Polymath Multidisciplinary Aptitude Assessment

A rigorous psychometric and technical diagnostic testing engine designed to measure intellectual breadth, analytical depth, and polymathic cross-domain transfer across 20 academic degree fields (15 technical + 5 non-technical disciplines).

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Key Features

• 20 Academic Curricula Covered:
  • 15 Technical Fields: Medicine & Clinical Diagnostics, Pure & Applied Mathematics, Physics & Mechanics, Electrical Engineering, Computer Science & Systems, Mechanical Engineering, Chemical Engineering, Civil & Structural Engineering, Aerospace Engineering, Biomedical Engineering, Cognitive Neuroscience & Psychology, Data Science & Machine Learning, Materials Science & Metallurgy, Genetics & Molecular Biology, and Robotics & Control Systems.
  • 5 Non-Technical Fields: Epistemology & Formal Logic, World History & Historiography, Linguistics & Literary Theory, Music Theory & Psychoacoustics, and Economics & Game Theory.
• Strict Difficulty Calibration (80 Problems Total):
  • Exactly two Easy problems (foundational theorems and definitions), one Medium problem (applied quantitative calculation or multi-step analysis), and one Hard problem (advanced theoretical edge cases and multivariable synthesis) per degree field.
• Assessment Tracks:
  • Full Polymath Exam (80 Problems): The comprehensive evaluation testing all 20 degree disciplines.
  • Partial Polymath Choice Sprint (22 Problems): A focused diagnostic featuring 8 technical fields and 3 humanities fields, with exactly 1 Easy and 1 Medium problem per discipline. Includes an interactive picker to customize which disciplines to test.
  • STEM & Technical Suite (60 Problems): Concentrated assessment covering all 15 scientific and engineering degrees.
  • Humanities & Social Sciences Suite (20 Problems): Concentrated assessment covering philosophy, history, linguistics, music acoustics, and economics.
  • Single Field Sprint (4 Problems): 4-tier deep dive into any chosen discipline.
• Dual Feedback Modes:
  • Instant Check Mode (Study Mode): Displays step-by-step scientific derivations, reference equations, and core epistemic principles immediately after answering.
  • Exam Mode (Formal Test): Answers remain private until completion, producing a clean final diagnostic report.
• Advanced Diagnostics & Telemetry:
  • Interactive 20-Axis SVG Radar Chart: High-precision vector spider chart displaying the complete cognitive footprint across all disciplines with interactive vertex HUD probes.
  • Renaissance Quotient (0–100) & Archetype Classifier: Evaluates breadth of competence, technical-to-humanities balance, and depth of hard problem mastery (Homo Universalis, Renaissance Scholar, Broad Generalist, STEM Polymath, etc.).
  • Domain Mastery Cards: Granular cards with accuracy percentages, difficulty tier indicators, and direct question navigation.
  • Comprehensive Answer Audit: Filterable review of all problems with full scientific rationales and core principles.
  • One-Click Share Results: Generates formatted ASCII summaries and social cards of radar scores directly to the clipboard.
  • Local Persistence & Hotkeys: Seamless session saving in localStorage and keyboard shortcuts (A–D, 1–4, ←/→, M for question map).

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Architecture & System Design Blueprint (Implementation Artifact)

Below is the architectural specification and design blueprint used to construct the evaluation engine.

1. System Architecture & Component Topology

┌────────────────────────────────────────────────────────────────────────┐
│                          POLYMATHOUS CORE APP                          │
├────────────────────────────────────────────────────────────────────────┤
│                                                                        │
│  ┌─────────────────┐   ┌──────────────────────┐   ┌─────────────────┐  │
│  │ Assessment Config│──▶│ Question Bank Store  │◀──│ LocalStorage Sync│
│  │ (Exam vs Instant│   │ (80 Tiered Questions │   │ (Resume State)  │  │
│  │  Full vs Sprint)│   │  across 20 Domains)  │   └─────────────────┘  │
│  └─────────────────┘   └──────────┬───────────┘                        │
│                                   │                                    │
│                                   ▼                                    │
│                 ┌───────────────────────────────────┐                  │
│                 │      Test Engine & Question UI    │                  │
│                 │  - Question Stage & Formula Box   │                  │
│                 │  - 4 Tiered Choices & Hotkeys     │                  │
│                 │  - Persistent 80-Item Grid Drawer │                  │
│                 │  - Instant Solution Modal/Drawer  │                  │
│                 └─────────────────┬─────────────────┘                  │
│                                   │ (Submission)                       │
│                                   ▼                                    │
│                 ┌───────────────────────────────────┐                  │
│                 │    Polymath Diagnostic Engine     │                  │
│                 │  - Renaissance Quotient (0-100)   │                  │
│                 │  - Technical vs Non-Tech Ratio    │                  │
│                 │  - Depth vs Breadth Coefficient   │                  │
│                 └─────────────────┬─────────────────┘                  │
│                                   │                                    │
│        ┌──────────────────────────┴──────────────────────────┐         │
│        ▼                                                     ▼         │
│ ┌──────────────────────────────┐              ┌──────────────────────┐ │
│ │  Interactive 20-Axis Radar   │              │ Domain Mastery Cards │ │
│ │  - 20 Discipline Radii       │              │ - 20 Field Summaries │ │
│ │  - Technical vs Humanities   │              │ - Strength/Weakness  │ │
│ │  - Interactive Vertex Probes │              │ - Full Answer Audit  │ │
│ └──────────────────────────────┘              └──────────────────────┘ │
│                                                                        │
└────────────────────────────────────────────────────────────────────────┘

2. Renaissance Quotient & Archetype Mathematics

A genuine polymath is not merely someone who knows trivia in one field; they possess both multidisciplinary breadth and analytical depth. The Renaissance Quotient ($RQ \in [0, 100]$) is computed through four weighted dimensions:

$$RQ = 0.35 \cdot A_{\text{raw}} + 0.25 \cdot B_{\text{fields}} + 0.25 \cdot D_{\text{depth}} + 0.15 \cdot C_{\text{balance}}$$

• Raw Accuracy ($A_{\text{raw}}$): The proportion of correct answers across all questions ($35%$).
• Breadth of Competence ($B_{\text{fields}}$): The percentage of tested disciplines where the user achieves $\ge 50%$ mastery ($25%$).
• Depth of Analytical Rigor ($D_{\text{depth}}$): Performance specifically on Medium ($2\times$) and Hard ($3\times$) questions ($25%$).
• Cross-Disciplinary Harmony ($C_{\text{balance}}$): The symmetry ratio between STEM and Humanities performance ($\min(T, H) / \max(T, H)$), penalizing hyper-specialization in favor of trans-disciplinary breadth ($15%$).

Archetype Tier Classifications:

1. Tier I · Homo Universalis (Universal Polymath) ($RQ \ge 88$, $\ge 16$ competent fields): Rare cross-domain synthesis combining advanced STEM mastery with deep humanistic insight (comparable to Leonardo da Vinci, Gottfried Wilhelm Leibniz, and Henri Poincaré).
2. Tier II · Renaissance Scholar ($RQ \ge 72$, $\ge 12$ competent fields): High-caliber multidisciplinary versatility across divergent scientific and qualitative domains.
3. Tier III · Broad Generalist Synthesizer ($RQ \ge 56$, $\ge 8$ competent fields): Well-rounded foundational fluency and intellectual curiosity across varied degree disciplines.
4. Domain Specialist (Skewed STEM $>70%$ or Humanities $>70%$): Concentrated mastery in one hemisphere with growth opportunity in the other.

3. Core Data Schema

export type DomainType = 'technical' | 'non-technical';
export type Difficulty = 'easy' | 'medium' | 'hard';

export interface Question {
  id: string;
  fieldId: string;
  fieldName: string;
  domainType: DomainType;
  difficulty: Difficulty;
  points: number; // Easy: 1, Medium: 2, Hard: 3
  question: string;
  formulaOrSnippet?: string;
  options: string[];
  correctIndex: number;
  explanation: string;
  corePrinciple: string;
  subtopic: string;
}

export interface DisciplineMeta {
  id: string;
  name: string;
  shortName: string;
  type: DomainType;
  category: string;
  description: string;
  iconName: string;
  color: string;
}

export interface UserAnswerRecord {
  questionId: string;
  selectedOption: number | null;
  isFlagged: boolean;
  timeSpentSec: number;
  submittedAt?: number;
}

4. Key Engineering Decisions & Rationale

• Deterministic Curated Bank vs. Real-Time LLM Invocations:
  • Decision: Embed the complete 80-problem bank directly in modular TypeScript files with verified solutions and scientific citations.
  • Rationale: Eliminates API latency during timed exams, guarantees zero hallucinated scientific keys or incorrect physics formulas, and ensures reproducible psychometric scoring.
• Zero-Dependency Vector SVG Radar Engine:
  • Decision: Implemented custom trigonometric SVG calculations with 20 radial axes, concentric score polygons, and hover probes.
  • Rationale: Zero heavy external chart library bundle overhead, zero React 19 compatibility conflicts, and complete styling harmony with Tailwind CSS tokens.
• Relative Asset Paths (base: './'):
  • Decision: Configured Vite with relative base resolution.
  • Rationale: Enables seamless one-click hosting on GitHub Pages (which commonly mounts applications under a subpath like /repo-name/) without broken asset URLs.

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Academic Curricula & Problem Distribution

#	Degree Discipline	Category	Easy (1 pt)	Medium (2 pts)	Hard (3 pts)
1	Medicine & Clinical Science	Biomedical	Anatomy & Circulation · Islet Endocrinology	Hemodynamics & Cardiac Output	ABG Acid-Base & Winter's Formula
2	Pure & Applied Mathematics	Formal Science	Product Rule Calculus · 2x2 Matrix Determinants	Triangular Spectral Eigenvalues	Green's Theorem & Conservative Fields
3	Physics & Quantum Mechanics	Physical Science	Kinetic Energy · Faraday's Induction Law	Carnot Engine Efficiency	1D Infinite Well Nodal Wavefunctions
4	Electrical Engineering	Applied Engineering	Parallel Resistance · NAND Gate Logic	Series RLC Angular Resonance	Laplace Pole Stability & Damping
5	Computer Science & Systems	Computational	Balanced BST Complexity · Program Counter Cycle	0/1 Knapsack Dynamic Programming	PACELC Distributed Systems Theorem
6	Mechanical Engineering	Applied Engineering	Hooke's Law Elasticity · Reynolds Number	Rankine Steam Cycle Efficiency	Blasius Boundary Layer Scaling
7	Chemical Engineering	Chemical Science	Le Chatelier Equilibrium · Arrhenius Kinetics	CSTR Design & Conversion Sizing	Positive Azeotrope Non-Ideal Vapor
8	Civil & Structural Engineering	Applied Engineering	Center-Point Beam Moment · Terzaghi Effective Stress	Euler Column Buckling Constraints	Tuned Mass Damper Frequency Splitting
9	Aerospace Engineering	Applied Engineering	Lift Vector Direction · Rocket Specific Impulse	Hohmann Transfer Semi-Major Axis	Normal Shock Wave Rankine-Hugoniot
10	Biomedical Engineering	Biomedical	Titanium Passivation · Pulse Oximetry Wavelengths	Standard Linear Solid Viscoelasticity	Counter-Current Dialyzer Clearance
11	Cognitive Neuroscience	Cognitive Science	Action Potential Depolarization · Patient H.M. Memory	NMDA Receptor Magnesium Block	Signal Detection Theory (d' & c)
12	Data Science & ML	Computational	Overfitting & Variance · Bayes' Theorem	L1 Norm Sparsity Geometry	Covariance SVD & PCA Duality
13	Materials Science	Physical Science	Bragg's Law Diffraction · FCC Packing Factor	Eutectic Invariant Reaction	Griffith Brittle Crack Mechanics
14	Genetics & Molecular Biology	Biological Science	Central Dogma Flow · PCR Thermal Cycles	Hardy-Weinberg Carrier Frequency	CRISPR SpCas9 PAM Sequence Motif
15	Robotics & Control Systems	Applied Engineering	PID Integral DC Offset · FK vs IK Mapping	Jacobian Kinematic Singularities	Kalman Filter Gain MMSE Optimality
16	Epistemology & Formal Logic	Humanities	Denying the Antecedent Fallacy · Tripartite JTB	Kantian Categorical Imperative	Modal System S5 Equivalence Frames
17	World History & Historiography	Humanities	Peace of Westphalia · Spinning Jenny	Late Bronze Age Systems Collapse	Braudel's Annales "Longue Durée"
18	Linguistics & Literary Theory	Humanities	Iambic Pentameter · Saussurean Semiotics	Grimm's Law PIE Consonant Shift	Wh-Island Subjacency Constraint
19	Music Theory & Psychoacoustics	Arts & Acoustics	Harmonic Series Overtones · Mixolydian Mode	Tritone Guide-Tone Substitution	Syntonic Comma & Meantone Tuning
20	Economics & Game Theory	Social Science	Inelastic Demand Pricing · Prisoner's Dilemma	IS-LM Monetary Expansion	Akerlof Lemon Market Unraveling

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Getting Started

Prerequisites

• Node.js (version 18 or later recommended)
• npm (or pnpm / yarn)

Installation & Local Development

1. Clone the repository:

   git clone https://github.com/Nate-Mina/Polymath.git
   cd Polymath

2. Install dependencies:

   npm install

3. Start the development server:

   npm run dev

   Open http://localhost:3000 (or the port specified in terminal) in your browser.

4. Build for production:

   npm run build

   The production-ready bundle will be compiled into the dist/ directory.

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Deploying to GitHub Pages

This project is pre-configured with relative asset paths (base: './' in vite.config.ts), ensuring it deploys seamlessly to GitHub Pages without asset path errors.

Method 1: Automatic Deployment with GitHub Actions (Recommended)

1. Push your repository to GitHub.
2. In your GitHub repository, navigate to Settings > Pages.
3. Under Build and deployment > Source, select GitHub Actions.
4. The included workflow in .github/workflows/deploy.yml automatically installs dependencies using npm ci (leveraging the root package-lock.json and Node cache) and builds the site with npm run build on every push to the main branch.
5. GitHub Pages will serve the static bundle directly from the uploaded artifact with zero server overhead.

Method 2: Manual Deployment via gh-pages

1. Install the gh-pages package:

   npm install -D gh-pages

2. Add deployment scripts to your package.json:

   "scripts": {
     "predeploy": "npm run build",
     "deploy": "gh-pages -d dist"
   }

3. Run the deployment command:

   npm run deploy

4. Go to Settings > Pages in your repository and set the branch to gh-pages / root.

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Technology Stack

• Framework: React 19
• Build Tool: Vite 8 (with relative base support)
• Language: TypeScript 5
• Styling: Tailwind CSS 4
• Icons: Lucide React
• Charts: Custom Zero-Dependency Mathematical Vector SVG Radar Engine
• State & Storage: React Hooks with automatic localStorage synchronization

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License

This project is licensed under the Apache License 2.0. See LICENSE for details.