eⁿ = ∑ xⁿ/n! ζ(s) = ∑ 1/nˢ ∫₋∞⁺∞ e⁻⁻x²dx = √π f(x) = ∑ aₙ xⁿ π²/6 = ∑ 1/n² ω(n) ~ log log n σ(n) = ∑𝔡|𝔯 d Pranav Krishnapuram

Pranav Krishnapuram

Rising 9th Grader · Mathematician · Researcher

I’m a rising high schooler in Silicon Valley, CA, passionate about proof-based mathematics, machine learning, and research. My journey spans advanced coursework through Euler Circle and Stanford ULO, research in number theory, competition math, and Synopsys/CSEF. Beyond academics, I find creative expression through origami tessellations, storytelling and poetry, and a deep interest in Japanese language and anime. I also have a philosopher’s curiosity about the ways of life and society — questions about how people think, what drives human behavior, and how the world is organized.

Feel free to browse around, and if anything catches your interest, I’d love to hear from you — reach out via the Contact tab!

Coursework

Advanced coursework spanning college-level mathematics and formal proof-based study.

Tessellations School / Stanford ULO
Stanford ULO
Discrete Mathematics
College-level course covering logic, combinatorics, graph theory, and proof techniques.
In Progress · 2026
Stanford ULO
Linear Algebra
Vector spaces, matrix transformations, eigenvalues, and inner product spaces.
Grade A · 2026
AP Exam
AP Calculus BC
Limits, derivatives, integrals, sequences and series, and parametric/polar calculus.
Score 5 · 2025
AP Exam
AP Statistics
Probability, inference, regression, and experimental design.
Score 5 · 2024
Euler Circle
Completed
Transition to Proofs
Foundations of mathematical proof-writing: logic, sets, induction, and formal argumentation.
Completed
Real Analysis
Rigorous treatment of limits, continuity, differentiation, and integration on the real line.
Completed
Differential Geometry
Curves, surfaces, curvature, and the intrinsic geometry of smooth manifolds.
Completed
Abstract Algebra
Groups, rings, fields, homomorphisms, and quotient structures.
Current · 2026
Algebraic Topology
Homotopy, fundamental groups, covering spaces, and simplicial homology.
In Progress

Activities & Clubs

Math, debate, and summer programs where I’ve grown alongside peers who share my passions.

School Club
Math Club — Tessellations School
Active member preparing for national math competitions. Coordinated middle school volunteer recruitment and operations for the Julia Robinson Math Festival, 2025.
School Club
Speech & Debate Club — Tessellations School
Parliamentary debate competitor. Reached Semi-Finalist at the National Parliamentary Debate League Parli Debate, 2025.
Summer Program · 2025
AwesomeMath Summer Camp
Intensive mathematics camp focused on olympiad problem-solving and advanced topics in number theory and combinatorics.
awesomemath.org ↗

Awards & Honors

Competition results, science fair honors, and recognition in mathematics and beyond.

01
1st Place — California Science & Engineering Fair, Junior Division, Mathematical Sciences · April 2026.
02
Castro Family Award — Synopsys Science Fair · March 2026. Nominated to CSEF and Thermo Fisher Scientific Junior Challenge.
03
AIME 2026 — Scored 8 out of 15 on the American Invitational Mathematics Examination.
04
MATHCOUNTS State Contestant — Northern California region, 2024 & 2026.
05
Perfect Score on AMC 8, 2026 · Scored 25 out of 25 on the American Mathematics Competition 8.
06
Distinguished Honor Roll in Algebra & Calculus — Berkeley Math Tournament (BMT) 2025.
07
Lenchner Award — Mathematical Olympiads for Elementary and Middle Schools (MOEMS), 2025.
08
Semi-Finalist — National Parliamentary Debate League Parli Debate · 2025.
09
Global Competition Round Qualifier — VEX AI Competition · 2025.

Research & Projects

Original mathematical research, independent papers, and ongoing investigations.

Independent Research · May 2026 · Ongoing
On Cantor Set Unions
Ongoing
Independent Research · 2025–Present
Redundancy Degree & Reconstructibility in k-Exact-Perfect Numbers
Original research in number theory exploring properties of k-exact-perfect numbers.
View slides ↗
Independent Research & Paper Writing · Euler Circle 2025
On the Central Limit Theorem and Its Extensions
Research paper examining the Central Limit Theorem and generalizations beyond classical settings.
Read paper ↗
Independent Research & Paper Writing · Euler Circle 2025
An Exposition on Minimal Surfaces
Explores minimal surfaces in differential geometry — catenoids, helicoids, and Scherk’s surface — proving mean curvature H = 0 for each.
Read paper ↗
Independent Research & Paper Writing · Euler Circle 2024
Volume of a Regular d-Dimensional Tetrahedron (d-Simplex)
Derives a closed-form formula for the volume of a regular d-simplex using determinants and induction.
Read paper ↗
AI Club · Jan 2024
Human Detection for Safety Applications Using Deep Learning
Investigated the use of YOLOv8 transfer learning to detect humans in CCTV footage for workplace safety. Achieved 88.5% mAP50 accuracy and deployed a virtual barricade alert system. Co-authored with Atul Dubey at AIClub, Mountain View.
Read paper ↗

Hobbies & Skills

Outside of mathematics, I find creativity and balance in an eclectic set of pursuits.

🦚
Origami
Intermediate–advanced; specializing in original tessellation pattern design.
✍️
Creative Writing
Click to read poems & essays.
🐍
Programming
Python, AI/ML workflows, and computational explorations.
🗣️
Languages
Learning Chinese (beginner) and Japanese (beginner–intermediate).
🤖
Robotics
VEX AI Competition — qualified for the Global Competition Round, 2025.
🎤
Debate
Parliamentary debate with NPDL; reached Semi-Finalist at nationals.

Get in Touch

Have a question or want to connect? Send me a message below.

Origami Portfolio

I create origami tessellations that explore the unique curvatures folding can produce. I’m fascinated by how the geometry of folds can leave a piece perfectly flat, or produce sharp dramatic curvature like the Chrysanthemum, or gentle organic curvature like the Ornate-Tess. I also enjoy pushing into miniature work — fine, intricate folds that challenge my dexterity and precision.

Click any design to cycle through front, back, and backlit views.

Creative Writing

I write about the things that don’t fit neatly into equations. The quiet absurdity of daily life in Silicon Valley, where ambition and stress fight to be in the driver’s seat. The life lessons buried in anime that we should talk about more often. The moments that make you laugh or giggle. And sometimes, something that surprises, or shocks, or brings a wry smile to your face.

I write about
  • Philosophy on daily life
  • Things that bring a smile or laughter
  • Mental health in Silicon Valley
  • Anime life lessons
  • Contrarian & controversial takes

The Zipline and the Race

Essay · Feb 2026

A Tale of Two Cities

Rope course at Norristown

In my elementary school, my class took a field trip to Elmwood Zoo in Norristown, PA to zipline. For many of us, it was the first time standing at that kind of height, gripping a wire that swayed just enough to remind you how far the ground was.

One classmate shuddered. The heights, the shakiness, the sheer exposure of it — she couldn’t move. She stood at the edge in tears, and our teacher did neither the easy nor the hard thing: she did nothing. No comfort, no push. Just silence.

So, we did it instead.

One by one, those of us who had already gone came back. We stood beside her. We told her what it felt like. We offered to go with her. We didn’t minimize her fear — we just refused to let her face it alone. After many of us had spoken, she stepped up. Shaking, yes. But willing.

When she landed, we all broke into applause — not politely, but genuinely, as if every one of us had crossed something that day. Because in a way, we had.

Later, our teacher gathered us and held up her hand. She pointed to each finger — different lengths, different strengths, different roles — and showed how they only make a fist when they come together. She told us that what happened on that zipline was leadership. Not the kind that charges ahead and expects others to keep up. The kind that stops, turns around, and says “I’ve got you.”

That lesson never left me. Leadership is not about always being first. It is about reading the moment, rising to the occasion, sometimes even sacrificing what matters to you so someone else can find their footing. That day, many of us gave up a second run on the course so we could stand with her instead. None of us regretted it.


I think about that zipline often now, living in Silicon Valley, the most ambitious zip code in the world, where breakthroughs happen in garages and the gold rush never ended.

A friend told me recently that in her school, she has no friends — only competitors. She said it plainly, almost matter-of-factly, as if it were simply the weather. It shook me. Not because ambition is wrong, but because somewhere along the way, a classmate had frozen into a benchmark.

I dread the thought of spending seven hours a day surrounded by that feeling. Of walking into a room and calculating rather than connecting. What produces such a thought in a teenager? Is it the parents? The college admissions machine? The culture that worships the outlier and quietly discards the rest? Perhaps all of it.

And sometimes I wonder what it means that we can all see the loneliness and quiet selfishness this system produces, yet continue feeding it as if competition were a law of nature rather than something we chose to build.

“1 mile”

Poetry · November 2025
I had a dog once Named him “1 mile” so I could say I walked “1 mile” every day I played with that dog once Threw a frisbee through the air Wind ruffling “1 mile”’s hair I fed that dog once Straight from my fingers Couldn’t satiate “1 mile”’s hunger I came home early for that dog once Out of fear of empty rooms Teaching “1 mile” how to be lonely That dog sat on my lap once Staring up at me with wide eyes Far larger than just a mile But something befell that dog once He stopped eating Stopped playing outside I loved that dog once Took him to the vet To find a panacea among those cramped shelves That dog was scared once “1 mile” stood quivering Ribs jutting beneath furless skin I didn’t know what to do with that dog once I couldn’t find an escape Had to put him out of his misery I ate that dog once Had no choice but this So we could stay together forever I can’t walk that dog anymore I’m sorry I couldn’t save you, 1 mile I’m still sorry

“Soytire”

4-Koma Manga · October 2025

A slice-of-life manga about tariffs, trade wars, and a father-son visit to their favorite café — one month apart. When China stops buying American soy, the “Tsoynami” hits home in ways nobody expected. I hope the soytire makes you laugh and ponder.

Soytire manga
More pieces coming soon…
✏️ Edit mode on — click any text to edit. Save the file when done.