AARAV NILESH LELE
Intangible Mechanisms
Exploring the underlying mechanisms that govern complex systems.
Mathematics
to deduce patterns.
Economics
to model behaviour.
Algorithms
to implement solutions.
About
LOVE
Puzzles, riddles, mysteries.
Anything that needs figuring out, count me in!.
DETEST
Coding.
Just not my cup of tea. I go nuts spending hours for a single bug.
LOVE
Running.
It eases and declutters my mind whenever I'm stressed.
DETEST
Playing cricket.
Especially fielding where I'm waiting endlessly for the ball to come towards me.
LOVE
Food.
Trying different cuisines feels like experiencing a new culture!
DETEST
My first MUN.
The sessions were so long and interminable, I didn't come back for Day 2.
LOVE
Solving problems.
Especially when there's no obvious path in plain sight.
DETEST
Overcomplicated projects.
When there's so much work that it feels like the ship isn't moving.
LOVE
Math & economics videos.
I like my entertainment to leave me with a new insight.
DETEST
Reading.
Page 2 was once my limit. I'm slowly making it further.
Academics
Structured exploration of mathematics, economics, and algorithmic thinking. Focused on building analytical depth and understanding systems through abstraction and application.
School Journey
GRADES 1–4
St. Gregorios High School
— Grades 1–4 · ICSE
GRADES 5–10 · PRESENT
JBCN International School, Chembur
— Grade 5 · IB PYP
— Grades 6–8 · Cambridge Lower Secondary
— Grades 9–10 · IGCSE
IGCSE SubjectsGrade 9 & 10
- Additional Mathematics0606
- International Mathematics0607
- Physics0625
- Chemistry0620
- First Language English0500
- French Foreign Language0520
- Economics0455
- Computer Science0478
Research
My research focuses on breaking down complex systems into simple, manageable parts and mechanisms that can be analysed and evaluated individually. I aim to apply this approach to real-world problems by simplifying intricate ideas and concepts into structures that can be better understood and applied.
Ideas in Progress
Questions, patterns, and ideas I'm currently exploring across mathematics and economics.
Length-to-Diagonal Ratio
Geometry · Higher Dimensions · Patterns
A square with side length n has a diagonal of n√2, while a cube has a longest diagonal of n√3. In 4D, this becomes 2n. What happens in higher dimensions — and what about rectangles, cuboids, and other shapes?
Factorial Analysis of n×n×n Rubik's Cubes
Combinatorics · Permutations · Functions
How does the number of possible combinations grow as the size of a Rubik's Cube increases? Can this factorial behaviour be analysed and extrapolated as a function or graph?
Pareto's Law / 80–20 Rule
Inequality · Market Conditions · Rationality
In a free-market economy, does disproportionality continue to increase without government intervention because of an intangible mechanism?
Powers of 11 and Pascal's Triangle
Number Theory · Algebra · Combinatorics
When base 11 is raised to different powers, it starts to show the patterns of Pascal's Triangle: 11, 121, 1331, …, corresponding to a+b, (a+b)², (a+b)³, ….
Poker Outcomes Through Game Theory
Probability · Game Theory · Rational Decision-Making
Can the possible outcomes in poker be predicted using probability and player choices, assuming rational decision-making, and can game theory be used to find the optimal bets?
A Relationship Between π and e
Number Theory · Irrational Numbers · Algorithms
π⁴ + π⁵ ≈ e⁶. Can I produce an algorithm to find a direct or even closer approximation between these two irrational numbers?
The Ending Digits of Powers of 5
Number Theory · Modular Arithmetic · Patterns
How do the ending digits of powers of 5 evolve as the exponent increases? The values seem to repeat — but at what frequency, and can a formula be derived from this?
Recurring 9s and Countable Infinity
Number Theory · Infinity · Set Theory
Since 0.999… = 1, could the idea of recurring 9s also be used to think about countable infinity? If infinity can be approached but never reached, is there a similar relationship between recurring numbers and infinity?
Modular Arithmetic and Digit Patterns
Number Theory · Modular Arithmetic · Patterns
For any n-digit number, there is at least one digit divisible by n, or a combination of two or more digits whose sum is divisible by n. Can similar modular arithmetic ideas be applied to multiplication, subtraction, other operations, or different patterns?
Rethinking the Shape of Diminishing Marginal Utility
Behavioural Economics · Mathematical Modeling · Real-World Context
Theoretically, diminishing marginal utility is often shown as a smooth decline. But in real choices, could the decline be uneven — sometimes steep, sometimes gentle, or even shifted by certain units because of behavioural factors and individual choices?
19 entries
A Theory of Rational Addiction
Gary S. Becker & Kevin M. Murphy · 1988 · Behavioural Economics · Paper
Source ↗A Walk Through Combinatorics
Miklós Bóna · 2006 · Combinatorics · Book
An Elementary Introduction to Number Theory, 3rd Edition
Calvin Long · 1995 · Number Theory · Reference
An Introduction to Cryptography
Ed Schaefer · — · Cryptography · Lecture Notes
Anthropic's Claude tried to solve the Riemann hypothesis and found something new instead
Skye Jacobs · 2026 · AI & Number Theory · Article
Source ↗Applied Combinatorics, 4th Edition
Allan Tucker · 2002 · Combinatorics · Reference
Discrete Mathematics and Its Applications, 4th Edition
Kenneth Rosen · 1999 · Discrete Mathematics · Reference
Intermediate Microeconomics
Hal R. Varian · 2014 · Microeconomics · Reference
Introduction to Cryptography with Coding Theory
W. Trappe & L. Washington · 2002 · Cryptography · Reference
Mathematical Reflections: In a Room with Many Mirrors
Peter Hilton, Derek Holton & Jean Pedersen · 1997 · Mathematics · Reference
Source ↗Mathematical Statistics with Applications, 6th Edition
Dennis Wackerly, William Mendenhall III & Richard Scheaffer · 2002 · Mathematical Statistics · Reference
Mathematical Vistas: From a Room with Many Windows
Peter Hilton, Derek Holton & Jean Pedersen · 2002 · Mathematics · Reference
Source ↗Mathematicians used Minecraft mobs to calculate Pi without writing a single line of code
Skye Jacobs · 2026 · Mathematics & Monte Carlo Methods · Article
Source ↗Precalculus, 4th Edition
Lial, Hornsby & Schneider · 2009 · Precalculus · Reference
Prospect Theory
Daniel Kahneman & Amos Tversky · 1979 · Behavioural Economics · Paper
Interactive Explorations
Exemplar Models & Projects
Interactive models and experiments exploring mathematical and economic ideas. Each project explains the underlying idea, how the model works, and provides ways to explore it through examples and interaction.
Mathematics
Visual and interactive explorations of mathematical patterns, structures, and curiosities.
Modular Arithmetic
Origin
This is a "modular addition table" which is based on the branch of mathematics called Number Theory, specifically Modular Arithmetic. It's based on the principle that if the sum of non-negative integers exceeds or falls exactly at the agreed number n, it will loop back. That is: for whole numbers x, y (0, 1, 2, 3, ...), if x + y ≥ n, where n is a positive integer and the agreed modulus, the possible values you can get for the sum x + y can correspond to set z: {0, 1, 2, 3, ..., n − 2, n − 1}. With that being said, since the sum will always result in a non-negative value, the sum can be represented as n × m + q, where m, q are whole numbers and q is an element in set z.
How it works
Choose your "n" value, ideally between 1–10 for simplicity, and say n = 5. A table will be generated with the headers of rows and columns being: 0, 1, 2, 3, 4. For example, according to modular arithmetic: 0 + 1 = 1, 3 + 2 = 0 (because 3 + 2 ≥ 5, so it can be represented as 5 × 1 + 0, thus we get zero). Similarly, 4 + 4 = 3 (4 + 4 ≥ 5 and 5 × 1 + 3); To simplify this, when n = 5, calculate the sum of two numbers in algebra, then repeatedly subtract n until the new value is less than n but still non-negative: 4 + 4 = 8, and 8 − 5 = 3, and 0 ≤ 3 < 5, so in modular arithmetic, 4 + 4 = 3.
Explore
Please feel free to explore this feature, and I highly suggest observing any noticeable and recurring trends or patterns. You can try the same steps but with multiplication on your own if you are really fascinated by this concept!
Economics
Interactive models and experiments exploring economic ideas, relationships, and systems.
Supply & Demand
Origin
Supply and demand is a fundamental economic model used to understand how prices and quantities are determined in a market. It describes the relationship between what consumers are willing to buy and what producers are willing to sell.
How it works
As price increases, quantity demanded generally decreases while quantity supplied increases. The point where the two curves meet is the market equilibrium.
Explore
Start the model and change the market price. Observe how quantity demanded and quantity supplied respond, and use the difference between them to identify a surplus or shortage.
Initiatives
Student Council Member & Valiant Vikings House Captain
As a member of the Learner Council, I worked on day-to-day student concerns and issues, upcoming school events, social-change initiatives, and student responsibilities across the school. I contributed to planning and supporting student-facing events, helped represent student perspectives, and worked alongside other council members to turn ideas into initiatives that could benefit the wider school community. As Valiant Vikings House Captain, I took responsibility for coordinating and motivating my house, with a focus on both performance and teamwork. I planned activities by understanding my teammates' strengths and placing them where they could contribute most effectively, while also making sure everyone was comfortable and happy with their choices. I regularly checked in with team members, followed their progress, and helped coordinate participation across activities. We ultimately won the House Trophy that year, completing a hat-trick of consecutive victories.
Selected Work
- JBCN Middle School MUN
- Inter-JBCN Football Tournament
- JBCN Women's Throwball Tournament
- JBCN InspirUs — Valiant Vikings Victory
- Composter Initiative — ongoing
- Tetra-pack Initiative — ongoing
- Orphanage Initiative — ongoing
- Behaviour Metric System — under development
- Felicitations for TDP and Sports Awards
Founding President — STEM Club
Co-founded and served as the founding president of JBCN's first STEM Club. The club focused on hands-on learning through practical experiments rather than purely theory-based activities, with the aim of fostering curiosity, critical thinking, and problem-solving. I helped organise guest lectures, university visits, and student-led workshops, giving members opportunities to learn from professionals as well as from one another.
Selected Work
- Marshmallow Vacuum Chamber Experiment
- Spaghetti Tower-Building Challenge
- Vedic Mathematics
- Design a Bridge
- Guest Lecture on Cloud Computing
- Student Lecture on Reverse Engineering
- Field Trip to Institute of Chemical Technology
- Fresnel Lens Experiment — Optics
- Paper Plane Aerodynamics Challenge
- DNA Extraction from Banana
- Make-a-thon Ideas
- Elephant Toothpaste Experiment
Bake Sale — Shraddha Foundation
Along with Arhaan Lightwalla, Shivaan Sharma, and Vir Gangoly, I organised a bake sale at school to raise funds for the Shraddha Foundation, a shelter for cancer patients and survivors in Chembur. The idea was to use a school event to create a direct contribution to a local cause. We proposed holding the bake sale during a Quarter 2 PRD, planning to sell simple, non-spillable, room-temperature items such as muffins, cupcakes, bagels, brownies, and cookies. The initiative eventually took place during a parent-teacher meeting on the school campus, allowing us to reach a much wider section of the school community. We baked and prepared items ourselves while also receiving contributions from other students, turning the sale into a broader student-led effort. All proceeds from the bake sale went to charity, supporting the Shraddha Foundation and helping contribute towards a Christmas celebration for the people it serves, including food and gifts.
Created Teen Health Decoded, a platform focused on making healthy eating and lifestyle information more accessible and relevant to teenagers. The idea grew from my interest in the relationship between food, health, behaviour, and the environments in which young people make everyday choices. This became particularly interesting as I explored the wider policy landscape around food in schools. FSSAI's school-food regulations restrict the sale of foods high in fat, salt, and sugar (HFSS) to school children in school canteens, messes, and hostel kitchens, as well as within 50 metres of school gates. The framework also encourages schools to promote safe and balanced diets and healthier food environments. Rather than viewing healthy eating simply as an individual responsibility, I became interested in how schools, food environments, policy, and education can collectively shape the choices available to teenagers. Teen Health Decoded is my way of contributing to that conversation by sharing practical, accessible ideas around food and healthier lifestyles through a platform created specifically with teenagers in mind.
Principles
“What matters most is the takeaway from each experience and how it shapes who you become.”
Pursuit of Knowledge
The principles that shape how I seek knowledge.
Continuous Growth
The beliefs that shape how I approach challenges through continual improvement.
Reflections
Observations, questions, and ideas that continue to shape my perspective.
Additional Thoughts
Curious ponderings born from childlike wonder.
Currently
📖 Reading
The Psychology of Money
by Morgan Housel
📄 Working On
Publishing my research paper on consumer behaviour and the diminishing marginal utility of consumption.
🏃 Training
Building endurance for a 5 km race.
Next milestone: 10 km.
🎓 Learning
Young Scholars Programme
🧩 Speedcubing
Practicing 3×3 solves, focusing on lookahead and consistency.
Best Single: 13.32s
Average: 14.91s
Recent focus: improving TPS and inspection efficiency
What's Next
Experience
Scroll Animations
Refine the way sections and elements appear as you move through the website.
Transitions
Add smoother transitions between states, sections, and interactions.
Micro-interactions
Introduce subtle interactions that make the website feel more responsive and alive.
Hover Effects
Add carefully designed hover states without making the interface feel excessive.
Mobile Experience
Refine interactions and layouts specifically for smaller screens.
Visual Design
Typography
Continue refining fonts, weights, hierarchy, spacing, and overall visual rhythm.
Visual Hierarchy
Make the relationship between headings, descriptions, and supporting details even clearer.
Spacing & Rhythm
Fine-tune spacing throughout the website so every section feels intentional.
Colour Palette
Refine the restrained colour system while keeping the aesthetic minimal.
Visual Details
Introduce subtle details that elevate the experience without adding clutter.
Interaction
Principle Cards
Improve the cards and modal interaction so they feel smoother and more natural.
Interactive Research
Turn selected research ideas into interactive models and experiments.
Mathematical Visualisations
Create visual ways to explore mathematical patterns and curiosities.
Content
Ideas in Progress
Document ideas that are still developing.
Research Library
Collect papers, books, lectures, documentaries, and resources and organize them like a library.
Research Restructure
Refine the research section into a more scalable library with clearer data organization, source types, reading status, search, filtering, and room for future expansion.
Personal Writing
Eventually make room for longer reflections and ideas. Complete Sections 03, 04 under Principles.
Navigation & Functionality
Better Navigation
Continue refining navigation, section tracking, and movement throughout the site.
Search
Eventually make research, notes, and projects searchable. Also a more structured way to explore literature using searchbar.
Filtering & Categories
Add filtering where it genuinely improves larger collections.
Expanded Connect
Develop the Connect section beyond LinkedIn and email.
Technical Foundation
Accessibility
Improve keyboard navigation, semantic structure, and contrast.
Performance
Optimise loading, rendering, and responsiveness.
Image Handling
Improve image optimisation and responsive behaviour.
Responsive Design
Continue refining the experience across devices.
SEO
Improve metadata, discoverability, and search-engine optimisation.
Code Quality
Keep components clean and maintainable.
Error Handling
Handle edge cases and unexpected states gracefully.
Experimental
Dark Mode?
Something to explore if it fits the visual identity.
Custom Cursor?
Only if it genuinely adds to the experience.
Sound?
An experimental possibility, with restraint first.
3D Elements?
Explore whether 3D can add value without distraction.
Experimental Navigation
Try unconventional ways of moving through the site.
A New Homepage
Because the website may eventually outgrow the homepage it started with.
Portfolio Version
Create an ultra-fast version of the website that summarises achievements, contributions, experiences, and academic work in a format designed for quick review.
The website is not finished. I don't think it should be.