MAJOR CONTRIBUTIONS OF GAUSS:
1.1. Number Theory
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Disquisitiones Arithmeticae (1801): His masterpiece, which laid the foundation for modern number theory.
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Introduced modular arithmetic and congruences (basis of modern cryptography).
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Proved the Law of Quadratic Reciprocity.
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Showed that a 17-sided polygon (heptadecagon) can be constructed with ruler and compass.
2. Gaussian Elimination
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A method for solving systems of linear equations — essential in linear algebra.
3. Gaussian Distribution
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Also called the normal distribution (bell curve) in statistics.
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He didn't invent it, but made major contributions and it's named after him.
4. The Fundamental Theorem of Algebra
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Gauss was the first to give a rigorous proof that every polynomial equation has at least one complex root.
5. Gauss’s Law (in Electrostatics)
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Part of Maxwell’s Equations.
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Describes the relationship between electric charge and electric field — foundational in physics.
6. Magnetism and Earth’s Magnetic Field
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Developed the first magnetometer.
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Measured Earth's magnetic field and contributed to geomagnetism.
7. Astronomy
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Calculated the orbit of the asteroid Ceres using least squares method.
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Helped develop techniques for predicting planetary motion.
At age 7 Gauss surprised his teacher by summing 1 to 100 instantly using the formula:
