Abhimanue Udayan

Builder & educator at the intersection of computing, physics, and scalable education systems.

ABOUT ME

Abhimanue Udayan

Founder of Hexagon Know

I am an avid reader and builder who develops systems at the intersection of computing, animation, and education to drive real-world impact. From an early age, physics, nature, and machines became my core interests, while art, gaming, and travel evolved into my most cherished pursuits.

My background spans computational physics, numerical computing, enterprise technical operations, and years of teaching physics and supporting the development of ed-tech solutions for 4 unicorn valued companies over a time of 6 years.

I began my tech career at AT&T through a business process by Sutherland Global Services, diagnosing and resolving technical issues across the USA remotely from Kochi. Solving 20-42 issues per day for 11 months, at extraordinary speed and precision, helped me with my technical problem-solving skills, customer management & effective troubleshooting skills just using a computer and an internet connection.

Later, I joined VNIT for my Master’s in Applied Physics, where I focused on classical and quantum computational physics, numerical programming, and high-performance computing. During this time, I explored Vedic Mathematics and integrated its principles with modern computational methods, engineering C++-based systems to solve hard equations called Diophantine equations with complete accuracy & remarkable speed. This work culminated in cracking the Archimedes' Cattle Problem, computing solutions exceeding 18 million digits with absolute accuracy.

Now I offer AI-powered training solutions for schools, organizations and also teach Physics to students through personalized online lessons focused on conceptual understanding, problem-solving, and exam success.

Work & Education

Experience

Founder

Hexagon Know Private Limited

Leading the development of HK Skill, an AI-powered workforce development platform, focusing on product development and interactive learning simulations.

Associate - Curriculum Development

Aakash+Byju’s Foundation

Managed curriculum development, content creation, and quality control, enhancing engagement for students across India.

Assistant Professor- Physics

Aakash Institute, Preet Vihar, Delhi

Taught NEET Physics to over 1000+ students and helped many secure amazing results including AIR 1 in AIIMS & AIR 2 in NEET 2019

Education

M.Sc. Applied Physics

Visvesvaraya National Institute of Technology (VNIT), Nagpur, India

Specialized in computational physics, quantum computing, and solved the Archimedes' Cattle Problem with a 206,545-digit solution.

B.Sc. Physics

Sacred Heart College, Thevara, Cochin, India

Trained in mathematical physics and numerical programming; served as Chief Editor for the college magazine.

Higher Secondary Education - Computer Science

SNDP HSS Udayamperoor, Cochin, India

Completed Higher Secondary Education, specializing in computer science, C++ programming and database management systems.

Archimedes' Cattle Problem

Explored and solved in 2017 during my Master's in Physics at VNIT Nagpur

The Archimedes' Cattle Problem is one of the most notorious puzzles in mathematical history—so complex that its solution spans 206,545 digits and remained unsolved for centuries without computational power. Solving it requires deep mastery of Diophantine equations, particularly large-scale Pell–Fermat systems.

During my master’s in physics, I specialized in Diophantine analysis and developed a high-performance C++ system capable of solving Pell–Fermat equations of arbitrary size. Built on the principles of Bhāskara II’s Chakravala method and extended with my own algorithm for linear congruences, this system was designed for scale and precision.

Using this framework, I solved over one million Pell–Fermat equations, generating insights on the solutions that were formally documented in my master’s thesis at VNIT. An interesting outcome of the project was solving the Archimedes' Cattle Problem on a standard i7 desktop—demonstrating that even historically “intractable” problems can be approached efficiently with the right mathematical and computational design.

This is just the tip of the iceberg—a powerful validation of Indian Vedic mathematics fused with modern computation.

View the complete solution

My Domains

Teaching & Mentorship

Years dedicated to training and mentoring students in Physics for competitive examinations.

Cybersecurity & Support

Over 5,000 support sessions taught me that trust beats hype.

AI & Learning Platforms

Using AI, I design tools that are both secure and user-friendly.

Creative Technology

Transforming ideas through art and tech.

Unity Development

Designs applications for my company Hexagon Know.

Full Stack Development

Worked on a large range of tech including quantum computing.

TECH STACK

HK Skill : How I Help Enterprises To Systematically Train & Grow

CREATIVE & EDUCATIONAL WORKS

BLOG

Join My Academies

The Right Program. The Right Foundation.

Structured. Focused. Result-Oriented.

A Level

Academy

A Level Physics
1-to-1 Coaching

Cambridge & Edexcel

Personalized online coaching for Cambridge & Edexcel A Level Physics.

Live 1-to-1 online classes
Past paper practice & exam strategy
Weekly progress tracking
Doubt solving between classes

Join Now

NEET

Academy

NEET Physics
Yearly Program

(Class 11, 12, 12+)

Full-year structured Physics program for Class 11, 12 and Repeaters

Strong focus on Class 11 fundamentals
Concept building + problem-solving
Weekly tests & performance tracking
Mentor support & doubt resolution

Join Now

Expert Mentors Learn from experienced Physics mentors.

Proven Results Rank-focused approach that works.

Concept Clarity Deep understanding over memorization.

Disciplined System Structured path to consistent improvement.

CONTACT ME

Send a message

Contact Info

Open to partnerships, consulting roles, contracts, and growth opportunities.

Email

abhimanue [at] hexagonknow [dot] com

Address

Ernakulam, Kerala, India

🧮 What are Diophantine Equations?

Diophantine equations are equations where you're only interested in integer solutions (whole numbers).

Simple example:

x + y = 5

→ many integer solutions like (2,3), (1,4), etc.

Hard example:

x² + y² = z²

→ gives Pythagorean triples like (3,4,5)

The challenge:

👉 No general method works for all Diophantine equations

👉 Some are insanely hard (even unsolvable in general — see Fermat's Last Theorem)

Named after: Diophantus — often called the "father of algebra"

🔥 Pell–Fermat Equation (Core Idea)

The Pell equation looks like:

x² − Dy² = 1

Where: D is a non-square integer (like 2, 3, 5, 7…)

Example:

x² − 2y² = 1

Solutions: (3,2), (17,12), (99,70)… → they grow very fast

Key Insight:

Once you find the smallest solution, you can generate infinite others.

Why it matters:

• Shows deep structure in numbers

• Connected to continued fractions

• Used in cryptography, algebraic number theory

Despite the name: It wasn't really discovered by Pierre de Fermat or Pell — Europeans misunderstood earlier Indian work (important 👇)

🇮🇳 Bhāskara's Chakravāla Method (The Real Power Move)

The Chakravāla method (meaning "cyclic method") was developed by Bhāskara II

This method solves:

x² − Dy² = 1

What makes it insane:

• It's an iterative algorithm

• Works efficiently even for huge numbers

• Way ahead of Europe by ~500 years

Basic idea (simplified):

You start with an approximate solution and repeatedly refine it using a cyclic process until you hit the exact solution.

It's like:

👉 Intelligent trial-and-error with mathematical structure

👉 Not brute force — guided convergence

Example:

For D = 61, the smallest solution is:

x = 1,766,319,049

y = 226,153,980

Bhāskara's method could handle this centuries before computers.

Abhimanue Udayan

ABOUT ME