17 Equations That Changed The World

Ian Stewart’s book, “17 Equations that Changed the World,” describes how these equations came to be used in machine learning :-

1. Pythagorean’s Theorem: Although this theorem is best recognized for its geometric uses, it is important in machine learning, particularly in relation to distance-based techniques like k-nearest neighbors.
2. Logarithms: These are used in ML approaches like feature engineering and normalization to scale and alter data.
3. Derivatives: Derivatives are a key component of optimization algorithms and are used to train machine learning models, which enables them to recognize patterns and get better over time.
4. The Law of Gravity: Despite their apparent disconnection, gravitational physics has inspired some optimization methods, such as gravitational search optimization.
5. Imaginary Numbers: Applied in ML for data analysis and signal processing, they are used in complex algebra.
6. Euler’s Formula, a unique equation that ties together calculus, trigonometric functions, and complex exponentials, provides insight into the mathematics behind brain networks.
7. Normal Distribution: A fundamental idea in machine learning (ML), it forms the basis of statistics and probability.
8. The wave equation is helpful in understanding data as waves and is used in signal processing and image analysis.
9. Fourier Transformation: A key step in the core machine learning (ML) technique of feature extraction in image and signal processing.
10. The Navier-Stokes equation is important for fluid dynamics simulations and can be employed in computational fluid dynamics for AI-based aerodynamics.
11. Maxwell’s Equations: Essential to electromagnetic theory and the foundation of innovations like machine learning (ML) image processing.
12. The second law of thermodynamics is related to the improvement of machine learning models and procedures, albeit being more oblique.
13. Relativity: Algorithmic strategies like GPS, necessary for location-based ML applications, are inspired by Einstein’s theories.
14. Schrodinger’s Equation: A key concept in quantum mechanics, a paradigm shift for machine learning.
15. Information Theory: Entropy and information gain, which are essential to decision tree algorithms, are based on Shannon’s work.
16. Chaos Theory: The randomness and unpredictability of chaotic systems has applications to machine learning.
17. Black Scholes Equation: Mainly employed in finance, but also useful in risk modeling, a crucial component of machine learning in trading.