Theory · Proof · Interaction

Theory Comes First.

Tools change. Thinking endures.

Laboratory

Pull the sliders. Watch the math move.

Adjust the mean and standard deviation of a normal distribution in real time. Not an animation — a live calculation, redrawn with every frame. This is what it feels like to hold a theorem in your hands.

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Case Studies

Data has a story. We find the ending.

Real clinical data. A real regression model. A real p-value that decides whether your blood pressure prediction is statistically meaningful — or just noise. Follow along step by step.

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Real-time Predictor

Live Data

Predicted Pressure

134.2

Hypertensive Stage 1

BSA Index

1.82 m²

Duration

4.5 yrs

N=72,000 OBS

R² = 0.89

Atlas · Core Theorems

The formula. Then the proof.

Every entry in the Atlas starts with a definition. But a definition isn't enough — press Start and watch the Central Limit Theorem conjure the Normal Law from pure random noise. Theory and evidence, side by side.

Open the Atlas

Atlas Codex · DIST_001

Normal Law

f(x) =

\dfrac{1}{\sigma\sqrt{2\pi}}\, e^{-\frac{(x-\mu)^2}{2\sigma^2}}

↳ CLT Proof in Action

Workshop

The math is right. Prove it with code.

Translating intuition into a working hypothesis test is where most students get lost. The Workshop gives you a live Python environment to run the actual test — import scipy, compute the p-value, and see the statistics speak.

Enter the Workshop

Research_Log.ipynb

# Verify the Null Hypothesis

import numpy as np

from scipy import stats

# Draw from a population

sample = np.random.normal(mu=0, sigma=1, n=30)

def test_hypothesis(data):

t, p = stats.ttest_1samp(data, 0)

return f"p={p:.4f}"

Inspired by the work of

Fisher, Breiman, & Tukey.

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