Written January 2026, Age 34
Arghya Sur
When I was 11, sitting at my desk in Delhi, staring at the decimal expansion of 1/7 = 0.142857142857..., I didn't know I was walking in Pierre de Fermat's footsteps from 1640.
I saw a pattern: the period was 6. When I tried 1/13, the period was also 6. But 1/11 had period 2. There was something here—some relationship between the denominator and the period length. I needed to capture this.
I called it "ORV" (Original Repeating Value) because I needed a name for what I was discovering. I created the R-series to track remainders, the M-series to track quotients, the π-function to measure the period. I was able to create a rigorous proof for Fermat's little theorem around class 8 using my own building blocks.
Only years later, in 2008, while preparing for the Regional Mathematical Olympiad (RMO), did I open a number theory book and learn that mathematicians call the ORV the "multiplicative order" and that my "Coprime Tendency (C_a)" was actually Euler's Totient Function φ(n), discovered in 1763.
Reading "Fermat's Little Theorem" in that book and realizing "Wait... I proved this two years ago, I called it 'Theorem on R-series'" was surreal.
For 18 years, this work sat in a handwritten diary, known only to my close circle. I never thought it had value—after all, everything I "discovered" had been discovered centuries ago.
But in January 2026, I decided to digitize and analyze this diary. One reason was - only latest model like Gemini 3.0 Pro was able to accurately read my handwritten diary and I could get deep analysis done by AI like Claude 4.5 Sonnet (my favorite model). But it is also because I finally realized: the value isn't in the destination, it's in the journey.
I'm sharing this because:
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It shows that deep mathematics is accessible: You don't need to be a "genius." You need curiosity, structure, and persistence.
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Independent discovery leads to genuine understanding: When you create your own framework, you understand it at a deeper level than when you memorize someone else's.
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The methodology matters: Observation → Pattern → Conjecture → Proof. This is how mathematical thinking works, whether you're 13 or 130.
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For math educators: Maybe there's pedagogical value in letting students "rediscovery" theorems before teaching them the classical versions.
At age 11-16, I didn't have textbooks that explained these concepts. So I had to create my own language:
- ORV wasn't just a name—it was a lens to view decimal patterns
- R-series wasn't just notation—it revealed the cyclic structure
- M-series wasn't random—it showed quotient distribution patterns
The act of creating the framework was the act of understanding.
Don't worry that it's already been discovered.
The value isn't in being first. The value is in the journey you're taking. Every hour you spend exploring these patterns, creating this notation, proving these theorems—that's building your mathematical intuition and problem-solving abilities in ways that no textbook could.
Keep going.
I didn't do this in a vacuum. Three factors were crucial:
- Science background
- Home education and guidance
- Ran math and science tutoring from home
- Provided weekly educational magazines
- Access to advanced educational materials
- Created environment where intellectual curiosity was encouraged
A formative moment: Age 11 (Class 6), I was watching older students in the home tutoring struggling with geometry. I shouted out the solution. I was scolded—not for being wrong, but for making the older students feel awkward.
That taught me two things:
- Mathematical ability doesn't correlate with age
- But social awareness matters too
This Bengali weekly magazine was everything. Every week, new issues with science and culture content.
The writer who changed my life: A science communicator Pathik Guha who wrote articles about:
- Mysteries in prime numbers
- Relativity and modern physics
- Space and particle physics
- The unsolved problems in mathematics
An article on prime numbers—the mystery of their distribution, the patterns, the conjectures—that was the spark. I read that article at age 11 and thought: "I want to understand this. I want to find patterns in numbers."
There was also a puzzle section with brain teasers, physics puzzles, and math challenges that trained problem-solving skills.
Without that popular science article, this diary wouldn't exist.
This sounds strange, but not having Google was an advantage.
Today, if a 13-year-old notices decimal period patterns, they'll Google "decimal period prime" and immediately find "multiplicative order" on Wikipedia. Discovery short-circuited.
In 2002, I couldn't Google it. The local library didn't have advanced number theory books. So I had to figure it out myself.
Constraint breeds creativity. The lack of immediate answers forced me to develop my own frameworks.
(Ironic note: By 2008 when I did get internet access, I was... mostly using it for other teenage things. And also preparing for RMO, which is when I finally learned the classical names.)
In November 2008, I took the Regional Mathematical Olympiad (RMO). I answered 4 out of 6 questions correctly and qualified.
This was the first time I realized: my independent research had given me a competitive advantage.
While other students had memorized theorems from textbooks, I had spent years exploring the patterns, creating proofs, understanding the why not just the what.
Number theory questions? I'd already explored those patterns for 3-4 years.
In January 2009, I took the Indian National Mathematical Olympiad (INMO)—one of the top ~30-35 students nationally. I didn't qualify for the IMO training camp, but reaching INMO validated something important:
This wasn't just "kid dabbling." This was competitive-level mathematics.
Before INMO, I attended a 4-day training course at the Indian Statistical Institute (ISI) in Kolkata. Walking into ISI, being surrounded by India's best math students, and holding my own—that's when I realized the years of independent work had value.
This experience taught me several meta-lessons about how humans learn:
You can memorize "Fermat's Little Theorem: a^(p-1) ≡ 1 (mod p)" in 30 seconds.
It took me weeks to discover it via decimal patterns.
But I understood it in a way that memorization never provides. I knew why it worked, when it applied, how it connected to other patterns.
When RMO asked proof questions, I didn't recall memorized steps. I reconstructed the proof from understanding.
The R-series notation wasn't just convenient shorthand. It shaped how I thought about modular arithmetic.
By tracking remainders as a sequence, I saw the cyclic structure. That led me to group theory concepts without knowing group theory existed.
Notation is discovery.
Not having textbooks forced me to invent my own approaches.
My proof of Fermat's Little Theorem via decimal periods? That's not how it's taught in textbooks. But it's pedagogically interesting because it starts from something concrete (decimals) rather than abstract (modular arithmetic).
I didn't randomly jump between topics. I had structure:
- Unit 1: Prime Numbers (5 chapters)
- Unit 2: Fibonacci Series (2 chapters)
Within each chapter, I had methodology:
- Observe a pattern
- Test with examples
- Form conjecture
- Attempt proof
- Refine and iterate
This systematic approach is what I use today in product development.
It wasn't all mathematical triumph. Let me be honest:
I was obsessed. From age 11-16, I spent hundreds of hours on this. Hours that other kids spent playing, socializing, doing "normal" teenage things.
I was already shy and introverted. This made it worse.
The diary entries are mixed with personal angst about school, friendships, and typical teenage struggles.
Math was partly exploration, partly escape.
Was it worth it? Yes. But I want to acknowledge: mathematical precocity often comes with social costs.
If I could go back, would I change anything? Maybe encourage my younger self to balance the math exploration with more social interaction. But probably not—I was who I was.
Most of what I discovered was already known. But a few things might have value:
The M-series (quotient sequence) analysis in Chapter 3—specifically the frequency distribution and equidistribution results—I haven't found exact classical counterparts.
This might be original, or it might be buried in obscure papers I haven't found. If any researchers know of prior work, please let me know.
My specific proof approaches, especially:
- Fermat's Little Theorem via decimal periods (pedagogically interesting)
- Wilson's Theorem via R-series (novel approach)
- Using remainder sequences to prove totient function properties
These aren't new results, but they might be new pedagogical approaches.
Whether ORV, R-series, M-series, π-function have value as teaching tools—that's for educators to decide.
If you're a math educator or researcher interested in:
- Mathematical exploration
- Case studies in independent discovery
- Alternative pedagogical approaches
This repository is offered as a data point. All materials are open. Feel free to cite, analyze, or use in educational contexts (with attribution under CC BY-NC-SA 4.0).
I'm happy to collaborate on any academic work that might emerge from this.
Why share this in January 2026, 18+ years later?
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I finally digitized it: The diary was handwritten. I used AI to transcribe it this month. Only latest model like Gemini 3.0 Pro was able to accurately read my handwritten diary.
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Perspective: At 34, I can see the value differently than at 16. Then, I was embarrassed it wasn't "new." Now, I see the pedagogical and personal value.
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Established: I'm established professionally as Senior Engineering Manager at leading Software company like Adobe. Sharing this doesn't feel like ego or desperation—it's genuine desire to contribute to mathematical education discussions.
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For educators: If even one math teacher reads this and thinks "maybe I should let students explore before teaching," it's worth it.
I'm not planning to become a mathematician. I love my work in software engineering and building stuff with AI.
But I might:
- Write articles explaining theorems in detail
- Give talks at math education conferences if there's interest
- Collaborate with researchers on case studies
- Help develop curricula that encourage "rediscovery learning"
If this resonates with you—whether you're an educator, a parent, a student who had similar experiences, or just someone curious about mathematical thinking—reach out. I'd love to hear your thoughts.
I spent ages 11-16 rediscovering mathematics that was 200-400 years old.
Some might say: "What a waste of time—it was already known!"
I say: It was the best education I could have received.
Because I didn't just learn what Fermat's theorem says. I learned how to discover it. I learned how to observe patterns, create frameworks, form conjectures, construct proofs, and systematically explore mathematical spaces.
The journey was the destination.
Arghya Sur
January 2026
Connect: LinkedIn | GitHub | arghyaknight@gmail.com