scenarios. The common practice is to perform these tests on an individual-member level, which, in addition to the inability to capture real fire scenarios and neglecting the mechanical influence of the other structural members, is also expensive and time-consuming. While BS 8414-1 cannot (economically) simulate the wide range of real-world fire propagation scenarios or predict structural behavior beyond visual flame spread, the proposed ML-based regression approach addresses this limitation by learning from comprehensive fire test data to predict continuous deformation patterns across diverse fire exposure conditions. Furthermore, empirical formulas derived from experimental results typically consider the temperature distribution along the beam's cross-section and use simplified assumptions to estimate the resulting deformations. However, these formulas often lack accuracy and fail to capture the complex behaviour of steel subjected to high temperatures. 

They also assume uniform heating across the beam, which is not representative of real fire scenarios. As a result, empirical formulas may lead to significant deviations in predicting the actual fire-induced deformations. Hence, numerical simulation is considered a useful tool to investigate, understand, and analyse such fires, and, of particular use, specific phenomena can be isolated and evaluated more easily in a mathematical and cost-effective way. Several studies have shown the feasibility and usefulness of numerical simulation for high-rise building fires. The application of computational fluid dynamics and fire dynamics simulator for numerical simulations entails a deeper analysis of the fire propagation pattern in the World Trade Centre after the incident. In addition to employing standard fire curves, some researchers successfully adapt multiple fire models to simulate complicated fire scenarios in more accurately and effectively. 

While these methods have provided valuable insights into the fire-induced deformation of steel beams, they have certain limitations. Some of the limitations include the complexity of developing a comprehensive model, which also requires advanced knowledge in mathematics as well as mechanics. They often rely on simplifying assumptions and may not accurately capture the intricate behaviour of steel under fire conditions. Additionally, traditional methods can be time-consuming, computationally expensive, and require significant expertise to implement.

Researchers at The University of Manchester, Shandong Jiaotong University and Harbin Engineering University have developed a machine learning framework, enabling rapid prediction of how protected steel beams respond during a fire, offering engineers a faster way to assess fire safety performance in industrial structures.

The study, published in the KSCE Journal of Civil Engineering, focuses on three-sided protected steel beams, a configuration commonly used in offshore and onshore oil and gas processing facilities. In these structures, the upper surface of the beam remains exposed, creating complex temperature patterns that can be difficult to model accurately.

Understanding how heat moves through these beams during a fire is an important part of structural fire engineering. However, temperature distribution is influenced by several interacting factors, including beam depth, insulation thickness and material conductivity, making conventional analytical equations challenging to apply across different scenarios.

To address this challenge, the researchers created an automated workflow that links computer modelling, simulation and data processing. The system combines Python, ABAQUS and MATLAB with machine learning techniques to automatically generate models, run simulations and train predictive algorithms.

The team generated a database containing 414 standard beam models and 63 welded beam models, covering beam depths ranging from 127 mm to 1500 mm and a variety of insulation configurations. These data were then used to train machine learning models capable of predicting beam temperatures during fire exposure.

“Current fire engineering assessments often rely on detailed numerical simulations, which require significant time and computing resources, while analytical equations are limited in accuracy by the number of parameters. Our framework demonstrates how machine learning can be combined with automated modelling techniques to deliver accurate temperature predictions much more efficiently. This could support the evaluation of fire protection systems across a wide range of steel beam configurations„...Dr Yang Li, Department of Civil Engineering and Management

The researchers found that the best-performing approach, based on gradient boosting, achieved a root mean squared error of just 1.34°C when compared with test data. More than 83% of prediction calculations were completed within 60 seconds, demonstrating the potential for rapid assessment of fire protection requirements.

The study also introduced a model generation agent incorporating a two-dimensional contact detection algorithm, enabling the automatic creation of beam heat transfer models. A dedicated data processing pipeline and batch-generation system were developed to support large-scale training while reducing memory requirements, allowing the work to be carried out using a single graphics processing unit.

According to the researchers, the approach could help engineers evaluate insulation strategies and fire protection requirements more efficiently, particularly in sectors where structural fire performance is a key design consideration. By reducing the need for repeated complex simulations, the framework has the potential to support faster decision-making during engineering design and assessment.

The research was conducted by Yang Li and Peijun Wang et al. The paper lists the Department of Civil Engineering and Management of The University of Manchester and Shandong University, as the authors' institutional affiliation.

The new artificial intelligence tool developed by researchers at the University of Manchester, in collaboration with Shandong Jiaotong University and Harbin Engineering University, promises to revolutionize and drastically accelerate fire safety assessments for protected steel beams. The model replaces lengthy, complex physical simulations with heat transfer predictions in record time.

The model's technical impact... Traditionally, engineers rely on expensive practical tests or Finite Element Analysis (FEA) simulations that require high computing power and hours of processing time. The machine learning-based approach overcomes these barriers with impressive results.

Remarkable speed: Over 83% of prediction calculations were completed in less than 60 seconds.

Surgical precision: The most efficient technique, based on gradient boosting, achieved a root mean square error (RMSE) of just 1.34°C compared to actual experimental data.

Accessible hardware: Thanks to a dedicated data processing and batch generation pipeline, memory requirements were drastically and efficiently reduced, allowing the entire large-scale training process to run on a single graphics processing unit (GPU).

Thermal model automation... In addition to predicting the failure temperatures of metal alloys, the study introduced an intelligent model-generating agent that incorporates a two-dimensional contact detection algorithm. This means the AI ​​itself can automatically create heat transfer models for the beams, enabling engineers to rapidly test a wide range of thermal insulation thicknesses and passive fire protection strategies.

This technology optimizes decision-making during the early stages of civil engineering projects, ensuring structurally safer buildings without inflating costs through endless simulations.

The University of Manchester

TECH

Fujitsu introduced microscopic defects into diamonds to create a new type of quantum computer

Forget traditional quantum chips for a moment. Fujitsu has just unveiled a prototype that uses diamonds, tin atoms, and light particles to tackle one of quantum computing's biggest hurdles: scaling up machine size without losing control of the qubits. While it still requires operating temperatures of an impressive -271.6°C, it features a characteristic that could completely transform how quantum computers are built.

The new computer developed by Fujitsu employs an approach known as "diamond spin."

This doesn't simply mean swapping silicon for a gemstone.

Researchers work with synthetic diamonds containing microscopic defects carefully engineered into their crystal structure. The prototype utilizes tin-vacancy centers, known by the acronym SnV.

In these centers, a tin atom occupies a position between two vacancies within the diamond's structure. These tiny defects allow for the creation and control of quantum states that function as qubits.

Similar systems traditionally use nitrogen-based NV centers. Fujitsu opted for tin because its structure offers greater symmetry and is less susceptible to certain types of external noise.

SnV centers can also emit light with an intensity roughly ten times greater than the conventional approach—an advantage that is particularly appealing given the company's future plans.

However, there is a detail that prevents any conclusion that Fujitsu has solved the issue of extreme temperatures in quantum computing.

The prototype operates at approximately -271.6°C, or about 1.55 Kelvin.

That is just a few degrees above absolute zero.

Even so, it is a higher temperature than the benchmark of approximately -273.13°C cited by Fujitsu for superconducting quantum computers.

Therefore, this new development is not a room-temperature quantum computer.

Far from it. The great promise lies in another feature: the modules can be connected using light.

And this aims to solve a fundamental problem.

Building a few qubits is one thing. Creating thousands or millions of them that work reliably within the same system is far more complex.

Instead of trying to fit everything into a single, gigantic structure, Fujitsu is betting on smaller modules that can be interconnected.

Light can transform small modules into a massive machine...The architecture uses photons to establish quantum connections between modules.

These links can occur between qubits located on different chips and even between systems housed in separate cryogenic units.

To make this possible, Fujitsu developed photonic circuits that combine nanometric diamond structures with alumina optical waveguides capable of carrying the light emitted by SnV centers.

It is like building a giant computer by assembling smaller parts, but using the quantum properties of light to enable them to work together.

This modular strategy could greatly facilitate future expansion.

Fujitsu and the QuTech institute at Delft University of Technology have previously demonstrated operations involving entanglement and quantum gates between NV centers housed in separate cryogenic units.

Now, the company aims to scale this concept up to a much larger architecture.

The 1,000-qubit milestone is still a few years away...This is where an important detail comes in. The computer unveiled now does not feature 1,000 logical qubits.

That figure is part of Fujitsu's technology roadmap.

The company plans to unveil a multi-module diamond-spin computer prototype in 2027. Subsequently, its goal is to achieve a system with 250 logical qubits in the 2030 fiscal year and reach 1,000 logical qubits in the 2035 fiscal year.

The word "logical" is also significant.

Physical qubits are extremely sensitive to noise and errors. Therefore, fault-tolerant quantum computers must combine multiple physical qubits to produce more reliable logical qubits. The hope is that the characteristics of diamond spins will allow for the formation of these logical qubits using fewer physical qubits than some competing approaches.

Fujitsu does not intend to abandon superconducting quantum computers.

Quite the opposite.

The company plans to develop technologies capable of integrating diamond-based systems with superconducting machines, leveraging the advantages of different architectures.

The current prototype has also already been operated in a test environment using the company's hybrid quantum computing platform.

There is still a vast gap between demonstrating a prototype and building a fault-tolerant quantum machine capable of solving commercially relevant problems.

But the experiment points to a possible way to overcome a fundamental obstacle: how to keep adding qubits without turning the computer into an uncontrollable structure.

Fujitsu's answer may lie in a rather unlikely combination.

Tiny defects within diamonds create the qubits. And particles of light may be responsible for linking them all together.

Comment from Vivek Mahajan, Corporate Executive Officer, Corporate Vice President, CTO, in charge of System Platform, Fujitsu Limited

"The diamond-spin approach we have applied in this prototype not only offers exceptional scalability in its own right, but also has the potential to be integrated with superconducting quantum computers to further extend their capabilities, enabling more complex and large-scale computations.

Under our roadmap to achieve a 250 logical qubit system by fiscal 2030 and a 1,000 logical qubit system by fiscal 2035, Fujitsu will continue advancing practical quantum computing across a broad range of areas, from software to hardware, while leveraging the key advantages of the diamond-spin approach, including high fidelity and optical connectivity."

Comment from Dr. Kees Eijkel, General Director, QuTech, Delft University of Technology...“We are delighted to announce this prototype diamond spin quantum computer as a result of the collaborative research conducted since 2020 between Fujitsu, Delft University of Technology, and QuTech. It is a major milestone in our strong collaboration. Demonstrating the scalability expected of diamond spin quantum computing remains a long and challenging journey. However, by further strengthening our collaboration with Fujitsu, we are committed to tackling this ambitious and meaningful challenge and leading the development of next-generation quantum technologies.”

Overview of developed technologies...The prototype features these three technologies developed by Fujitsu:

Heterogeneous material bonding and thinning technology for scalable quantum computing chips...To create quantum computing chips using SnV centers, Fujitsu developed heterogeneous material bonding technology to bond high-quality diamond substrates ion-implanted with tin to alumina/silicon dioxide substrates. Fujitsu also developed thinning technology to reduce the thickness of diamond substrates from several hundred micrometers to several hundred nanometers, making them suitable for use in quantum computing chips.

Photonics-integrated circuit fabrication technology for SnV centers...Fujitsu developed technology to fabricate photonics integrated circuits [3] that integrate nanometer-sized diamond crystals containing SnV centers with alumina optical waveguides, which are transparent in the visible light region, to extract single photons emitted from SnV centers during qubit readout. For diamond processing, Fujitsu utilized the results of joint research with The University of Tokyo.

Quantum circuit conversion technology for diamond spin approach...The diamond-spin approach requires qubit control by combining light, microwaves, and radio frequency waves. Fujitsu developed a mechanism to convert quantum circuits described by quantum gates into control sequence for these physical operations for the diamond spin approach, enabling control from the Fujitsu’s hybrid quantum computing platform.

mundophone

TECH

This design software reimagines everyday objects as self-aware devices

As a child, you likely saw a few Disney movies depicting inanimate objects, such as clocks, cups, and toys, as interactive companions to humans — an act of pure magic, seemingly. But scientists at MIT’s Computer Science and Artificial Intelligence Laboratory (CSAIL) are now doing something similar: transforming stationary items into self-aware tools that perceive and respond to human motion to complete a task.

Engineers have 3D-printed these dynamic items with built-in sensing, using conductive materials for sensors and traces (sort of like wires) inside. The issue: Both components were typically fabricated using the same material, so they’d emit similar signals. It’s sort of like hearing two radio stations at the same time, a mixup that’s hard to interpret. This confuses, say, a glove that relays instructions to a robotic hand about how to handle a specific object. The device couldn’t filter out the noise or verify the angle of a user’s motions, leading a humanoid student to make errors.

Researchers at CSAIL and Tianjin University (TJU) may have found a way to 3D print more precise interactive items. With their “X-Hinges” software, you can customize a design, and the tool will automatically embed two different materials: a filament for the sensors designed to send the strongest signal possible, and another for the wire-like elements that don’t interfere. Your interactions won’t get lost in translation, meaning you can fabricate objects that respond in real time, such as small robots, household decor, object-detection systems, and toys.

With X-Hinges, you can put together an item by selecting and connecting different shapes, then choosing how certain parts move. Your item won’t be limited to moving in just one way like previous approaches; instead, you can select up to three “axes”: compressing, up and down, or to the sides. If you built a robotic hand, for example, you’d likely want its fingertips to move vertically and laterally. CSAIL’s tool would then embed sensors where the object bends (in this case, its joints) to capture motion data from both angles. That way, the device can understand and respond to your interactions more dynamically once it’s 3D-printed.

“It’s kind of like adding a conscious element to everyday objects,” says Jiaji Li, MIT electrical engineering and computer science (EECS) postdoc and CSAIL researcher, who is a senior author on a paper introducing the work. “What you get is objects that better understand how they’re being used and have more ways to respond. In the same way an AI agent is programmed to make certain decisions based on our instructions, these creations have built-in sensing to adaptively react to human touch.”

Jiaji Li and lead author Xiang Chang, a Tianjin University PhD student and visiting researcher at CSAIL, used X-Hinges to create many clever devices. For example, they made a glove that can teach a robot how to grasp blocks. It adjusts to the size of a user’s hands, then records how the joints in their fingers bend via sensors before rapidly relaying that information to a humanoid hand to mimic it. The glove could be useful in factories or homes, where a robot often needs to learn new interactions quickly.

The researchers also produced a small, origami-style lamp using X-Hinges. It senses when a human pinches it closed and adjusts its brightness accordingly. When you turn on this adaptive, portable light source (sort of like a reading light), it looks like a piece of folded-up paper that sprouts into a lamp.

X-Hinges can even assemble devices that identify which objects have been placed on it. You could put a banana on top, for instance, and it’ll recognize the fruit almost immediately based on the tactile data it’s recorded using its sensors. This advanced physical awareness could be integrated into detection systems in places such as airports and grocery stores.

A shark tale...Behind each of the scientists’ creations is an easy-to-use interface that helps you design interactive objects from scratch. Users can choose how each part of their design looks and moves, just as the researchers did when making a video game controller that resembles a cartoon shark.

X-Hinges gives you four shapes to choose from: a custom option, cylinder, rectangle, and thin outline. To recreate the unique look of a shark’s tail, the researchers designed their own shape. They then chose how the toy bent, opting for its tail to move up and down, sort of like a joystick. Finally, the program embedded the sensors, and the scientists 3D-printed their device.

The researchers say that X-Hinges’ diverse motions are a novel feature compared to past attempts to 3D-print responsive everyday objects. “Most methods only allow for one axis of motion, often due to signal interference. X-Hinges enables your 3D-printed item to move from three angles,” says Chang. “Ultimately, you get a design with the intended movement you want. It also records motion data in each of those areas at the same time, making the device responsive to different kinds of interactions.”

The tool could help realize the untapped potential of the seemingly mundane. Objects we use every day for a specific purpose, like a water bottle for drinking or a lamp for lighting, could become interactive gadgets. Much like how a chatbot uses a sort of digital intelligence to answer your prompts, an object could leverage a kind of physical intelligence to execute a physical task when users interact with it.

For now, though, X-Hinges faces a calibration bottleneck. Each time an item is 3D-printed, its layout of electrical elements varies slightly, so two devices that appear identical from the outside may not make the same sensor readings. This is crucial if you’re building a deformable fitness glove, for instance, for two separate users. To fix this, Chang and Li built a computer vision system that can recalibrate outputs to align, ensuring data is accurate across two of the same items, though they hope to develop a built-in signal recalibration mechanism in the future.

That ambition traces back to the throughline in Jiaji Li's own research: letting actuation and sensing “grow” directly inside a 3D-printed object, instead of adding them on afterward. He previously built printed tendon-driven mechanisms that gave objects the ability to move; X-Hinges is how he's now building on the ability to sense. The next step, he says, is combining the two in a single print — it's actuation and sensing born together in the same fabrication process, opening the door to new physical platforms for embodied intelligence and AI agents.

Chang and Li wrote the paper with MIT associate professor of EECS and CSAIL principal investigator Stefanie Mueller and recent TJU graduate Haiyang Yan. Their work was supported, in part, by a postdoctoral research fellowship from Zhejiang University and the MIT-GIST Program.

 

MIT’s Computer Science and Artificial Intelligence Laboratory (CSAIL)

DIGITAL LIFE

Mathematics and AI

The creator of ChatGPT announced on Tuesday that one of its AI models had solved a century-old mathematical equation in less than four days.

That announcement was overshadowed by public statements from Australian mathematician Tristan Buckmaster, who questioned the similarities between his own work—predating OpenAI's project—and that of the AI ​​model.

Artificial intelligence "offers the potential to strengthen and accelerate the study and understanding of mathematics," renowned researchers wrote in an open letter on Friday.

"The mathematics profession will have to adapt to these changes in various ways," they explained.

For mathematicians, it is "human decisions controlling this technology" that will determine, "to a large extent," whether it proves beneficial to the field or has a destructive effect.

The 25 medalists therefore call on leading AI companies to "urgently address" these questions.

Since last year, several of these companies have reported breakthroughs in the world of mathematics, but the solution to the Navier-Stokes equation, announced on Tuesday, is the most notable.

It is one of the seven "Millennium Prize Problems" selected in 2000 by the research-supporting Clay Mathematics Institute, each carrying a $1 million prize.

Over the past few months, the mathematical capabilities of large language models (LLMs) have improved dramatically, to the point where they can solve major unsolved problems in many fields of mathematics. However, the push by AI companies to solve mathematical problems as a benchmark is detrimental to the field of mathematics and to the mathematical community. The goals of AI companies and those of the mathematical community are severely misaligned. We view these as part of broader alignment issues affecting other scientific and creative professions, as well as society as a whole.

Mathematical research focuses on understanding the basic structures of shapes, numbers, and natural phenomena. Over the course of generations, it has built up a vast body of sophisticated ideas, methods, abstractions, and other tools for understanding the mathematical landscape. In turn, modern technologies and sciences are based on mathematical tools.

Famous problems have often served as landmarks and beacons against which one can gauge a deeper understanding of this field. Solving one of these problems has been a sure sign of new insights and interesting methods, which would then be studied by a community of mathematicians through a long and arduous process of talks, discussions, and simplifications. At the end of this process, one will ideally find a textbook presentation of the results suitable for any graduate or even undergraduate student to study. Some of these mathematical ideas continue their journey even further, becoming—decades or centuries later—tools that are understood and used by the general public.

The mathematical community functions, in many ways, as a miniature version of humanity. It consists of individuals who use a wide variety of different approaches, united by core values. The most precious resources of our profession are students and ideas, and we nurture them with great care. We feel responsible for helping them reach their full potential, until they can stand on their own in the mathematical world. For students, we often suggest problems with the primary goal of developing skills that will position them well for advances in research and beyond. We disseminate our ideas through talks, private discussions, and carefully crafted write-ups, connecting them to the previous ideas of others. These processes invariably take time and are based on human interaction.

In recent months, AI’s success in solving major mathematical problems has made headlines even outside mathematical circles. But problem-solving is only a tool and a means to an end—the primary goal of conceptual understanding and insight. Forgetting this in the world of AI may cause the tool to work against that primary goal. Indeed, the mass production of “true/false” statements at an ever-faster pace could destroy fertile ground instead of breathing life into new ideas.

Often these solutions are announced in a hurry, leaving no time for a proper write-up, the identification of new methods and ideas, and the citation of relevant prior work by others. As in all creative professions, this raises serious questions regarding attribution and plagiarism. Moreover, without the willing mathematicians who must oversee their development and integration into the mathematical canon, AI-conceived ideas would never fully come to life, and the crucial human chain of transmission among mathematicians would be lost.

We are witnessing a general threat to intellectual work, with a misalignment between the outcome of AI use and its original purpose. In many fields and activities, years of training have traditionally served not only to produce a final answer or product, but also to develop understanding and the ability to formulate new questions and ideas. However, building on a vast body of previous human work, AI systems are becoming increasingly capable of producing the results of such work directly, and these goals are no longer aligned. The challenges the mathematical community now faces are similar to those facing other scientific and creative professions, and point to challenges that all of humanity may face: how to ensure that, as AI changes the way work is done, we do not lose sight of what that work was meant to achieve in the first place.

AI offers the potential to enhance and accelerate genuine mathematical study and understanding. The field of mathematics will need to adapt to these changes in several ways. However, whether these changes ultimately benefit the field or have a destructive effect will largely depend on the decisions made by the people in control of this new technology.

Mathematicians rebel against AI...Here is the statement, signed by Terry Tao among many other math notables, most of you probably have read it by now.  I do not accept the most cynical interpretations of this proclamation.  Some of you for instance may recall that I made and indeed stressed a similar point in the last chapter of my recent “generative book” on marginalism.  In some near future, perhaps fewer economists will carry around marginalist insights and modes of thought in their heads, since you can just get the right answer by pressing the proverbial button on the AI.

I find this future disturbing, and not altogether pleasant for me personally, given how much personal status I have wrapped up in particular modes of economic thought.  Yet I also know the Bastiat distinction between the seen and the unseen, and I expect the benefits to economic science from AI will be enormous, even if current practitioners cannot foresee most of those benefits today.

I do very much differ with at least one part of the mathematicians’ proclamation.  They write: “…whether these changes ultimately benefit the field or have a destructive effect will in large part be determined by the decisions of the humans in control of this new technology.”  There is no actual argument for that proposition, and I would sooner expect that the main “action variable” is how well the mathematicians adapt to the new reality.  For instance there is nothing stopping the mathematics community from awarding status, pay, and promotions to people who “fill in the important blanks in math understanding,” even if an AI already has proven or disproven the underlying theorems.  If that kind of work is so important, we still can do it and reward it professionally.  In the meantime, I expect the funding for mathematics, and the interest in the topic, to rise considerably, at least in the medium term.  All of a sudden, math matters much more than it used to, all the more so if P vs. NP happens to go the wrong way, or if the distribution of the primes turns out to be a little too predictable.

The mathematicians may not in every way enjoy being the subordinates or handmaidens of the AIs, but that is a change in status they simply will have to get used to, just as I realize AIs someday will end up as better column and blog writers than I am.  I do not look to the companies — which I fully expect to “act like companies” — to somehow manage, moderate, or assuage that pending trend.  It really is up to me to parlay my current intellectual portfolio into new, more AI-compatible intellectual and yes also marketing approaches.  I’ve been given plenty of “legs up” along the way already, as is true for the Fields Medal winners as well, and it is up to me to figure out how to contribute in the future.

Might someone not invent/discover/prompt a way to use AIs to produce, articulate, and teach “more mathematical understanding” along the way?  I get that solving famous dramatic math problems is the current commercial priority of the major AI companies.  But as the AI space grows, these other paths hardly seem unlikely to me, and in fact the human mathematicians are the ones who can do the most to lead the way along those dimensions.

In this regard the current manifestation of complaints seems oddly early.  “I didn’t like the first week or two of your intellectual revolution” is an accurate, and perhaps better reframed way of putting it.  At which point perhaps a bit of patience is needed before anything else?  These days, we all have more mathematical resources at our disposal, and so a bit of celebration is in order as well.

mundophone

 

TECH

How randomness tames vast network problems

Networks are everywhere. They connect computers across the internet, carry electricity through power grids and represent transport routes for moving people and goods. Yet many problems that appear to have nothing to do with networks can also be represented and solved as networks. Examples include matching passengers with drivers in a ride-hailing app or distributing computing tasks across servers.

The research group of theoretical computer scientist Rasmus Kyng develops new computational methods for solving equations that describe very large networks. The challenge lies in the scale of these networks.

Once a network contains millions or even billions of connections, solving the equations becomes particularly demanding. Methods that work well on small networks often require so much time and memory that they become impractical at this scale.

Kyng's work combines two activities: developing exceptionally fast algorithms, the mathematical procedures that guide a computation, and turning these algorithms into practical software.

Recently, Kyng, his former student Yuan Gao and his one-time doctoral supervisor Daniel Spielman presented a new solver for Laplacian equations in the SIAM Journal on Scientific Computing. A solver is a computer program that automatically solves mathematical equations.

The prototype of the new solver already proved both reliable and substantially faster than existing software across a wide range of test cases. "The results show that methods developed in theoretical computer science can become practical tools for solving very large network problems," says Kyng.

A two-stage research process...The story of Laplacian solvers provides a particularly clear example of how a theoretical proof can eventually become software for supercomputers. Kyng's research typically proceeds in two stages: mathematical theory and practical implementation.

The first stage centers on fundamental mathematical questions such as this: Can one prove that a problem can be solved by an algorithm whose computational cost grows only moderately as the problem becomes larger?

This question matters because the computational cost of many algorithms rises sharply as problems grow. If a network becomes 10 times larger, one would ideally want the required computation to increase by roughly the same factor. In practice, however, the computational effort often increases much more rapidly than the size of the problem.

A major focus of Kyng's research is the development of algorithms with nearly linear running times. In such algorithms, the computational effort grows almost in step with the size of the problem. In recognition of his scientific work on highly efficient algorithms, Kyng received the 2025 ETH Zurich Latsis Prize.

Alongside the goal of making computational efforts grow as close as possible to the size of the problem itself, another central question guides his work: What information can a computation ignore without losing accuracy?

The mathematical question and its proof are only the beginning. A second stage focuses on turning theoretical insights into practical software that works reliably on real computers. This stage is often challenging: It requires retaining the core mechanisms that create the speed-up, shedding the rest of the theoretical machinery and making those mechanisms work on a real computer.

But is it worth spending years proving that an algorithm is efficient if it initially exists only on paper? "The history of Laplacian solvers provides a compelling answer," says Kyng. "It shows how theoretical insights push the boundaries of what is possible and how they gradually evolve into usable software."

The long path from proof to supercomputer...Back in 2004, computer scientists Daniel Spielman and Shang-Hua Teng proved mathematically that Laplacian equations could be solved in nearly linear time. The result marked a major breakthrough. Yet their approach relied on highly complex mathematical constructions and was not well suited for practical use.

Following this theoretical breakthrough, Kyng and Sushant Sachdeva introduced a much simpler approach in 2016, called Approximate Cholesky. The latest work by Gao, Kyng and Spielman now makes this approach work well in practice.

To build the software prototype, the researchers relaxed some of the very strict theoretical requirements of the 2016 method. The result was a significant increase in speed. In experiments, the software ran about five times faster while remaining reliable across a broad range of Laplacian equations, including problems on which existing software fails.

The work is not finished, however. In the open-source project apxchol, Kyng and his doctoral student Yves Baumann are developing the method into robust software for scientific computing on supercomputers.

Left: When a node is removed, many new connections appear between neighbouring nodes. This makes computations increasingly demanding. Right: Approximate Cholesky considers only a small random sample of these connections. As a result, computations can be significantly accelerated without materially reducing the quality of the results. Credit: Conceptual illustration based on work by Kyng, Sachdeva and collaborators

Pushing beyond existing limits...Why are computations involving Laplacian equations so demanding in the first place?

The researchers build on a technique known as Cholesky elimination. It simplifies a network step by step by removing individual nodes. However, every time a node is removed, new connections appear between the remaining nodes. As a result, the computations become increasingly demanding, requiring ever more computation time and memory.

For small networks, this additional effort is usually manageable. For very large networks, however, it can grow so much that the computations become difficult to carry out in practice.

The Approximate Cholesky method developed by Kyng follows a different strategy. Instead of taking all newly created connections into account, it considers only a small, carefully selected random sample of them. These few connections are sufficient to obtain almost the same results as the full network. As a consequence, computations become much faster without significantly reducing accuracy.

Any remaining errors can then be corrected iteratively. The solution is repeatedly checked and refined until the desired level of accuracy is reached.

The new method is therefore faster than previous approaches while remaining highly reliable across many different test cases. The solver was even able to handle problems on which existing programs failed.

Ultimately, the work demonstrates how a mathematical idea can become a practical tool, capable of solving network problems that were once beyond reach.

The strategic use of randomness allows for solving complex problems in massive networks by drastically reducing computational effort without sacrificing result accuracy. Recently, computer scientists led by Rasmus Kyng at ETH Zurich transformed theoretical concepts into practical software capable of analyzing large networks in near-linear time.

The challenge of traditional networks:

Data explosion: Conventional methods lose speed and require massive amounts of memory when handling immense networks.

Connection buildup: When a network node is removed during standard mathematical calculations (based on so-called Laplacian equations), countless new connections emerge between neighboring nodes, making the process heavy and slow.

The solution: Approximate Cholesky and randomness:

Smart sampling: Instead of recording and processing every newly generated connection, Kyng's algorithm selects only a small, carefully designed random sample of these connections.

Maintaining accuracy: This fraction of connections is statistically sufficient to yield a result virtually identical to what would be generated by analyzing the entire network.

Iterative correction: Any discrepancies or residual errors are repeatedly refined and corrected until the desired level of precision is achieved.

Practical impact and speed:

Five times faster: In real-world experiments, the software prototype ran about five times faster than traditional competitors.

Solving failures: The new system demonstrated high reliability, successfully solving complex problems where previous software simply crashed or failed.

Open source: The breakthrough is being integrated into the open-source software *apxchol*, aiming to accelerate large-scale scientific simulations on supercomputers.

 

Provided by ETH Zurich

TECH

3D-printed houses are no longer science fiction—but they don't work quite the way many people imagine

Imagine arriving at an empty lot in the morning and finding, two days later, the walls of a 120-square-meter house practically finished. It sounds like an exaggeration, but large concrete 3D printers are already capable of doing part of this work. The technology is gaining ground in Argentina, too, promising to cut construction times and waste, and even reduce some costs. However, there is one important difference between what we picture as a "printed house" and what these machines actually deliver.

Forget the small desktop 3D printer that produces plastic objects.

In construction, the equipment can form massive structures set up around the site where the building will rise. A print head moves, following the exact coordinates defined by the digital design.

Instead of plastic, it deposits a special cement-based mixture.

The material flows out continuously, building up layer upon layer. Gradually, walls, partitions, and spaces for doors and windows take shape.

The equipment used by a company that introduced this technology on a large scale to the Argentine market, for instance, measures approximately 11 by 11 meters and stands about seven meters tall. It operates by connecting to a central mixing unit and a pump that transports the concrete to the print head.

The advantage lies precisely in the automation.

Since the machine follows a digital file, it deposits material only where it is needed, reducing the cutting, waste, and measurement errors common in conventional processes.

A 120-square-meter house can reach the "grey shell" stage in 48 hours... This is where the figures really grab attention.

According to estimates released by companies working with this technology, the structure of a home measuring approximately 120 square meters can reach the "grey shell" stage—the basic structural framework—in about 48 hours.

Furthermore, those behind the technology estimate a reduction of nearly 35% in construction time compared to conventional systems. But there is one essential word in this promise: structure.

The machine doesn't start working on Monday and deliver a furnished home ready for residents by Wednesday.

It primarily accelerates the construction of walls and specific structural components.

After that, electricians, plumbers, carpenters, and other professionals are still required.

Electrical and plumbing systems, windows, doors, flooring, wall coverings, painting, finishing touches, and—depending on the design—the roof itself still rely on traditional methods.

Therefore, 3D printing does not eliminate conventional construction.

It seeks to transform one of the most time-consuming stages of the process.

Rapid construction grabs attention, but there is another important promise hidden within the layers of concrete:

Less material waste.

In conventional construction, cuts, offcuts, and waste are part of the process. A printer works differently: it deposits a controlled amount of material exactly along the path dictated by the design.

European researchers indicate that certain additive construction systems can save up to 50% on material in some applications, as walls do not necessarily need to be completely filled with concrete. Internal voids can also be utilized for insulation or utility installations.

This freedom offers another unexpected advantage.

Curved shapes and complex geometries no longer have to be a construction nightmare.

In certain projects, the geometry itself allows for less material usage while maintaining the necessary structural strength.

It is an interesting shift: for decades, building unusual shapes usually meant increased costs and complexity. With 3D printing, some of these shapes can simply be designed on a computer and reproduced by the machine.

The dream of printing houses also faces very traditional limitations...Despite its futuristic appearance, the technology remains subject to the same basic realities as any construction project.

The site must be suitable. The structure must comply with local regulations. The concrete must provide sufficient strength, and the design must take into account climate, soil conditions, logistics, and seismic factors where necessary.

There is also the initial cost of the machines themselves and the need for professionals capable of operating them. This helps explain why 3D printing tends to be particularly attractive for repetitive or large-scale projects.

Imagine a development with dozens of similar houses.

Once the digital design is prepared and the equipment is set up, the machine can repeat the same movements countless times with high precision.

It is precisely in this type of scenario that automation, waste reduction, and speed can begin to yield greater economic advantages.

The construction industry may be entering its automation phase... 3D-printed houses already exist in various parts of the world.

In the United States, ICON participated in a Texas development featuring over 100 homes built using 3D printing. In Europe, residential projects are also experimenting with the technology, while various initiatives explore its application in infrastructure.

This does not mean that bricklayers will disappear or that entire neighborhoods will be printed overnight.

The transformation will likely be far less cinematic.

Machines will take over certain repetitive steps, while professionals will remain responsible for countless other construction tasks.

But a significant shift is underway.

For centuries, building a wall meant manually placing units or materials, one after another.

Now, a machine can receive a digital file, move a print head across the site, and transform those coordinates into a physical structure.

The house of the future might not emerge fully formed from a printer.

But an increasingly large part of it could begin exactly that way.

What are 3D Printed Houses? A 3D-printed house is exactly what it sounds like: a home whose walls and structural components are built layer by layer using a robotic 3D printer and a custom concrete or mortar mix. Instead of laying bricks or assembling timber frames, these machines extrude material along precise paths to shape walls, curves, and foundations.

Most 3D-printed homes still use traditional roofing, insulation, doors, and windows, the printing is mostly for the structure.

Gantry-based systems...These are large, fixed-frame setups where the print head moves along rails (like a giant 3D printer). They’re often used for printing simple, box-like homes quickly.

✅ Pros: Stable, efficient for mass production, good for identical units.

❌ Cons: Limited in design freedom, harder to scale or move to new sites.

How are 3D Printed Houses Built?...‍‍Building a 3D-printed house might seem like pressing “print” and walking away, but the actual process involves multiple phases—and a lot of human coordination.‍

1. Design & Preparation...Everything starts with a digital model. Architects or engineers design the structure in 3D modeling software, often using parametric design tools. This model is then converted into a printable path using slicing software, which translates the design into robotic movement and material extrusion instructions.

At Vertico, this step is where the innovation lives—parametric design lets us go beyond basic rectangles and explore curves, overhangs, and biomimicry-inspired structures.

2. Site setup & foundation...The printing usually begins once a traditional concrete foundation is poured. Leveling is key—any unevenness in the base can throw off the precision of the robotic print.

3. 3D Printing the Walls...A robotic system—either gantry-based or arm-based—extrudes a custom concrete mix in horizontal layers. The system follows the toolpaths created in the design stage, printing everything from straight walls to rounded corners or even custom textures.

Some systems include rebar or reinforcement, while others rely on wall geometry.

Printing takes hours to days, depending on the complexity and scale.

4. Post-processing & integration...This is where reality sets in. After the printing is done, there’s still a long to-do list:

Windows & doors need to be fitted

Insulation is installed manually

Plumbing and electrical work is added conventionally

Roofing is almost always traditional

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