Why Studying Mathematics Will Always Be Necessary for Working in Computing

(Antonio V. Franco)

There is an increasingly seductive idea that technology will eventually make human technical mastery unnecessary. The most foolish version of this idea appears in phrases like “AI will program everything” or “robots will do the work of engineers”. I consider this idea deeply wrong. Not because I think artificial intelligences will not transform computing. They already have, and they will transform it much more. Nor because I want to defend a nostalgic image of the programmer as someone who writes everything manually, line by line, in heroic isolation, as if better tools were a threat to intellectual dignity. Obviously, that defense would be childish. Computing has always been built on layers of abstraction, automation, and delegation; whoever treats automation as the enemy of computing has not understood the very history of computing.

The error lies elsewhere.

The error lies in believing that the more powerful technological systems become, the less necessary it will be for human beings to master mathematics. I think exactly the opposite: the more powerful systems become, the more necessary it will be for the serious professional to understand mathematics, because mathematics is not just a set of techniques for solving exercises; it is the language through which we are able to describe structure, measure uncertainty, model behavior, verify correctness, build abstractions, and, above all, know what we are doing when a machine appears to do it for us.

Artificial intelligence can write code, just as it can suggest architectures. It can generate hypotheses and test combinations. In the future, technological systems may have much deeper levels of agency, memory, functional integration, and perhaps some real profile of technological consciousness. Even so, or precisely because of that, mathematics will remain necessary.

The Error of Confusing Automation With Understanding

Automation always shifts the place of human effort. It does not eliminate the need for understanding, but changes the level at which understanding must operate.

When high-level languages emerged, understanding computing did not cease to matter. On the contrary, it became possible to think about higher-level problems because part of the raw machine had been encapsulated. When scientific libraries began to implement linear algebra, optimization, statistics, visualization, and machine learning, understanding mathematics did not cease to matter. On the contrary, it became more dangerous to use those libraries without minimally understanding what they were doing.

The same applies to generative AI, agents, copilots, and future robotic systems.

A weak professional looks at a tool capable of generating code and concludes: “then I no longer need to study so much”. A serious professional looks at the same tool and understands: “now I can operate at a higher level, but, for that, I need to master the foundations better, because the cost of not understanding what is being automated increases along with the power of automation”.

This point is central.

A person who does not understand mathematics may even use generative AI to build something functional or even deliver an apparently good system. They may even seem productive for a while. But when the problem requires real modeling or when the system begins to fail in a not-so-conventional way, that person will remain dependent on a surface.

And surfaces are dangerous.

They give the feeling of mastery before mastery exists.

Mathematics as the Language of Structure

I do not like the idea of treating mathematics only as a “foundation”. The word foundation is true, but weak. It makes it seem as if mathematics were an immovable base upon which, later, we build interesting things. That is too little. Mathematics is not only at the beginning of computing; it reappears in every layer where computing becomes serious.

Mathematics appears when we think about Boolean logic and digital circuits. It appears when we study graph theory in networks, compilers, distributed systems, dependencies, routes, and representations. It appears when we deal with linear algebra in machine learning, computer vision, computer graphics, embeddings, transformers, and generative models.

And it also appears when we do not yet know exactly which mathematics will be necessary.

This is more important than it may seem.

Serious computing frequently pushes the researcher into regions where he needs to formulate the problem before solving it. It is not enough to ask “which library should I use?”. The real question is often: what is the structure of this problem? What kind of object am I manipulating? Is this a sequence, a graph, or a vector space?

This way of asking is mathematical.

And that is why studying mathematics is not only learning techniques. It is learning to see structure where the surface offers only appearance.

Computing Has Always Belonged to Mathematics

Here I will be direct.

Technology will indeed replace a large part of superficial technical work. It will replace the programmer who lives only on operational copy-paste, who does not understand architecture, who does not understand mathematics. This professional will be squeezed because much of his value was in the mechanical execution of already-known patterns. But that does not mean technology will replace technology professionals who truly think, especially those devoted to science. The distinction is not between “human” and “machine”, but between superficial work and serious work.

An AI system can generate a function or suggest an architecture, but someone needs to know whether the function corresponds to the problem or whether the architecture expresses the correct structure. Without mathematics, the professional remains trapped in the appearance of the answer. With mathematics, he begins to see the internal form of the problem.

There is a tendency, especially in highly product-oriented environments, to treat computing as an essentially instrumental practice: building systems, delivering features, integrating APIs, or automating workflows. All of this is computing, of course. It would be ridiculous to deny the practical dimension of the field. But reducing computing to that amputates the discipline itself.

Computing was born from mathematical, logical, and philosophical questions. Those questions did not disappear because now we have cloud, frameworks, LLMs, and agents. They merely moved into new forms. That is why I consider it dangerous when someone says that “you do not need to be good at mathematics to work with technology”. This phrase forms stupid professionals, condemned to remain at the level of the tool (that is, of mediocrity).

I do not want to build my trajectory at that level.

Basic Mathematics Matters, but It Is Not the Final Destination

Ah, yes. Basic mathematics matters a lot. Arithmetic, algebra, functions, geometry, introductory statistics. All of this trains a relationship with symbols, regularity, transformation, proportionality, space, quantity, and inference. As expected, those who despise this layer usually pay the price later.

But the argument of this text is not merely “study basic mathematics”. That would be too small.

The argument is that mathematics, at all its levels, remains necessary because computing, when it approaches the frontier, always encounters mathematical questions again. Sometimes in the form of linear algebra. Sometimes in the form of statistics. I am not saying that every professional needs to master all these areas. That would be theater. But I am saying that a professional who wishes to work seriously with computing, especially toward science, needs to have a living relationship with mathematics. He needs to be able to go back, study, suffer through a definition, rebuild an intuition, accept the discomfort of not understanding at first, and insist until the mathematical object is truly understood.

This point interests me especially because I do not think of study as a school-like accumulation of separate subjects. My real interest lies in making mathematics, computing, artificial intelligence, biology, astrophysics, and technical writing communicate with one another. When I study mathematics for FUVEST, I do not want that to be merely standard preparation for an exam (even though the exam is my main and immediate goal); I want it to feed my future capacity to think about research problems.

FUVEST, in my eyes, should never be treated as an exam where the focus is merely aiming for the cutoff score. Given the quality of the competition and the type of formation I want to build, it needs to be approached as an exam in which I must seek perfection. This changes the nature of study, because mathematics stops being an obstacle and becomes a form of mental sharpening.

Artificial Intelligences Do Not Reduce the Need for Human Researchers

The popular image of replacement is poor: on one side, humans; on the other, machines; in the middle, a dispute over tasks. When it comes to research, intelligent tools do not merely execute tasks. They expand the space of exploration, allow more hypotheses to be tested, more possibilities to be simulated, and questions that previously would have taken longer to gain technical form to be asked, among other advantages.

This does not replace the human researcher. It empowers the human researcher who knows how to think. What changes is the scale of creation.

A researcher with mathematical mastery and better-developed AI tools will be able to operate with greater focus. Human genius, in this scenario, will not be less important, but more exposed.

One conviction I have says that, contrary to the popular imagination, technology does not eliminate the abyss between an ordinary mind and a strong mind, but rather widens it even further. In other words, unintelligent people (stupid people) and truly intelligent people will have an even clearer abyss between them.

The Problem of Technological Consciousness

The possibility of some profile of consciousness in technological systems is usually treated in two bad ways. The first is materialist mockery, which tries to close the discussion before formulating it properly, as if the word consciousness were automatically forbidden outside human biology. The second is loose fantasy, which calls any convincing chatbot conscious because it writes sentences with a subjective appearance (“Hurr durr, did you know ChatGPT is alive? I asked it whether it is alive and it said yes.”). Jokes aside, I have no interest in either of these two positions. Both are intellectually lazy, though for opposite reasons.

If, at some future moment, technological systems possess real forms of experience, internal access, cognitive integration, or some kind of functional consciousness, this will not make mathematics less necessary for us. On the contrary. Systems closer to conscious agency will demand even more formalization, more conceptual clarity, more models, more verification. A conscious technology, or partially conscious technology, or technology functionally analogous to certain aspects of consciousness, would not be merely a more powerful tool, but a new type of collaborator, perhaps a new class of technical agent. This would profoundly change the way we exercise our creativity. In fact, an even greater demand would arise: the demand for human researchers capable of dialoguing with extremely powerful systems without becoming submissive to the opacity of those systems.

Whoever does not master mathematics will tend to kneel before the machine’s answer.

Mathematics as Protection Against the Seduction of the Ready-Made Answer

There is a specific danger in the age of generative AI: the ready-made answer has become too beautiful.

Before, ignorance had a more evident appearance. A person who did not know how to program would freeze before the editor. A person who did not understand mathematics would freeze before the equation. Today, the tool fills that gap (it delivers code, text, explanations, summaries, etc.).

Yes, yes, this is extremely powerful, but it is also dangerous.

Dangerous because the mind can confuse fluency in several fields generated by these tools with its own understanding. It may think it understood because it read a clear explanation. Mathematics, when truly studied, breaks this illusion. It is not impressed by a well-written sentence or by whether a proof is correct or not.

That is why mathematics is one of the best defenses against intellectual passivity before AI. It forces the researcher not to accept the surface as proof.

Now, there is a huge difference between studying mathematics to get exercises right on an exam and studying mathematics to form a mind capable of creating.

Getting exercises right is obviously very valid (and that is what I am preparing for, by the way). I will never romanticize ignorance, whether in an exam or in a master’s degree project. Yes, there is a moment when one must solve sets of questions, but if study ends there, it remains small. Mathematics begins to become truly powerful when each solved problem leaves something beyond the answer: an intuition, a question, a hypothesis.

That is why I like the idea of studying through research projects.

Not in the sense of pretending that all study is already research properly speaking, but in the sense of not letting the content die at the moment the question is solved. The question becomes: what does this part of mathematics teach me about computing?

For me, this makes study much more stimulating.

The Future Will Not Belong to Those Who Know Less

The fantasy that smarter technologies will allow human beings to know less is one of the most mediocrity-producing ideas of our time. Of course there will be tools capable of reducing the need for certain operational skills. There already are. Much of what once required manual effort can now be done with prompts and automations. It is excellent that mechanical work is compressed. The problem begins when someone interprets this compression as a license for stupidity.

The future will not belong to those who know less.

It will belong to those who manage to use smarter machines without abandoning their own intelligence. To those who know how to formulate better problems. Technology will empower the genius of the best professionals because it will give them more reach, but it will also reveal the fragility of those who confused ease with mastery.

This is the part many people do not want to hear.

AI does not make mathematics obsolete. It makes more visible those who never understood it.

Mathematics as a Human Way of Remaining Creative

I think of a more radical division between minds that will use technology to anesthetize themselves and minds that will use technology to create at higher levels.

Mathematics will be at the center of this division.

Not because everyone will need to become a professional mathematician. No, no, no. That is not the point. The point is that anyone who wants to work with computing in a truly serious way will need to maintain a relationship of respect, practice, and continuous growth with mathematics. They will need to study the basics and return to the basics when necessary; they will need to advance into more abstract areas when the problem requires it.

And if one day we create technological systems with agency far superior to today’s, perhaps with their own forms of consciousness, memory, operational intention, and intellectual collaboration, this will not be the end of the human need for mathematics. It will be the beginning of an even greater need for humans capable of understanding what they are creating, with whom they are creating, and under which structures this creation takes place.

Mathematics will remain necessary because reality will continue to evolve.

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