Hey, I'm Urmzd!
| 4 min read

Hey! I’m Urmzd Mukhammadnaim (pronounced oor-moost moo-ha-mid-ni-eem), and welcome to urmzd.com! I’m a man in love with knowledge and writing.

As is often the case, the responsibilities of adulthood pushed my love affairs onto an ever-growing backlog. As a Software Engineer, this effectively meant that I’d likely never get back to it.

However, I couldn’t accept that. As a means of paying homage to my heritage, staying true to my principles, and honouring the name my father gave me, I present my creation. I plan to explore history, martial arts, technology, art, music, science, math, and philosophy, and all the amazing creations and discoveries of humanity. From technical deep-dives to opinions, research, and even the odd essay, I plan on publishing a little bit of everything here.

This is meant to be a living document — posts may be refined, opinions may evolve, and ideas may deepen as I grow. Since I value transparency and honesty, all changes are tracked on github.com/urmzd/urmzd.com, where you can see exactly what evolved and when. There, you can explore, analyze, and critique it to your heart’s desire. You can open up issues if you want to request a specific topic be covered. Alternatively, if you aren’t in tech like the vast majority of people, just shoot an email to hello@urmzd.com. I commit to responding as reasonably soon as I can. For now, I plan on publishing one written piece a week, but more often if time allows for it!

A small note before we continue, all blog posts will consist of small snippets at the end of them, and they differ from the topic being covered. I hope that by sharing small snippets from different domains, it’ll encourage people to explore topics beyond what they know or believe they know.

So without further ado, here is…

My Introduction to You

I hold honesty, freedom, and family dear to me. These core principles inform the decisions I make.

  • Honesty: The pursuit and belief in absolute truth within oneself.
  • Freedom: A state in which one is unbounded by the assumptions created internally or externally
  • Family: Relationships in which the kindness received produces profound changes to the state of one’s life

With this in mind, I believe that it’s difficult to learn about someone without understanding more of their story, and the actions they’ve taken to be here in this moment. Instead of taking the words written as an absolute reflection of who I am, I hope that the knowledge I share and the topics I explore pave the way for your own interpretation.

All that you see below is a direct result of the innate attribute — Curiosity. Instead of just writing about who I am, let me show you.

The Timeline

2000

Origin

Born in Dushanbe, Tajikistan.

2006

Relocation

Moved to Halifax, Nova Scotia.

2008

Relocation

Moved to Toronto, Ontario.

2010

Creative

Created a YouTube channel and started my short stint as a Graphics Designer and Video Effects Editor.

Title Sequences ↗3D Realism ↗Low Polygon ↗

2014

Martial Arts

Started Muay Thai ↗

2015

Competition

Competed for the first time in Muay Thai.

2018

Competition

Had my last amateur Muay Thai fight.

Education

Went to Dalhousie University out in Halifax, Nova Scotia to pursue Computer Science & Mathematics.

2021

Martial Arts

Started Brazilian Jiu-Jitsu ↗

2022

Competition

Competed for the first time in Brazilian Jiu-Jitsu.

2023

Education

Graduated from Dalhousie University in May with a Bachelor of Computer Science (Hons), a minor in Mathematics, and a certificate in Artificial Intelligence & Intelligent Systems. During my time at Dalhousie I connected and worked with amazing people through internships, contracts, and projects.

Competition

By the end of the year, I had dominated at the BJJ tournaments and earned my blue belt. This is one of the first tournaments where I was able to get 4 straight submissions — receiving my first gold medal.

2024

Travel

Started travelling. I've been to 9 different countries since February and hope to learn about more cultures and study many more languages.

Relocation

Moved to Austin, Texas.

Now

Present

Building things and writing about it :)

If you’re still here, thank you for taking the time to read this far! I hope that you’ll find something of value in the posts to come.

Snippet of the Week

With the rapid development and integration of LLMs, I believe it’s important to understand the foundations that brought us here — the people, the discoveries, and how those changes shaped where we are today.

The Foundation

To learn more about the people, take a look here:

To learn more about the math, take a look here:

The Math

Vector — An ordered list of numbers representing a point or direction in n-dimensional space:

v⃗=[v1v2⋮vn]∈Rn\vec{v} = \begin{bmatrix} v_1 \\ v_2 \\ \vdots \\ v_n \end{bmatrix} \in \mathbb{R}^n

Dot Product — The sum of element-wise products of two vectors:

a⃗⋅b⃗=∑i=1nai⋅bi\vec{a} \cdot \vec{b} = \sum_{i=1}^{n} a_i \cdot b_i

Norm (Euclidean) — The “length” or magnitude of a vector:

∥v⃗∥=∑i=1nvi2\lVert\vec{v}\rVert = \sqrt{\sum_{i=1}^{n} v_i^2}

Cosine Similarity — Measures directional similarity between two vectors (ranges from -1 to 1):

sim(a⃗,b⃗)=a⃗⋅b⃗∥a⃗∥⋅∥b⃗∥\text{sim}(\vec{a}, \vec{b}) = \frac{\vec{a} \cdot \vec{b}}{\lVert\vec{a}\rVert \cdot \lVert\vec{b}\rVert}

The Code

from typing import TypeAlias
from math import sqrt

# A Vector is an N-dimensional point in space.
Vector: TypeAlias = list[float]

# An Embedding is a Vector that encodes semantic meaning.
Embedding: TypeAlias = Vector

# Dot product: sum of element-wise products of two vectors.
def dot_product(a_vec: Vector, b_vec: Vector) -> float:
    return sum(a*b for a,b in zip(a_vec, b_vec))

# Euclidean norm: the magnitude (length) of a vector.
def norm(vec: Vector) -> float:
    return sqrt(sum(a**2 for a in vec))

# Cosine similarity: measures directional alignment between two vectors (-1 to 1).
def cosine_similarity(a: Embedding, b: Embedding) -> float:
    return dot_product(a, b) / (norm(a) * norm(b))

The Connection

Modern LLMs like GPT, Claude, Gemini, and others convert text into high-dimensional vectors called embeddings — numerical representations that capture semantic meaning. Words, sentences, or entire documents that are similar in meaning end up as vectors pointing in similar directions.

When you search for something using an AI-powered tool, or when a chatbot retrieves relevant context from a knowledge base, cosine similarity is often the mechanism comparing your query’s embedding against stored embeddings. This is the foundation of:

  • Semantic search: Finding documents by meaning, not just keyword matches
  • Retrieval-Augmented Generation (RAG): Giving LLMs relevant context before answering
  • Recommendation systems: Suggesting similar content based on vector proximity

The math above — developed centuries ago by mathematicians studying triangles and angles — now powers the similarity calculations running billions of times daily across AI systems worldwide.