The AI & Quantum Computing Chronicle

Modular forms are mathematical functions defined by extremely restrictive symmetries. This rigidity makes it possible to reconstruct their global behavior from a fundamental region and to transform complex problems into far more tractable structures. This is why they have played a decisive role in number theory, in the proof of Fermat’s Last Theorem, and in counting problems through generating functions. Their appli…

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Thermodynamic Computing What if thermal noise, rather than being a problem, could actually help us compute? This new form of computing harnesses natural energy fluctuations to explore possible solutions, moving through an “energy landscape” until it reaches more stable states. It follows a logic similar to the process that allows proteins to fold correctly inside a cell. Companies such as Normal Computing and Extro…

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Large language models learn by building associations between words, encoded as relationships in a high-dimensional embedding space. Like Hebb's principle in neuroscience, correlated activity strengthens connections, bringing related concepts closer together. But association alone cannot tell a system when reality has moved beyond its model. Faced with something genuinely novel, it does not recognise the boundary of i…

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Knowing When to Stop Every decision is risky business. Selecting the best time to stop and act is crucial. When Microsoft prepares to introduce Word 2020, it must decide when to quit debugging and launch the product. When a hurricane veers toward Florida, the governor must call when it’s time to stop watching and start evacuating. “While much of mathematics has roots that reach back millennia to Euclid and even ear…

In the last few days we have read about how an AI disproved a conjecture that had stood since 1946 (https://www.scientificamerican.com/article/ai-just-solved-an-80-year-old-erdos-problem-and-mathematicians-are-amazed/). What they don't tell you is that It could not tell you whether its own proof was right. That gap is the whole story, and most of the coverage missed it. Recently an OpenAI model produced a counterex…

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The Fourier Transform allows us to take a complex signal and decompose it into elementary frequencies. It turns something apparently “chaotic” into an interpretable structure of components. The Quanta article explains this through very clear examples: the ear separating sounds, heat spreading along a rod, JPEG compression, noise filtering, images as 2D functions, and the connection with quantum mechanics through pos…

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What is a decision? It seems trivial until you try to define it. Decision theory explains how we choose, but rarely what a decision is. Choosing is just the outcome. Ronald A. Howard defined it as an allocation of resources. But what truly drives a decision is uncertainty. If the future were known, we would not decide. Warren B. Powell goes further: a decision is a form of information. It defines how we respond to…

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This paper provides a complete, ground-up explanation of how Large Language Models (LLMs) work. A central section walks through the entire forward pass with concrete numbers: embedding lookup, Query/Key/Value matrices, the dot-product score matrix, softmax weights, weighted Value sums, layer-by-layer refinement, and the final word prediction. It explains how backpropagation adjusts every matrix in response to predict…

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In 1935, the Austrian physicist Erwin Schrödinger showed the absurdity of common interpretations of quantum mechanics with his famous cat-based thought experiment. The cat is put into a box with vial of poison, which will be released if a radioactive atom decays. If the box remains isolated from its environment, the atom exists in a superposition of both decayed and not-decayed, and until observed, the cat is an unde…

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The article explains how mathematicians have achieved an important breakthrough in a classic problem of Fourier analysis, one of the mathematical pillars for understanding waves and signals. More than half a century ago, Sarvadaman Chowla posed a puzzle about sums of waves (cosines): given a set of numbers, how low can the sum of their cosines go? While the maximum is clear (it is simply the size of the set), the mi…

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A century ago, Erwin Schrödinger formulated an equation that describes how a quantum system evolves when it is not being observed. This equation, now known as the Schrödinger equation, remains one of the fundamental tools for understanding the quantum world. 🔹 The equation allows physicists to calculate the so called wave function, which does not describe a single outcome but rather all the possible states of a syst…

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This paper offers a broad perspective on how machine learning is being integrated into the business world, not from a deep technical standpoint but through its impact on management, innovation, and decision making. Through a large scale analysis of scientific publications, it shows that the focus is no longer only on algorithms, but on how organizations adopt these technologies within their real operational structure…

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