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Here are ten formulas that have had a profound impact on the world: 1. E = mc²: This is Einstein's famous equation, which shows that energy and mass are interchangeable. It underpins our understanding of nuclear energy and led to the development of nuclear weapons. 2. F = ma: This is Newton's second law of motion, which relates force, mass, and acceleration. It helped lay the foundation for modern physics and engineering. 3. PV = nRT: This is the ideal gas law, which describes the behavior of gases. It is used in a wide range of applications, from engineering to chemistry. 4. Pythagorean theorem: This is a fundamental theorem in geometry, which states that in a right-angled triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides. a² + b² = c² (where a, b, and c are the sides of a right-angled triangle) 5. Schrödinger equation: This is a fundamental equation in quantum mechanics, which describes how the wave function of a physical system changes over time. iℏ ∂ψ/∂t = Hψ (where ψ is the wave function, t is time, H is the Hamiltonian operator, and ℏ is the reduced Planck constant) 6. Maxwell's equations: These are a set of equations that describe the behavior of electromagnetic fields. They are used in many areas of physics, including optics and electrical engineering. ∇×E = -dB/dt, ∇×H = J + dD/dt (where E and H are the electric and magnetic fields, B and D are the magnetic and electric flux densities, J is the current density, and t is time) 7. Ohm's law: This law states that the current flowing through a conductor is proportional to the voltage applied across it, with the constant of proportionality being the resistance of the conductor. It is the foundation of electrical engineering. V = IR (where V is voltage, I is current, and R is resistance) 8. Black-Scholes formula: This is a formula used to calculate the theoretical price of options contracts, which has revolutionized financial markets. Black-Scholes formula: C(S,t) = SN(d₁) - Ke^(-rt)N(d₂), where C is the price of the option, S is the current stock price, t is time to expiration, K is the strike price, r is the risk-free interest rate, and N is the cumulative distribution function of the standard normal distribution. 9. Drake equation: This is an equation that estimates the number of intelligent civilizations in the universe. It has stimulated discussion and research on the possibility of extraterrestrial life. N = RfpneflfifcL (where N is the number of communicating civilizations in our galaxy, R* is the rate of formation of stars in the galaxy, fp is the fraction of stars with planets, ne is the number of habitable planets per star system, fl is the fraction of habitable planets that develop life, fi is the fraction of life-bearing planets that develop intelligent life, fc is the fraction of intelligent civilizations that develop technology capable of interstellar communication, and L is the length of time such civilizations release detectable signals into space) 10. Moore's law: This is not a specific formula, but rather an observation that the number of transistors on a microchip doubles approximately every two years. This has driven the rapid advancement of computer technology over the last several decades.

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