What are Schrödinger Bridges?
An exploration of elegant typography and mathematics
Introduction
In this document, we'll demonstrate how to combine Tufte CSS with mathematical notation using LaTeX and MathJax.
Inline Mathematics
Euler's identity, $$e^{i\pi} + 1 = 0$$, is often considered the most beautiful equation in mathematics. This equation combines five fundamental mathematical constants: e, i, π, 1, and 0.
Display Mathematics
The Gaussian integral is a classic example of an improper integral:
$$\int_{-\infty}^{\infty} e^{-x^2} dx = \sqrt{\pi}$$This result is particularly useful in probability theory and statistics.
Mathematical Notation in Sidenotes
The Riemann zeta function is defined for complex s with real part greater than 1 by the absolutely convergent infinite series The Riemann zeta function: $$\zeta(s) = \sum_{n=1}^{\infty} \frac{1}{n^s}$$
Conclusion
Tufte CSS, combined with LaTeX rendering, provides an elegant solution for presenting mathematical content on the web, allowing us to create beautiful and readable documents that seamlessly integrate complex equations and elegant typography.