In Pursuit of the Unknown
| Company type | Nonfiction book |
|---|---|
| Industry | Publishing |
| Founded | 2012 |
| Founder | Ian Stewart |
| Products | Book |
| Parent | Basic Books |
In Pursuit of the Unknown: 17 Equations That Changed the World is a nonfiction publication from 2012 authored by British mathematician Ian Stewart and released by Basic Books. Stewart examines how mathematics has influenced human civilization, tracing developments from the Pythagorean theorem to the formula that transformed financial markets in the twenty-first century, the Black–Scholes model.
Content
This work presents seventeen fundamental equations:
| # | Equation name | Equation |
|---|---|---|
| 1 | Pythagorean theorem | <math>a^2 + b^2 = c^2</math> |
| 2 | Logarithms (product rule) | <math>\log{xy} = \log{x} + \log{y}</math> |
| 3 | Calculus (definition of derivative) | <math>\frac{\mathrm df}{\mathrm dt} = \lim_{h \to 0} \frac{f(t+h)-f(t)}h </math> |
| 4 | Newton's law of gravity | <math>F = G\frac{m_1 m_2}{d^2} </math> |
| 5 | Imaginary unit | <math>\mathrm{i}^2 = -1 </math> |
| 6 | Euler characteristic | <math>F-E+V= 2 </math> |
| 7 | Normal distribution | <math>
\mathbf{\Phi}(x) = \frac{1}{\sqrt{2\pi\sigma^2}} \mathrm{e}^{-\frac{(x-\mu)^2}{2\sigma^2}} </math> |
| 8 | Wave equation (one-dimensional form) | <math>
\frac{ \partial^2 u}{\partial t^2 } = c^2 \frac{ \partial^2 u}{\partial x^2 } </math> |
| 9 | Fourier transform | <math>
\hat{f}(\xi) = \int_{-\infty}^{\infty} f(x)\ e^{-2\pi \mathrm{i} x \xi}\mathrm{d}x </math> |
| 10 | Navier–Stokes equations (momentum conservation principle) | <math>
\rho \left(\frac{\partial \mathbf{v}}{\partial t} + \mathbf{v} \cdot \nabla \mathbf{v}\right) = - \nabla p + \nabla \cdot \mathbf{T} + \mathbf{f} </math> |
| 11 | Maxwell's equations (vacuum, Gaussian units) |
<math>\nabla \cdot \mathbf{E} = 0\,;</math> |
| 12 | Second law of thermodynamics | <math>\mathrm{d}S \geq 0 </math> |
| 13 | Special relativity (Mass–energy equivalence) | <math>E = mc^2 </math> |
| 14 | Schrödinger equation | <math>i \hbar \frac{\partial}{\partial t} \Psi = \hat{H}\Psi </math> |
| 15 | Information theory (Shannon entropy) | <math>H = - \sum_x p(x) \log p(x)</math> |
| 16 | Chaos theory (logistic map) | <math>x_{t+1} = k x_t (1-x_t) </math> |
The concluding equation, known as the Black–Scholes equation, forms the foundation of contemporary financial markets:
| Equation name | Equation |
|---|---|
| "Black–Scholes equation" |
<style type="text/css">.mw-parser-output math {font-size:90%;}</style> <math>\frac{1}{2}\sigma^2 S^2 \frac{\partial^2 V}{\partial S^2} + rS\frac{\partial V}{\partial S} + \frac{\partial V}{\partial t} - rV = 0</math> |
Reviews
Kirkus Reviews commended the book for delivering "concise and clear explanations of the equations' functioning without overwhelming readers with complex derivations."
Maclean's characterized it as a "chronicle of humanity expressed through equations," authored by the "most outstanding math popularizer alive today."
The New York Book Review praised Stewart as a "brilliant mind" who skillfully imparts enthusiasm and a "meaningful understanding" of making mathematical formulas engaging and science accessible.
According to Physics Today, Stewart's "accessible writing style" both informs and captivates readers.
Business Insider described the work as "exceptional and thoroughly researched."
In its review, the Association for Computing Machinery's SIGACT News acknowledged Stewart as a "gifted narrator," capable of captivating audiences even with Greek notation. The review underscored how Stewart illustrates that novel equations have spawned entirely new scientific disciplines, providing historical background and highlighting their enduring relevance in the 21st century.
The Notices of the American Mathematical Society portrayed Stewart as a "seasoned author" focusing on a general audience rather than specialists. The critique noted that Stewart largely succeeds in presenting key ideas in an accessible manner, though it suggested a more concise style might be preferable, while recognizing the approach fits the target readership.
Themes
Within 17 Equations, Stewart detailed how the Black-Scholes equation served as the "mathematical foundation for trading," playing a crucial role amid a complex blend of financial recklessness, political shortcomings, distorted incentives, and insufficient oversight that contributed to the 2008 financial crisis. He stressed that "the equation itself was not the fundamental issue," but rather its improper application within financial markets.