From the wonderful book by Ian Stewart, here are the equations themselves; read the book to know more about them.
1. Pythagoras Theorem
$$ a^2 + b^2 = c^2 $$Pythagoras, 530 BC (Wikipedia)
2. Logarithms
$$ \log xy = \log x + \log y $$John Napier, 1610 (Wikipedia)
3. Calculus
$$ \frac{df}{dt} = \lim\limits_{h \to 0} \frac{f(t+h) - f(t)}{h} $$Newton, 1668 (Wikipedia)
4. Law of Gravity
$$ F = G \frac{m_1 m_2}{d^2} $$Newton, 1687 (Wikipedia)
5. The Square Root of Minus One
$$ i^2 = -1 $$Euler, 1750 (Wikipedia)
6. Euler’s Formula for Polyhedra
$$ F - E + V = 2 $$Euler, 1751 (Wikipedia)
7. Normal Distribution
$$ \Phi(x) = \frac{1}{\sigma\sqrt{2 \pi}}e^{- \frac{(x - \mu)^2}{2 \sigma^2}} $$C.F. Gauss, 1810 (Wikipedia)
8. Wave Equation
$$ \frac{\partial ^2 u}{\partial t^2} = c^2 \frac{\partial ^2 u}{\partial x^2} $$J. d’Alembert, 1746 (Wikipedia)
9. Fourier Transform
$$ f(\omega) = \int_{-\infty}^\infty f(x)\,e^{-2 \pi i x \omega} \,dx $$J. Fourier, 1822 (Wikipedia)
10. Navier-Stokes Equation
$$ \rho(\frac{\partial v}{\partial t} + v \cdot \nabla{v}) = - \nabla \rho + \nabla \cdot T + f $$C. Navier, G. Stokes, 1845 (Wikipedia)
11. Maxwell’s Equations
$$ \nabla \cdot E = 0 $$ $$ \nabla \times E = - \frac{1}{c} \frac{\partial H}{\partial t} $$ $$ \nabla \cdot H = 0 $$ $$ \nabla \times H = \frac{1}{c} \frac{\partial E}{\partial t} $$J. C. Maxwell, 1865 (Wikipedia)
12. Second Law of Thermodynamics
$$ dS \geq 0 $$J. Boltzmann, 1874 (Wikipedia)
13. Relativity
$$ E = mc^2 $$Einstein, 1905 (Wikipedia)
14. Schrödinger’s Equation
$$ ih \frac{\partial}{\partial t}\psi = H \psi $$E. Schrödinger, 1927 (Wikipedia)
15. Information Theory
$$ H = - \sum p(x) \log p(x) $$C. Shannon, 1949 (Wikipedia)
16. Chaos Theory
$$ x_{t + 1} = k x_t (1 - x_t) $$Robert May, 1975 (Wikipedia)
17. Black-Scholes Equation
$$ \frac{1}{2} \sigma^2 S^2 \frac{\partial^2 V}{\partial S^2} + r S \frac{\partial V}{\partial S} + \frac{\partial V}{\partial t} - rV = 0 $$F. Black, M. Scholes, 1990 (Wikipedia)
PS: reference for $\LaTeX$ symbols and syntax, used to write the symbols in the Markdown source file of this entry.