While governments and companies compete for more infrastructure and greater computing power, scientific communities warn that without a solid mathematical foundation, the development of AI will be fragile, unreliable, and difficult to sustain in the long term. Behind the systems that today generate text, recognize images, or automate financial decisions, there is a complex mathematical framework that often remains outside public debate. However, this underlying structure has become a strategic factor in defining who leads—and who depends—in the new digital economy.
The Equation Behind the Rise of AI The relationship between mathematics and artificial intelligence is not new. At this intersection, a virtuous circle is formed: mathematics drives AI, and AI, in turn, opens up new scientific questions. But beyond the technological enthusiasm, there is a fundamental issue.
AI is not built with enthusiasm alone, commercial applications, or large infrastructure budgets. Without solid mathematics, AI systems face limitations in reliability, interpretability, verification, energy efficiency, and security—critical factors for their adoption in financial, industrial, and utility sectors.
A Two-Way Exchange The relationship between mathematics and AI does not flow in a single direction. In the global race for AI, mathematics is not an accessory; it is the silent engine that determines who advances and who is left behind.
In Mexico, there are already projects connecting advanced mathematics and AI. Machine learning tools are used to identify patterns, explore conjectures, and even support proofs, while mathematical advances allow for the design of more efficient and understandable models.
Mexico: Adoption or Development For countries like Mexico, the debate is strategic: to participate in the development of artificial intelligence or to limit itself to consuming it. AI is advancing at great speed, but its limit is not only in chips or data centers; it is in mathematics. Without such investment, AI is reduced to an imported, dependent, and expensive technology. International experience shows that sustained technological progress arises from the interaction between basic science and applied engineering. Although public attention has focused on the first two, algorithmic innovation—directly fed by mathematics—has been key to improving efficiency, reducing costs, and expanding applications. More stable algorithms with better convergence and efficiency are a demonstration of how basic research can elevate the performance of AI.
The risk is concrete. Infrastructure without science is not enough. This warning has been underscored by the Society for Industrial and Applied Mathematics, which points to a growing gap: investment in AI infrastructure is advancing faster than the strengthening of its scientific foundation. The solution lies in strengthening human capital development and research in mathematics, statistics, and basic sciences.
