Posts – Random Bits of Knowledge

When a Nobel Laureate Uses an LLM to Prove a Theorem: A Turning Point for Mathematical Discovery

How AI-assisted proof discovery is reshaping the practice of mathematics

machine learning

This article analyzes Giorgio Parisi and Francesco Zamponi’s 2026 paper, A Proof of an Identity for the Critical Exponents of Jamming, as a turning point in AI-assisted mathematical discovery. The paper proves the identity (a+b=1) between two critical exponents in the full replica-symmetry-breaking theory of jamming, a relation previously supported by high-precision numerical evidence but lacking an analytical proof. Its broader significance lies in the authors’ explicit statement that the…

Antonio Montano

The Leiden Declaration and the Governance of AI-Assisted Mathematics

How mathematicians are answering the new cognitive infrastructure of proof

machine learning

The Leiden Declaration on Artificial Intelligence and Mathematics is a significant collective response from mathematicians to the rapid entry of generative AI, formal proof search, and machine-assisted discovery into mathematical research. It should not be understood as a rejection of artificial intelligence, nor as a purely technical statement about proof assistants. Its deeper purpose is to defend the conditions under which mathematics remains a reliable, intelligible, and humanly…

Antonio Montano

The New Cognitive Infrastructure of Science

AI, mathematical thought, and the rise of automated research

machine learning

This article interprets recent progress in AI-assisted mathematics as an early signal of a broader transformation: the emergence of a new cognitive infrastructure for science. Starting from Tanya Klowden and Terence Tao’s thesis in Mathematical methods and human thought in the age of AI, it argues that AI should not be understood merely as a productivity tool, but as part of a longer history of cognitive technologies that externalize, amplify, and reorganize human thought. The central issue is…

Antonio Montano

The Erdős Moment of AI

When a language model entered frontier mathematics and why this changes more than mathematics

machine learning

This article comments on the announcement that an OpenAI model contributed to resolving a major conjecture related to Paul Erdős’s unit distance problem, a classical question in discrete geometry. The result matters not only because of the specific mathematical problem, but because it suggests that AI systems are beginning to participate in forms of abstract search, construction, and reasoning that were previously considered strongly human domains. The article interprets the reaction of…

Antonio Montano

When Vulnerability Databases Become Triage Systems

NIST’s NVD update, record CVE growth, and the economics of AI-scaled cyberattacks

machine learning

NIST’s April 2026 update to the National Vulnerability Database marks a structural change in the public vulnerability-management ecosystem. The issue is not simply that more CVEs are being published, but that the volume of disclosed vulnerabilities has exceeded the realistic capacity of centralized enrichment processes. As NIST moves toward prioritized enrichment, enterprises can no longer treat NVD metadata as a complete and uniformly available decision layer. A CVE identifier names a…

Antonio Montano

KDE, the Sovereign Tech Fund, and Europe’s Search for Digital Sovereignty

Why public investment in open source desktop infrastructure is becoming a strategic matter for European states

EU digital sovereignty

The Sovereign Tech Fund’s investment in KDE is not a marginal subsidy for a desktop environment, but a signal of Europe’s broader attempt to treat open-source software as strategic digital infrastructure. The article interprets the funding decision within the European search for digital sovereignty, where dependence on foreign proprietary platforms creates operational, legal, and geopolitical asymmetries. KDE becomes relevant because desktop environments, application frameworks, and…

Antonio Montano

Process Mining: From Theory to Execution

Why quantitative process intelligence is becoming essential for enterprise architecture and digital transformation

digital transformation

enterprise architecture

professional practice

A reflection on the Celonis Academy course Process Mining: From Theory to Execution, completed in 2022, and on why process mining is becoming a strategic capability for enterprises that need to understand, measure, compare, predict, and improve their real operational behavior.

Antonio Montano

Code Sovereignty Starts with the Forge

Why the Dutch government’s Forgejo-based code platform matters for European digital sovereignty

EU digital sovereignty

Digital sovereignty is usually discussed in terms of cloud platforms, data spaces, artificial intelligence, cybersecurity, and strategic autonomy. Yet every digital public service ultimately depends on a more fundamental layer: the infrastructure where source code is written, reviewed, stored, released, and maintained. This article analyses the Dutch government’s Forgejo-based code.overheid.nl platform as a concrete example of sovereign software-development infrastructure. Using only official…

Antonio Montano

The French state becomes machine readable through an AI layer

Inside the data.gouv.fr MCP server and the new interface stack for public data

EU digital sovereignty

machine learning

France’s experimental MCP server for data.gouv.fr is more than a technical connector. It signals a broader shift in how a state can expose public information in the age of AI. Rather than limiting access to web pages for humans and APIs for developers, the French open data platform is beginning to add a third interface layer: a standardized machine readable protocol through which AI agents can search datasets, inspect metadata, discover public APIs, and query part of the national open data…

Antonio Montano

France’s Linux Desktop Turn and the European Logic of Digital Sovereignty

From a French workstation migration signal to the broader European effort to regain control over critical digital infrastructure

EU digital sovereignty

France’s announced move from Windows toward Linux based public sector workstations is not merely a desktop migration story. It is a visible manifestation of a deeper strategic objective: reducing structural dependence on extra European digital platforms and rebuilding operational control over critical layers of the state’s information systems. This article examines what the official French sources actually say, distinguishes formal commitments from extrapolation, and situates the initiative…

Antonio Montano

Quantum Cryptography at the Edge of Feasibility: Resource Estimates, Architectural Divergence, and Systemic Risk

An analysis of the Google and Oratomic results on Shor’s resource estimates and their implications for the convergence of quantum circuit optimization, error correction, and hardware architectures

quantum computing

Recent results from Google Quantum AI and from Oratomic, Caltech, and Berkeley have significantly refined the quantitative understanding of the quantum threat to public-key cryptography, shifting the discussion from theoretical possibility to explicit engineering resource estimates. This article analyzes these developments from first principles, distinguishing between logical and physical qubits, circuit complexity, and error-correction overhead, and examining how improvements at each layer…

Antonio Montano

Quantum Computing Threats and the Advantage of Acting Now

Why trust expires before systems fail, and how early remediation becomes a strategic program rather than an emergency rewrite

quantum computing

risk management

Quantum computing does not need to break your systems to break your trust. The risk arrives as retroactive forgery, long lived key abuse, and evidentiary collapse. This article explains the threat mechanics and shows why starting remediation today is an opportunity to build agility and reduce future overhaul costs.

Antonio Montano

Beyond De-Skilling: Intelligence Explosion and the End of Skill as a Stable Category

Why generative AI forces a redefinition of mastery, agency, and human value

machine learning

A critical commentary on The Atlantic’s The Age of De-Skilling, arguing that the article underestimates the paradigm shift introduced by accelerating artificial intelligence. Rather than a story of skill erosion, this post frames AI as an intelligence explosion that dissolves skill as a stable category and forces a redefinition of human mastery, agency, and accountability.

Antonio Montano

What Is a World Model?

From psychological theory to machine learning architectures

machine learning

The concept of a world model describes the ability of an intelligent system to internally represent the structure and dynamics of its environment in order to predict future states and evaluate the consequences of actions. Although the term is widely used in contemporary machine learning and robotics, its conceptual origins lie in earlier work in philosophy, psychology, and neuroscience. In 1943, Kenneth Craik proposed that intelligent organisms carry a “small scale model” of external reality…

Antonio Montano

Architecting Change

How I blend enterprise architecture, technology, and interim leadership to transform organizations

digital transformation

enterprise architecture

interim management

professional practice

A deep reflection on my work as an interim manager and enterprise architect, where urgency, systems thinking, and human leadership intersect. I show how architecture, technology, and culture blend into transformation that is both immediate and sustainable.

Antonio Montano

Simulating Tethered Buoy Dynamics

How a barely noticed update triggered forgotten emotions

mathematical modeling

professional practice

This reflection examines the design and simulation of a tethered buoy system, an enterprise bridging nearly inextensible cables, quaternion-based orientation, and implicit time-stepping. It traces the technical challenges and day-to-day engineering realities of merging advanced finite element concepts with real-world ocean conditions. Through the interplay of mixed methods and iterative solvers, supported by the vibrant research community at MOX, it recounts the milestones, hurdles, and…

Antonio Montano

GPT-4 Anniversary

One year of a mass phenomenon

machine learning

March 2023 marked a turning point in the field of artificial intelligence with the release of OpenAI’s GPT-4. This powerful language model, boasting significant advancements over its predecessors, sent shockwaves through various industries and ignited discussions about the future of human-machine interaction. One year later, it’s clear that GPT-4’s impact has been wide-ranging and continues to evolve.

Antonio Montano

Intervento al DABS Day 2024 - Università Ca’ Foscari

GenAI: Dall’intelligenza artificiale all’amplificazione dell’intelligenza?

machine learning

professional practice

Bel pomeriggio presso l’Università Ca’ Foscari di Venezia, ospite del Dipartimento di Economia e dell’evento DABS Day 2024.

Antonio Montano

Color Space Sampling 101

How to uniformly sample a color space?

The evolution of color spaces is a testament to the intersection of art, science, and technology. Each color space has been developed to meet specific needs - from artistic expression and print media to digital interfaces and scientific research. Understanding these spaces is crucial for professionals in fields like photography, design, and digital media, where color accuracy and consistency are paramount.

Antonio Montano

Singletons in Python

Ensuring a single instance for shared resources

The singleton pattern is a creational design pattern that ensures a class has only one instance while providing a global point of access to that instance. This post explores the concept of singletons in Python, exploring various implementation methods including naive approaches, base classes, decorators, and metaclasses. We also discuss the advantages and disadvantages of using singletons, their impact on design principles like the Single Responsibility Principle, and provide thread-safe…

Antonio Montano

Quantum Key Distribution and Post-Quantum Cryptography

Concepts, roles, and correct use

quantum computing

Quantum computing does not break cryptography in general; it selectively collapses the mathematical assumptions underlying modern public key systems. This distinction is frequently obscured in discussions that conflate encryption, authentication, and key distribution, leading to misplaced expectations around so-called quantum-safe solutions. This article clarifies the respective roles of Quantum Key Distribution (QKD) and post-quantum cryptography (PQC), demonstrating that they address…

Antonio Montano

Cybersecurity in an Era with Quantum Computers: Interpreting Mosca’s Risk Inequality

Why x plus y greater than z turns quantum readiness into a present day governance problem

quantum computing

risk management

A commentary on Michele Mosca’s 2018 paper that formalizes quantum cyber risk as an inequality: security shelf life plus migration time versus cryptographic collapse time. The piece introduces quantum computing threats, explains the inequality in plain terms, and derives concrete implications for enterprise and institutional governance.

Antonio Montano

Controllo delle Partite IVA in Excel Tramite il Servizio VIES

Per utenti senza esperienza di programmazione

personal productivity

Questa guida ti mostra come utilizzare un file Excel per controllare la validità delle Partite IVA tramite il servizio VIES (VAT Information Exchange System).

Antonio Montano