What is AI?
An Applied Mathematician's Attempt at a Rigorous Answer.
I find it a little funny that I'm only getting to this article now. As an applied mathematician, I have a deep-seated need for rigor, for building arguments from first principles. In a field as dynamic and hype-driven as Artificial Intelligence, a rigorous definition can feel elusive. This article is my attempt to provide one. Not in the form of a dense mathematical proof, but through a structured framework that is both intuitive and fundamentally sound: viewing the core learning mechanisms of AI through the lens of child development.
My own "AI genesis" story wasn't seeing a robot, but coding a neural network from scratch and realizing the 'magic' was just calculus and matrix transformations. That revelation is the core of this post: AI is not a magic box. It is a set of mathematical tools. And to truly understand them, we must first understand how they "grow up."
Learning Through Guidance and Imitation: ML & DL
A child's first and most essential way of learning is by observing the ordered world their parents create for them. This is the domain of Machine Learning (ML) and its powerful subfield, Deep Learning (DL).
Machine Learning as Cultural Conditioning
Think of how a child learns the specific, non-negotiable rules of a Filipino household. They are taught to say "po" and "opo" to elders. They learn to take off their shoes or slippers the moment they step inside. This isn't learned through abstract reasoning; it's learned through direct instruction and imitation.
This is a perfect parallel for supervised Machine Learning. The model is given a massive dataset of specific inputs (an elder speaks to you) and the correct, labeled outputs ("opo"). It learns the function to map one to the other, perfectly mimicking the "correct" behavior it was shown.
Deep Learning as Internalizing Values
A child doesn't just parrot rules forever. Eventually, they move beyond mimicry and grasp the underlying concept of respect. They begin to apply it in novel situations, showing deference to other figures of authority even if they were never explicitly told to.
This is Deep Learning. The neural network's layers allow it to learn not just the surface-level pattern, but the deeper, abstract principles behind the data. It builds an internal model of "respect," allowing for a more flexible and intuitive application of the learned rules.
Learning Through Consequence: Reinforcement Learning (RL)
But not everything can be learned from a guiding hand. A child must eventually face the world on their own and learn from its direct, unfiltered feedback. This is the world of Reinforcement Learning (RL), and it is a process of conquering chaos.
Reinforcement Learning as Learning to Walk
The best analogy for RL is a toddler learning to walk. There is no instruction manual. No parent can perfectly explain the infinite micro-adjustments of balance and muscle control. The child must learn through brutal trial and error.
The agent is the toddler.
The environment is the physical world, governed by the unforgiving laws of gravity.
The action is attempting to take a step.
The penalty is the immediate, painful feedback of falling.
The reward is the exhilarating success of staying upright and moving forward. (and probably the applause of your parents)
The toddler is not trying to imitate a perfect "walk" from a dataset. They are developing their own strategy to maximize reward and minimize punishment, building a robust understanding directly from the consequences of their actions. This is how RL agents master complex games and robotic controls—by bravely confronting the chaos of their environment and structuring it through experience.
Conclusion: Think Like a Mathematician, Not a Movie Director
So when we ask, "What is AI?", the answer is multifaceted. It’s the carefully guided student, learning the cultural rules of its environment (ML/DL). And it’s the determined toddler, courageously facing gravity to learn to stand on its own two feet (RL).
The next time you interact with an AI, I challenge you to see past the code and think of its upbringing. Was it taught by the book, or did it learn from the school of hard knocks? Understanding its developmental journey demystifies its capabilities. Because beneath it all, whether it's a child internalizing respect or a toddler learning to walk, the engine is the same: a mathematical function, optimizing for a goal, and turning the unknown chaos of the world into the ordered structure of knowledge.
