I Had to Teach It Before I Could Understand It

For a long time, I thought understanding meant being able to continue.

If I could follow the lecture, solve the exercise, use the formula, write the code, and arrive at the expected answer, then I understood. What else could the word mean?

This is one of the convenient lies education teaches us. A person can continue for years on a structure he has never inspected. Every new technique gives him another floor to stand on. Every correct result reassures him that the building must be sound. He does not notice that some of the stairs are missing because he has become very good at jumping.

I became good at jumping.

In the previous writeup, I wrote about speaking the language of school fluently without being able to think through it naturally. But that is only the story of the fracture. This is the story of what I did afterward: how I rebuilt mathematics in English, how I began explaining machine learning in Darija, and how teaching other people forced me to rebuild deep learning from first principles.

I thought I was creating a path for other people into the field. I was also creating the path through which I would finally understand the field myself.

English gave me a path back through the mathematics. Teaching in Darija made me organize deep learning into something more coherent than a collection of models, papers, and implementations. Between the two, I stopped being satisfied with knowing how the field worked and began asking why it had been built that way at all.

That is where research began for me.

Mathematics changed languages before it became mine#

Until university, I studied mathematics in Arabic.

Then I arrived at university and the language changed to French.

The symbols remained familiar. A derivative did not acquire a new shape at the university gate. A matrix did not rearrange its entries because the professor named it in French. Mathematics likes to present itself as independent of language, and at the level of notation this can seem true. The equation survives the border.

The mind reading it does not.

Everything surrounding the notation changed at once: the definitions, the instructions, the names of operations, the way a proof announced its direction, the small connective phrases that tell you whether a statement is a consequence, an assumption, an exception, or an intuition. The symbol was the visible part of the concept. Its language was the tissue holding it to everything else I knew.

When that tissue was cut, the mathematics did not disappear. It became loose.

I often recognized what a professor was doing before I could fully understand what was being said about it. I could match a French term to an Arabic term, and then try to match both to the object in my head. Sometimes the chain held. Sometimes it produced an almost-correct meaning: enough to complete the exercise, not enough to know where the idea began, why it was necessary, or what would happen if one of its assumptions changed.

The transition did not simply add French to mathematics. It divided my mathematical memory into a before and an after.

Basic ideas lived on one side in Arabic. Advanced ideas arrived on the other in French. To connect them, I had to translate backward through years of education. The more advanced the subject became, the more it depended on connections that the language change had made expensive to retrieve.

So I learned the practical skill students learn when the system moves faster than their understanding: I learned to proceed.

Proceeding can look exactly like competence. You identify the family of the problem. You remember the form of the solution. You follow the manipulation. You become fluent in the rituals of the field. If the answer is correct, nobody asks whether every step belongs to the same internal world.

But research eventually asks.

Research gives you a problem whose family is unknown. There is no example whose surface you can imitate. The assumptions are not highlighted because discovering them may be the work. At that point, every bridge you pretended was complete becomes visible.

You cannot keep jumping over what your later work depends on.

I started again in English#

The repair did not happen by adding more advanced material. It happened when I gave myself permission to go backward.

I began studying mathematics again in English, from the ground up.

Going back can feel humiliating when you have already reached a level at which people expect you to know the basics. You open a lesson on an idea you have used for years and feel that you are moving in the wrong direction. Your titles, grades, code, and completed projects all argue that this material should be beneath you.

But nothing you do not understand is beneath you. It is underneath you.

I did not return because English is naturally more mathematical than Arabic or French. No language owns abstraction. I returned through English because it had become the most continuous route available to me. The elementary explanation, the advanced textbook, the lecture, the code documentation, the research paper, and the conversation around new work could all exist in the same language. For once, I could climb without the staircase changing names between floors.

I also controlled the speed.

I could stop at a word that felt familiar and ask whether I truly knew it. I could compare definitions from several sources. I could move from an intuitive picture to a formal statement, then to a proof, then to an implementation, and back again. I could remain with one idea until its different forms began to feel like views of the same object rather than separate things to memorize.

The strange part was how often the most basic material changed the advanced material above it.

A definition I had carried for years would suddenly become precise. A formula I had treated as a rule would reveal the problem it was designed to solve. A proof would stop looking like ceremonial algebra and start looking like a sequence of necessary decisions. Sometimes I discovered that I had not misunderstood the entire idea. I had missed one distinction near the beginning, and everything after it had inherited the blur.

Restudying did not erase what I had learned in Arabic or French. It reconnected it. English became a temporary workshop where I could place pieces from both sides of the fracture on the same table.

The goal was not to replace one educational language with another. The goal was to build a base that remained still long enough for me to examine it.

Then I tried to build a path through deep learning in Darija#

Rebuilding the mathematics made me more capable. Teaching it in Darija made me less able to lie to myself about that capability.

I began giving talks, creating content, and guiding people through machine learning in Darija. At first, the purpose seemed to face outward. There were people who could reach the ideas more easily if someone met them in the language of ordinary Moroccan life. I knew what it meant to spend part of a lesson fighting the language before the learning could even begin. If I could remove some of that distance for somebody else, I wanted to.

But every explanation came back toward me.

The field had already given me polished English sentences for gradient descent, generalization, attention, kernels, and representations. In Darija, that shelter disappeared. Before deciding how to explain an idea, I had to decide what the idea actually was: which detail could wait, which one was essential, and which apparently minor condition held the entire mechanism together.

You cannot guide someone across a field you know only as disconnected destinations. You need the roads between them. You need to know what must come first, what depends on what, and which apparent shortcut will create confusion later.

That difference became obvious the moment I faced an audience.

An audience can hear the missing step#

When you study alone, your confusion learns your habits.

You skip the same step every time. You accept the same vague phrase. You use the same example that never tests the edge of your understanding. Because the gap has your shape, you move around it without seeing it.

Another person does not know the choreography.

Someone listening to a talk asks the question you stopped asking years ago: Why? Why do we normalize this? Why does this operation preserve that property? Why must the function have this form? What would break if we removed this term? Why is the model learning rather than only remembering? Why should this distance mean similarity?

A question can sound elementary and reach the assumptions faster than an advanced one.

If I answered with the English phrase used in the literature, I might preserve the official explanation while losing the person. To answer in Darija, I had to open the phrase. I had to inspect every assumption packed inside it, then put the idea back together in front of someone who was not obligated to be impressed by its vocabulary.

Darija is especially unforgiving of decorative expertise. A sentence that sounds authoritative in the language of a paper can sound ridiculous when brought into the language of the street. The prestige disappears. What remains is the idea and whether it makes sense.

That was useful to the audience. It was transformative for me.

Every time I could not explain something simply, I found a place where my own knowledge had been compressed too early. Sometimes I needed a better analogy. Sometimes the analogy failed because the formal statement contained a condition I had ignored. Sometimes I reached for the derivation and discovered that I knew how to follow it but not why anyone had chosen that route. Sometimes a listener’s confusion was not their failure to understand my answer. It was evidence that my answer had not reached the question.

Teaching turned misunderstanding into data.

Creating a curriculum gave me what school had not#

Giving one explanation is a local task. Guiding people over time is different. It forces you to build a map.

To create useful content, I had to decide where deep learning actually begins. Does it begin with a neural network, or with optimization? Can optimization be understood without calculus? Can a loss function be understood without probability and geometry? When should someone meet linear algebra as a list of operations, and when should they see it as the language of spaces, transformations, and representations?

These were teaching decisions, but they were also questions about the structure of the field.

I could not guide people by reproducing the order in which I had encountered things, because my own path had been fractured. It contained university courses, code, tutorials, papers, unexplained jumps, and concepts learned long after the methods that depended on them. To teach, I had to create the sequence I wished I had received.

That work gave me my foundation in deep learning research.

Preparing a talk forced me to follow one idea downward until I reached what it assumed. Creating a series forced me to follow it sideways into the ideas it connected to. Guiding a person forced me to follow it forward and see which later confusions were produced by an earlier gap. Repeating this process turned the field from a catalogue of architectures into a dependency graph I could move through deliberately.

Darija was the language in which I did much of this work, but the achievement was not translation. I was not searching for Moroccan substitutes for English technical terms and calling the job complete. I was deciding what a learner needed to understand, in what order, through which intuition, and with how much mathematical precision. Some terms could remain in English. The logic could not remain implicit.

Content creation became a second education. The first had asked whether I could arrive at the answer. This one asked whether I could reconstruct the route and notice where it was incomplete.

The gap in an explanation can become a research question#

Most people imagine research beginning with an answer nobody has found.

Mine often began with an explanation I could no longer accept.

Teaching repeatedly brought me to sentences the field uses because everyone in the field has learned to continue after hearing them. A model learns features. A network represents knowledge. Attention finds what matters. A kernel measures similarity. An embedding captures structure.

These sentences are not necessarily false. They are often worse for a curious mind: they are true at a level that permits us to stop asking what, exactly, is happening underneath.

When I tried to explain them in Darija, their verbs became suspicious. What does learns mean here? Where is the feature? In what mathematical object does the representation live? What is preserved when the input becomes an embedding? Why does this similarity function deserve to be trusted? Which part of the architecture creates the behavior we attribute to the whole network?

The need to explain stripped the field’s familiar language from the mechanism. Once the mechanism stood without its usual words, I could see where the words were covering a gap.

That is how teaching began leading me toward research from mathematical first principles. The better I became at explaining an idea without hiding behind its accepted language, the harder it became to tolerate explanations that named a phenomenon without accounting for it.

Research began when implementation was no longer enough#

Machine learning makes it possible to travel very far through implementation.

You can assemble architectures, run experiments, tune parameters, improve a metric, and build something genuinely useful. This is real knowledge. It should not be dismissed simply because it is empirical.

But building gives some questions no reason to appear.

If a component works, the practical task may be finished. If an explanation is good enough to choose the next experiment, there may be no incentive to examine its assumptions. The system rewards the result, and the result closes the case.

Teaching reopened it.

The person in front of me did not only need to know which operation to use. They needed a picture of why the operation existed. To give them one, I had to descend from the library call to the equation, from the equation to the assumptions, and from the assumptions to the problem that made them necessary.

After enough descents, I began remaining there.

The foundational level stopped looking like remedial material and started looking like unexplored territory. Basic questions became powerful because they crossed boundaries the specialized vocabulary had hidden. An apparently simple question about similarity could lead into geometry and kernel methods. A question about what a neuron contains could become a question about representation. A question about why attention works could become a question about the mathematical structure being computed.

The deeper I went, the less research felt like adding something clever to the top of the field. It began to feel like returning to an old sentence and refusing to step over the word nobody had defined carefully enough.

The child who had once built years of knowledge on almost-correct meanings had become an adult unwilling to leave an almost-correct meaning alone.

English rebuilt the mathematics; teaching built the researcher#

It would be easy to tell this as a story about English saving my education.

That would repeat the hierarchy I am trying to describe.

English mattered enormously. It let me rebuild mathematics inside one continuous ecosystem, connect the basics to current research, and move between theory, papers, software, and international conversations without changing the language of thought at every step. But access and a way of doing research are not the same gift.

English repaired the mathematical sequence that the transition to French had broken. It let me study the fundamentals again without another institutional deadline forcing me forward. Teaching deep learning in Darija did something different: it made me construct the field as a connected body of knowledge. It made me decide which principles were load-bearing, trace methods back to their assumptions, and remain with a gap until I could guide someone across it.

One process rebuilt the mathematics beneath my work. The other built my way of doing research above it.

Deep understanding required both.

I thought I was only helping other people enter the field#

I began with the idea that I had learned something and could make the path easier for the person coming after me.

That did happen. But it was not the whole exchange.

Every talk required me to study again. Every piece of content required me to choose a structure rather than inherit one. Every person I guided revealed a dependency I had treated as obvious. Once the ideas were connected, I could see where an empirical success lacked a satisfying account or a familiar explanation named the result without deriving the mechanism. Some of those discontinuities became research questions.

This matters beyond my own path. We often speak about teaching science in local languages as an act of inclusion, as if the only benefit were that more people could receive knowledge produced somewhere else. That benefit is already enough to justify the work. But it is not the limit.

When people can study and discuss a field through a language close to their lives, they are not limited to receiving simplified answers. They can remain in the conversation long enough to question the structure, build on it, and guide the next person. They can become critics, builders, and researchers.

A community does not join science only when it gains access to existing answers. It joins science when its people build strong enough foundations to produce new questions.

The basics were not behind me#

I used to think expertise meant moving far enough from the basics that nobody could confuse you for a beginner.

Now I think expertise is the ability to return to the basics without shame and find that they are not basic at all.

The basics are not the part of a field we finish before the interesting work begins. They are where familiarity buries the deepest assumptions, and where a question can sound simple enough to be embarrassing while being difficult enough to become a research program.

Mathematics first came to me in Arabic. University asked it to continue in French. The transition fractured connections I did not yet know how to protect. I learned to proceed anyway. Later, English let me reconnect the mathematics. Guiding others in Darija then made every idea I could not reconstruct a message about the limits of my own understanding.

What began as communication became diagnosis. Diagnosis became study. Study became a demand for foundations. And the demand for foundations became research.

I still write papers in English. I still use the formal vocabulary of the field. I still work through equations whose symbols belong to no single spoken language. But when I want to know whether an idea has truly entered me, I imagine having to explain it without the shelter of the sentence in which I learned it.

Can I say what problem it solves?

Can I explain why its pieces are necessary?

Can I rebuild it from an example close to life, then return to the formal object without losing precision?

Can I answer the person who asks the question the field has trained itself not to ask?

If I cannot, I do not treat the failure as proof that the audience is not ready. I treat it as a direction in which my own understanding can still grow.

I thought I was giving talks in Darija because I had knowledge to share.

I did not know that Darija would ask me to earn it again.

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