Mathematician Levent Alpege published a potential counterexample to Jacobi's conjecture on the social network X, which is one of the known problems in the field of algebraic geometry. According to him, this counterexample was discovered using the language model Claude Fable.
The general formulation of this conjecture remained unsolved since 1939, as there were neither proofs nor refutations. Jacobi's conjecture postulates that if the components of a mapping are represented by polynomials, and the determinant of the Jacobian matrix (Jacobian) remains a constant non-zero value throughout the space, then this mapping possesses a global inverse mapping whose coordinates are also expressed by polynomials.
The origins of this idea trace back to Ludwig Krauß, who formulated the conjecture for the case of two variables in 1884. Otto Heinrich Keller presented it in its general form in 1939. In 1998, Stephen Smale included this problem in the list of 18 most important mathematical problems of the 21st century under number 16.
In practice, realizing the conjecture involves creating a mapping by combining several polynomials of different variables. For example, in the three-dimensional case, the mapping takes inputs x, y, and z and outputs three new values: F(x, y, z) = (F1, F2, F3).
To verify this, the Jacobian matrix must be constructed, including the derivatives of each output coordinate with respect to each input. If the determinant of this matrix is not zero, it means the mapping is locally invertible, i.e., there exists an inverse mapping in a small area around any point.
On July 20, Alpege published a specific counterexample to Jacobi's conjecture obtained using Claude Fable. The mapping itself has the form: F1 = (1 + xy)^3z + y^2(1 + xy)(4 + 3xy), F2 = y + 3x(1 + xy)^2z + 3xy^2(4 + 3xy), and F3 = 2x − 3x^2y − x^3z.
The values of this mapping coincide for three different points: (0, 0, -1/4), (1, -3/2, 13/2), and (-1, 3/2, 13/2). Furthermore, the determinant of the mapping's Jacobian matrix at all these points is -2. Thus, despite meeting the conditions of the conjecture, the mapping is not unique, as three different points in space map to the same image, precluding the existence of an inverse mapping. This proves that Jacobi's conjecture in its original formulation is false.
Currently, the counterexample is only available on the social network X and is not accompanied by a peer-reviewed publication or preprint. However, given that it represents a relatively compact polynomial mapping in three dimensions, mathematicians were able to quickly verify the calculations. If this counterexample is deemed correct, it will refute not only Jacobi's conjecture but also the equivalent Dixmier conjecture, and it will influence research in the fields of algebraic geometry and polynomial mappings.
In the current climate, banking sector executives are facing complex challenges. The recent launch of the open model Kimi K3 by the Chinese startup Moonshot AI caused market fluctuations: the S&P 500 index dropped by one percentage point, the benchmark in Taiwan fell by more than 6%, and the Nasdaq index lost 1.4%.
This incident is reminiscent of events in January 2025 when DeepSeek also triggered similar market turbulence, although American markets recovered quickly. It is becoming evident that the capabilities of advanced Large Language Models (LLMs) are becoming a commodity, and Kimi K3 serves as another harbinger for major players in the corporate sector. This raises the question: if the smartest model will soon be available, is the race for global dominance in the LLM sphere meaningless?
Three weeks before the frenzy surrounding Kimi K3, the research department of the largest hedge fund, Bridgewater, in collaboration with the Thinking Machines Lab's Mira Murati, published results. They showed that a refined version of Qwen3-235B, an open-weight base model from Alibaba, outperformed all tested state-of-the-art models in six financial judgment tasks based on daily investor work.
Surprisingly, this custom model achieved an average accuracy of 84.7% compared to 78.2% for the best state-of-the-art system, while its operational costs were approximately fourteen times lower. It should be noted that these figures were assessed within Bridgewater's internal system, not an independent benchmark.
Nevertheless, this underscores the critical importance of using proprietary data and insights applied through established judgment. In highly specialized fields, such elements can rarely be expressed as a simple prompt. They must be trained on examples labeled by internal experts, using data exclusively held or processed within the organization. When this is achieved, even a relatively modest model improved with its own data can surpass giants at significantly lower costs.
These reflections led to considerations about banks and bankers. During a live discussion at the VivaTech event in Paris last month, The Atlantic's CEO, Nicholas Thompson, questioned Inrupt CEO John Bruce and co-founder Sir Tim Berners-Lee about the impact of AI on banking. Inrupt helps banks and other financial institutions implement decentralized data infrastructure.
Thompson highlighted Bruce's view that the worst nightmare for a bank is not a competing chatbot, but a situation where a customer uploads their statements to ChatGPT to obtain a loan, thereby taking the relationship with the data and the power granted by data ownership outside the bank. Inrupt's answer is the Charlie agent—a personal AI agent situated between the user and model providers that decides which data leaves the device.
Banks find themselves in a David versus Goliath situation against LLMs. At the same time, African banks are fighting a second front against the mobile telecommunications industry, which has long stopped being satisfied with monetizing calls and text messages. Thus, it is indeed difficult for banking sector executives.
However, large players on both sides of this confrontation tend to rely on assumed birthright privileges. There is instinctive maneuvering around banking licenses, spectrum, regulatory barriers, and distribution power, based on the assumption that inherited influence and scale will win by default. Nevertheless, Bridgewater's results suggest that this premise needs to be reconsidered by top management.
It becomes clear that the value held by an African bank or telecom company lies in decades of transactional data that no one else in the world possesses. This includes repayment histories, agency network cash flow patterns, and seasonal cash flow rhythms of informal traders.
Systematizing the judgments of top credit specialists into labeled training data is slow, subtle, internal work that yields very little short-term benefit. Added to this is the complexity of empowering internal staff to create something that could undermine their own sources of income before external competitors do. In other words, it is work done in the interest of a leadership agenda focused on long-term ecosystem enrichment, not short-term profit.
When the author profiled the AI-based analytics platform Papermap in January, co-founder Benedict Quartey said that AI would eventually become a commodity, and once it does, 'the only thing that truly matters is what you do with it.' The Kimi K3 events and the Bridgewater findings, occurring within two weeks of each other, truly look like the realization of this concept.
It remains unclear whether African major players have the resources, patience, and desire to undertake this subtle work aligned with the new trend. However, it seems that the 'thin layer' will be built regardless.
After graduating from college, securing a good job has always been the main dream of young people. However, in the age of artificial intelligence (AI), this dream is becoming increasingly complex. At recent graduation ceremonies in many American universities, students openly expressed their concerns about jobs and AI. These issues are relevant not only to America but also to millions of students studying engineering and management in India, who are contemplating how AI will change their careers.
According to the American educational portal The Hechinger Report, the greatest threat from AI comes to roles that were previously considered career starting points. These roles include data processing, basic coding, report preparation, research assistance, and customer service.
The reason is that companies have begun delegating many tasks that were previously performed by new employees using AI tools. This leads to a reduction in entry-level vacancies, making it difficult for recent graduates to find employment.
Nevertheless, there is another side to the coin. Many economists believe that while AI will eliminate some jobs, it will also create entirely new types of employment. High demand is expected in the coming years for skilled professionals in fields such as healthcare, cybersecurity, data analysis, and AI management.
Experts note that the era where having only a diploma was enough for employment is rapidly passing. According to specialists, future success will depend on professionals' ability to use AI not as a competitor, but as an assistant. Companies are now looking for candidates who can work alongside AI, and these skills are becoming critical for students in engineering and management fields.
Every year, thousands of students complete courses in engineering, management, and other professional fields in India. However, a significant number of institutions still rely on outdated curricula. Although some institutions have started including disciplines such as machine learning and data science in their programs, the industry believes these changes are still insufficient. A lack of coordination between universities and companies is also noted.
Specialists emphasize that in the coming years, technical knowledge alone will not be enough. Students need to gain experience through internships, projects, and working on real-world problems.
Although concerns about AI are growing, experts view this technology not just as a threat. They believe that technology has always changed the nature of work. The difference is only that the pace of these changes is very high right now. Thus, the question is not whether AI will take jobs, but how quickly today's students can prepare for these changes, as in the future, career guarantees will be based not only on diplomas but also on new skills and the ability to continuously learn.
OpenAI's first attempt to enter the hardware market has generated significant consumer skepticism. The company announced a smart speaker whose design was developed by Jony Ive.
According to Mashable, this gadget is a hybrid of Apple HomePod and Furby devices. While the HomePod is a premium smart speaker from Apple, Furby is a nostalgic, fuzzy robot toy known for its expressive moving eyes and ears.
Particular attention is drawn to OpenAI's collaboration with Jony Ive, former Apple design director. Because of this, the new product bears a striking resemblance to devices created by his former company.
During his time at Apple, Ive played a key role in creating products such as the iMac, iPod, iPhone, iPad, MacBook, and Apple Watch. The new smart speaker was presented last week, just a few days after Apple filed a lawsuit against OpenAI for trade secret theft.
The timing of the announcement is also telling, as there are rumors that Apple plans to change its primary AI development partner, switching from OpenAI's ChatGPT to Google Gemini to support Apple Intelligence.
OpenAI clearly aims to expand its ecosystem beyond software to solidify its status as a leading and recognized force in artificial intelligence. The smart speaker is positioned as a home companion capable of controlling other smart devices on the same Wi-Fi network. Furthermore, the device will be equipped with a camera to enhance functionality and achieve a more accurate understanding of user requests.
Nevertheless, it remains unclear why consumers would prefer to purchase a smart speaker from OpenAI, given the availability of well-integrated alternatives like the iPhone and HomePod.
