Ajeet Kumar

Ajeet Kumar

Applied Mathematician with Specialization in Full Stack Machine Learning and Data Science

Blog posts

2026

System Design Part 9

less than 1 minute read

Published:

System Design from First Principles - The Mathematics of Attempts

System Design Part 8

less than 1 minute read

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System Design from First Principles - CAP Theorem & PACELC

System Design Part 7

less than 1 minute read

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System Design from First Principles - Sharding: When One Disk is Not Enough

Operational Ecosystems of LLMs in Python - Part 2

1 minute read

Published:

Module 2 : Re-Engineering and Verification Workflow

Module‑1 showed you that LLMs are not magic but a composition of code, math, and hardware, all reachable from Python if we know where to look. It traced how LLMs sit in the stack: Python as glue, PyTorch as the modeling layer, and hardware‑specific backends (CPU, GPU, etc.) as the execution engines.

Operational Ecosystems of LLMs in Python - Part 1

7 minute read

Published:

The first question came into the my mind when i started thinking about the operational ecosystem of LLM is that Why LLMs matter in the AI ecosystem ? LLMs are a core component of modern artificial intelligence. In practice, we use Python extensively for almost any task in AI and data‑driven decision‑making from simple scripts to complex production pipelines. Today, the ecosystem surrounding Python is rich and specialized for nearly every problem domain, there exist dedicated tools that can be easily integrated because they live inside Python’s operational environment. So, they are the natural evolution of this ecosystem they turn language into a computational interface but still sit on top of same stack of tools, hardware and orchastration layers that power the rest of AI.

System Design Part 6

less than 1 minute read

Published:

System Design from First Principles - The Taxonomy of Storage: How to Architect Data

System Design Part 5

less than 1 minute read

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System Design from First Principles - The Physics of Persistence

System Design Part 4

less than 1 minute read

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System Design from First Principles - The Anatomy of a Request (DNS, BGP, and the Edge)

System Design Part 3

less than 1 minute read

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System Design from First Principles - The Cost of Communication

Mathematics

less than 1 minute read

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In mathematics we study mathematical objects , relationship between objects and how relationship between objects changes w.r.t to others and many more lead to the special class of mathematical structures that mathematicians are interested to explore through geometry, algebra and analysis etc.

System Design Part 2

less than 1 minute read

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System Design from First Principle - The Math of Scale

Attention Mechanisms

63 minute read

Published:

Attention Mechanisms - All You Needed To Know

Llama Lineage

7 minute read

Published:

A Study of Llama Lineage : A Transformer based LLMs

AI Model Optimization Part-1 by Applied Mathematician

1 minute read

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AI Model Optimization is an interdisciplinary field that involves collaboration between researchers, system engineers, and hardware architects to make models better, cheaper, and faster with the goal of maximizing throughput and minimizing computational costs and latency.

अत्रेय महाकाव्य: शून्य से सृजन और आजमगढ़ की पावन कर्मभूमि की अमर गाथा

1 minute read

Published:

क्या आपने कभी उस ‘शून्य’ के बारे में सोचा है जहाँ से इस अनंत ब्रह्मांड का उदय हुआ? क्या आप जानते हैं कि आजमगढ़ की पवित्र नदियाँ—तमसा, मंजूषा और कुँवर—किन महान ऋषियों की साधना की साक्षी रही हैं?

Notebook : Chanakya(Kautilya) Niti Sutra

18 minute read

Published:

“Establish yourself in Self-Control, plan with Secrecy, act with Courage, and let Truth be your final destination.” — Ajeet Kumar

A Case Study of MacBook Air M4(16/256GB) for AI Model Production by Applied Mathematician

4 minute read

Published:

I was using Asus Notebook(i3/8GB/1TB-HHD) since 2021. After completion of M.Sc Mathematics and Computing degree at BHU Varanasi, went to the IIT Delhi(Cloud Computing and HIPC Lab SIT), New Delhi for the AI Research Internship. I am greatfull enough that i have worked onto the the two most interesting research problem

  1. LLM for OpenAPI Specification Generation from the given server source code.
  2. Lean4 Proof generation for the given theorem in lean4

2025

Lean4agent

less than 1 minute read

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How to become a mathematician ?

6 minute read

Published:

I don’t know from where to start to tell you about my story because i have’t become a mathematician until now, but on the track in the race of becoming a mathematician. So, whatever i will tell you that will be the my thoughts during learning and understanding in the journey of continuum hard work how i am actually transforming myself from a first class passed out master student that have a litle exposure to the research due to my masters thesis on topics of discrete differential geometry and its applications to become a researcher in mathematics after publishing papers.

MLOps for LLMs

30 minute read

Published:

Introduction to operations for Large Language Models(LLMs) also called as MLOps for LLMs.

Machine Learning Systems by

5 minute read

Published:

What does it mean to master machine learning systems—not just design models?

2020

2012

less than 1 minute read

Published:

This is a sample blog post. Lorem ipsum I can’t remember the rest of lorem ipsum and don’t have an internet connection right now. Testing testing testing this blog post. Blog posts are cool.