Amazon project

• 

  Axiom99

Inspiration

The inspiration for Axiom99 came from the desire to bridge abstract mathematical concepts with intuitive, interactive visual computing. Traditional mathematical tools often obscure the underlying logic behind dense code or rigid interfaces. We wanted to build a platform that allows researchers, students, and engineers to explore 99 foundational mathematical axioms in real time, making complex proofs and dynamic systems visually accessible and engaging.

What it does

Axiom99 is an interactive mathematical exploration platform and proof engine. Key capabilities include:

Real-time Axiom Simulation: Interactive visualization of mathematical theorems across linear algebra, calculus, and dynamical systems. Symbolic & Numerical Verification: Instant validation of user-defined proof steps alongside automated mathematical evaluation. LaTeX Math Rendering: Seamless rendering of inline equations like e^{i\pi} + 1 = 0 and complex standalone formulas: \int_{-\infty}^{\infty} e^{-x^2} \, dx = \sqrt{\pi} How we built it

We built Axiom99 using a modern, performant web stack:

Frontend: Next.js (React) and Tailwind CSS for a responsive, clean user interface. Mathematical Rendering: KaTeX for fast client-side LaTeX math layout. Interactive Canvas: HTML5 Canvas / Three.js for high-performance 2D and 3D geometric visualizations. Backend Engine: Python (FastAPI) utilizing SymPy and NumPy for symbolic computation and matrix operations. Challenges we ran into LateX Parsing & Rendering Performance: Rendering dynamic mathematical expressions on the fly without causing UI layout shifts or dropped frame rates during animations required fine-tuning event listeners and debouncing user input. Numerical Precision: Handling edge cases involving floating-point rounding errors during large matrix computations required enforcing strict precision thresholds in our backend verification pipeline. Accomplishments that we're proud of Built a lightweight, zero-latency proof renderer that processes mathematical inputs in real time. Successfully mapped complex multidimensional concepts into intuitive, interactive visual graphs. Developed a cohesive visual aesthetic that makes advanced math approachable and engaging. What we learned Strategies for optimizing heavy mathematical computations on both client and server sides. Effective state management patterns for syncing live mathematical inputs with web-based graphics engines. The importance of clean documentation and intuitive UX when designing developer tools for technical domains. Built with React Next.js Python FastAPI SymPy NumPy KaTeX Tailwind CSS Three.js Amazon Developer:- At Amazon, operating at hyper-scale means managing millions of distributed services, event streams, and database transactions simultaneously. Debugging complex state discrepancies across microservices often felt like hunting for needles in a haystack. Axiom99 was born out of a desire to enforce strict mathematical invariants (axioms) across live AWS infrastructure—ensuring zero data drift, absolute state consistency, and deterministic verification for critical services operating at 99.999% availability.

Built With

• css
• fastapi
• next.js
• numpy
• python
• react
• sagemaker
• sympy
• talwind