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17 Equations That Changed the World by Ian Stewart 1. Pythagoras’s Theorem a² + b² = c² Pythagoras, 530 BC 2. Logarithms log(xy) = log(x) + log(y) John Napier, 1610 3. Calculus df/dt = lim₍h→0₎ (f(t + h) - f(t)) / h Newton, 1668 4. Law of Gravity F = G·(m₁m₂) / r² Newton, 1687 5. The Square Root of Minus One i² = -1 Euler, 1750 6. Euler’s Formula for Polyhedra V - E + F = 2 Euler, 1751 7. Normal Distribution Φ(x) = (1 / √(2π)) · e^(-x²/2) C.F. Gauss, 1810 8. Wave Equation ∂²u/∂t² = c² ∂²u/∂x² J. d’Alembert, 1746 9. Fourier Transform f(ω) = ∫₋∞⁺∞ f(x) e^(-2πiωx) dx J. Fourier, 1822 10. Navier–Stokes Equation ρ(∂v/∂t + v·∇v) = -∇p + ∇·T + f C. Navier, G. Stokes, 1845 11. Maxwell’s Equations ∇·E = 0 ∇×E = (1/c) ∂H/∂t ∇·H = 0 ∇×H = (1/c) ∂E/∂t J.C. Maxwell, 1865 12. Second Law of Thermodynamics dS ≥ 0 L. Boltzmann, 1874 13. Relativity E = mc² Einstein, 1905 14. Schrödinger’s Equation iħ ∂ψ/∂t = Hψ E. Schrödinger, 1927 15. Information Theory H = -Σ p(x) log p(x) C. Shannon, 1949 16. Chaos Theory x₍t+1₎ = kxₜ(1 - xₜ) Robert May, 1975 17. Black–Scholes Equation (½)σ²S² ∂²V/∂S² + rS ∂V/∂S + ∂V/∂t - rV = 0 F. Black, M. Scholes, 1990

@uotiop69 @Math_files (a^2+b^2)/(ab + 1) can be square of any random integer and not necessarily of a

@uotiop69 @Math_files Ok..but how is (a^2+b^2)/(ab + 1) = a^2?

This problem is widely remembered as one of the most difficult mathematics problems of its time, originating from the International Mathematical Olympiad. In 1988, when the IMO was held in Australia, the final question—Problem 6—became legendary for its extreme difficulty. Only 11 students managed to achieve a perfect score on it. Even Terence Tao, a 13-year-old prodigy representing Australia at the time and later a Fields Medalist—the highest honor in mathematics—scored just one point on this problem. What makes the story even more remarkable is that when the problem was reviewed by the panel of experts before the exam, even they were unable to solve it. Despite this, it was still included in the competition.

@uotiop69 @Math_files Basis for b= n^3 ?

@ParryRamMe @Math_files Let a=n b = n^3 then (n^2 + n^6) / (n^4 + 1) now factor it, (n^2 * ( n^4+1)) / (n^4 +1 ) cancel out (n^4+1) Then n^2 remains, So, for any a=n, and b=n^3, result is proven to be n^2 remains.

@uotiop69 @Math_files That is obvious. Prove it in terms of a and b

@Math_files a=2, b=8 a=3, b=27 a=4, b=64 a=5, b=125 a=6, b=216 a=7, b=343 a=8, b=2 a=8, b=30 a=8, b=512 a=9, b=729 a=27, b=3 a=27, b=240 a=30, b=8 a=30, b=112 a=64, b=4 a=112, b=30 a=112, b=418 a=125, b=5 a=216, b=6 a=240, b=27 Many solutions, Lol,

@Matt_Pinner Given the proposition in the tweet...It Follows (2014)

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If you solve this, your IQ is high 🔥 What should come instead of ?

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