Richardson Lima

The Transformer architecture is the foundational neural network design behind Large Language Models (LLMs). It uses a mechanism called self-attention to understand the relationships and dependencies between words in a sequence, which is crucial for tasks like natural language understanding and generation. Unlike older models, Transformers process entire sequences at...

Think of a max‑heap as a balanced amphitheater. Every seat below must host a value no larger than those above it. The stage is always the maximum, ready to exit first.

Recursion is one of those ideas that feels magical at first sight. A function that calls itself? It sounds paradoxical, like a poem writing its own verses. Yet recursion is one of the most natural ways to express problems in computer science, and its foundation lies deeply connected with mathematical...

Quicksort is the study of how a single decision, the pivot, sculpts an entire computation. Choose well and you glide with logarithmic grace. Choose poorly and you fight a quadratic headwind. In practice, with a bit of randomness, it sings near the theoretical best.

In our journey through algorithms, we have seen recursion as both a programming style and a reflection of induction in mathematics. Today we turn to one of the most elegant children of recursion: MergeSort, the sorting algorithm that embodies the spirit of divide and conquer.

In the previous posts we explored growth rates, Big-O, and induction as the mathematical backbone of reasoning about algorithms. Today we begin our journey through sorting algorithms, and we start with the most human of them all: Insertion Sort.

In our previous explorations, we studied algorithmic growth rates, induction, and recursion. Now we open the next chapter: elementary data structures, the building blocks of computation.

Imagine a long ordered list of user IDs. How can we quickly find whether a given ID is in the system? If the list were unordered, the only choice would be to scan all elements a linear search with time complexity $O(n)$. But if the list is ordered, a far...

Neurodivergence is not a deficit; it is a spectrum of cognitive architectures. Within this spectrum lie forms of brilliance that are often misunderstood: giftedness and high abilities, autism spectrum condition level 1 (formerly called Asperger), and attention related profiles such as ADD/ADHD. In the world of technology, these minds are...

There is a peculiar beauty in proofs that extend a finite gesture to an infinite horizon. Mathematical induction is one such proof technique. It is not about piling evidence, but about showing with absolute certainty that if one case holds, all others will follow. Think of dominoes, of staircases, of...

When Villa-Lobos wrote his Bachianas Brasileiras, he was not merely composing music. He was weaving a dialogue across centuries and continents: Johann Sebastian Bach’s mathematical rigor braided with the raw, breathing soul of Brazil.

The efficiency of an algorithm is one of the most important aspects in computer science. It is not enough for an algorithm to be correct , it also needs to be feasible for large inputs.

The world sighs and time bends when the first notes of Come, Sweet Death emerge in five cello voices. There is no hurry, no unnecessary ornament, only the weight of sound spreading like fog across a silent morning field.

Reading order matters. This post is a direct sequel to our previous article on growth rates and asymptotic notation. We’ll use those ideas to prove properties, design recursive algorithms, and analyze their running time.

There’s a whisper in the tides, A herald of the days to come, Where every wave arrives carrying The hint of lives not yet begun.

A language model is a musical instrument that plays probability. Every token is a note, and attention is the conductor that decides who must be heard.

Natural Language Processing (NLP) is a subfield of artificial intelligence (AI) that focuses on the interaction between computers and humans using natural language. It involves the development of algorithms and models to enable machines to understand, interpret, and generate human-like language.

A poetic meditation on two inner currents: one dazzling yet fragile, like a crystal that fractures under pressure; the other steady and guiding, like a star or a rock that sustains. A reflection on learning where to anchor the soul. There are those who can tear your soul apart, devastate...

A bond so steady, a love so true, between a father and his daughter too. Unconditional, patient, quiet, sure— a shelter of grace that will endure.

DataOps is a new term that has been gaining traction in the data management industry. It is a set of practices and techniques that aim to improve the speed and quality of data analytics by streamlining the development, deployment, and maintenance of data pipelines. DataOps focuses on collaboration, automation, and...

Artificial Intelligence is not merely a technological trend. It has become a field where mathematics, engineering, ethics, and philosophy converge. Much like astronomy reshaped humanity’s understanding of the cosmos, AI reshapes our view of cognition, agency, and automation.

Go is a language for building systems that must breathe under load and still feel simple to the hands. In this guided tour we keep our feet on the ground with code, and our head in the stars with ideas.

Now it’s too far away and looking at the horizon lines distracts me, our dreams are what I miss the most when we looked together in the same direction. Where are you now besides here, inside of me? We did it right unintentionally, It was time who got it wrong,...

“The song’s immaculate slow build, the melancholy of its minor keys, the exuberance of the string section at the peak… all of this allows it to lend poignant resonance to any scene in which it’s used.” — cherwell

When I was a child, one of my earliest fascinations was with the universe. Among the questions that stayed with me, black holes stood out as both terrifying and beautiful. I remember asking my teacher about them—though the conversation never happened in detail, the curiosity never left me.

Big-O is more than a notation. It is the universal score sheet where algorithms reveal their rhythm in the face of infinity. If Θ sets the tempo and Ω marks the bass line, O describes the dramatic crescendo of the worst case.