This post first appeared on Function Space.
Carl Gauss a prodigy mathematician born to a poor, working class parents in Brauschweig, Germany surprised his elementary school teacher by adding all the integers from 1 to 100 simply by observing that the sum of 50 pairs of numbers is 101. The story goes that he had figured that 100 numbers could be determined by the equation n(a+b)(1/2)=50(a+b) where n=100, a = the first digit in the sequence and b = the last digit in the sequence.
His mathematical talent befuddled his teachers and mentors such that he grew up to become an influential mathematician of his century.
Gauss’s wide range of discoveries, from his fundamental theorem of algebra to his ground breaking work in number theory has shaped the field to the present day.
The true genius of his work, experts think is how he ultimately took these theories and applied them to in many fields, including number theory, statistics, analysis, differential geometry, electrostatics, astronomy and optics.
He once wrote, “All the measurements in the world are not worth one theorem by which the science of eternal truth is genuinely advanced.” It was at the same time he took up the job of geodesic survey mapping irregularly shaped curved surfaces across the country. Although, he failed to produce an accurate map of Hannover, he succeeded in creating a number of important advances in mathematics of curved surfaces, development of curvilinear coordinates and established ideas on non Euclidean geometry.
To which Einstein later wrote, “If Gauss had not created his geometry of surfaces, which served Riemann as a basis, it is scarcely conceivable that anyone else would have discovered it. The importance of Gauss for the development of modern physical theory and especially for the mathematical fundamentals of the theory of relativity is overwhelming indeed.”
Gauss’s list of discoveries extends to modular arithmetic, prime numbers, number theory, squares, quadratic reciprocity etc. But it was more astonishing that he worked on these discoveries independently without any collaborators or co workers!
This Thanksgiving lets be grateful to the man who overcame all the difficulties while pursuing mathematics and continued to discover more and more fundamentals that shaped the field to what it is today!
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