From the article:
Sam Raskin has wrapped his head around a math problem so complex it took five academic studies — and more than 900 pages — to solve.
The results are a sweeping, game-changing math proof that was decades in the making.
Yale’s Sam Raskin has solved a major portion of a math question that could lead to a translation theory for some areas of math.
Artificial consciousness is inevitable, says new study. Mathematical model unifies theories and paves the way for sentient robots.
Posted in chemistry, mathematics, physics
On this day in 1992, the Vatican admitted that Galileo was correct in believing that the earth went around the sun.
2. In the first place, I wish to congratulate the Pontifical Academy of Sciences for having chosen to deal, in its plenary session, with a problem of great importance and great relevance today: the problem of ‘the emergence of complexity in mathematics, physics, chemistry and biology’
The emergence of the subject of complexity probably marks in the history of the natural sciences a stage as important as the stage which bears relation to the name of Galileo, when a univocal model of order seemed to be obvious. Complexity indicates precisely that, in order to account for the rich variety of reality, we must have recourse to a number of different models.
This realisation poses a question which concerns scientists, philosophers and theologians: how are we to reconcile the explanation of the world – beginning with the level of elementary entities and phenomena – with the recognition of the fact that ‘the whole is more than the sum of its parts’?
Dr. Sanjeev Namjoshi, a machine learning engineer who recently submitted a book on Active Inference to MIT Press, discusses the theoretical foundations and practical applications of Active Inference, the Free Energy Principle (FEP), and Bayesian mechanics. He explains how these frameworks describe how biological and artificial systems maintain stability by minimizing uncertainty about their environment.
Namjoshi traces the evolution of these fields from early 2000s neuroscience research to current developments, highlighting how Active Inference provides a unified framework for perception and action through variational free energy minimization. He contrasts this with traditional machine learning approaches, emphasizing Active Inference’s natural capacity for exploration and curiosity through epistemic value.
The discussion covers key technical concepts like Markov blankets.
generative models, and the distinction between continuous and discrete implementations. Namjoshi explains how Active Inference moved from continuous state-space models (2003−2013) to discrete formulations (2015-present) to better handle planning problems.
He sees Active Inference as being at a similar stage to deep learning in the early 2000s — poised for significant breakthroughs but requiring better tools and wider adoption. While acknowledging current computational challenges, he emphasizes Active Inference’s potential advantages over reinforcement learning, particularly its principled approach to exploration and planning.
Namjoshi advocates for balanced oversight that enables innovation while maintaining appropriate safeguards. He expresses particular concern about the rapid pace of AI development potentially outpacing our understanding of risks and regulatory frameworks.
Dr. Sanjeev Namjoshi.
Researchers explore an intriguing phenomenon in quantum systems, drawing inspiration from a recent quantum computing experiment.
Earlier this year, researchers at the Flatiron Institute’s Center for Computational Quantum Physics (CCQ) announced that they had successfully used a classical computer and sophisticated mathematical models to thoroughly outperform a quantum computer on a task that some thought only quantum computers could solve.
A 1930s-era breakthrough is helping physicists understand how quantum threads could weave together into a holographic space-time fabric.
A type of mathematical problem that was previously impossible to solve can now be successfully analysed with artificial intelligence.
Srinivasa Ramanujan embodies the myth of the self-taught genius.
Born poor in colonial India and dead at 32, Ramanujan had fantastical, out-of-nowhere visions that continue to shape the field today.
On their own, addition and multiplication are simple operations. But the relationship between them is a complicated mystery that mathematicians are still working to understand.
A new proof about prime numbers illuminates the subtle relationship between addition and multiplication — and raises hopes for progress on the famous abc conjecture.
A mathematical study finds that three definitions of what it means for entropy to increase, which have previously been considered equivalent, can produce different results in the quantum realm.
