Carl Friedrich Gauss, referred as "The Prince of Mathematicians" was a German mathematician, who contributed to many fields including Number Theory, Algebra, Statistics, Differential Geometry and Elctrostatics.
At age of 7, he surprised his teacher by adding number 1 thru 100 almost instantly by quickly figuring 50 pairs of numbers by taking the first number 1 and last number 100, then second number 2 and second last 99 and so on, with each pair summing to 101 like: 1+100, 2 + 99, 3 + 98, 4 + 97, 5 + 96, 6 + 95, 7 + 94, 8 + 93, 9 + 92, 10 + 91, 11 + 90, 12 + 89, 13 + 88, 14 + 87, 15 + 86, 16 + 85, 17 + 84, 18 + 83, 19 + 82, 20 + 81, 21 + 80...31 + 70....41 + 60....49 + 52, 50 + 51.
So, the total summation = 50 x 101 = 5,050
This can be applied to any arithmetic series by the formula: N/2 (A1 + An), where N is the total number and A1 is the first number and An is the nth number.
At 15, Gauss was the first to find any kind of a pattern in the occurrence of prime numbers, a problem which had exercised the minds of the best mathematicians since ancient times. Although the occurrence of prime numbers appeared to be almost competely random, Gauss approached the problem from a different angle by graphing the incidence of primes as the numbers increased. He noticed a rough pattern or trend: as the numbers increased by 10, the probability of prime numbers occurring reduced by a factor of about 2 (e.g. there is a 1 in 4 chance of getting a prime in the number from 1 to 100, a 1 in 6 chance of a prime in the numbers from 1 to 1,000, a 1 in 8 chance from 1 to 10,000, 1 in 10 from 1 to 100,000, etc). However, he was quite aware that his method merely yielded an approximation and, as he could not definitively prove his findings, and kept them secret until much later in life.
Gauss gave the first clear exposition of complex numbers and of the investigation of functions of complex variables in the early 19th Century. Although imaginary numbers involving i (the imaginary unit, equal to the square root of -1) had been used since as early as the 16th Century to solve equations that could not be solved in any other way, and despite Euler’s ground-breaking work on imaginary and complex numbers in the 18th Century, there was still no clear picture of how imaginary numbers connected with real numbers until the early 19th Century. Gauss was not the first to intepret complex numbers graphically (Jean-Robert Argand produced his Argand diagrams in 1806, and the Dane Caspar Wessel had described similar ideas even before the turn of the century), but Gauss was certainly responsible for popularizing the practice and also formally introduced the standard notation a + bi for complex numbers. As a result, the theory of complex numbers received a notable expansion, and its full potential began to be unleashed.
At the age of just 22, he proved what is now known as the Fundamental Theorem of Algebra (although it was not really about algebra). The theorem states that every non-constant single-variable polynomial over the complex numbers has at least one root (although his initial proof was not rigorous, he improved on it later in life). What it also showed was that the field of complex numbers is algebraically "closed" (unlike real numbers, where the solution to a polynomial with real co-efficients can yield a solution in the complex number field).
On his death anniversary - February 23, 1855 , we would like to pay tribute to the great mathmatician.
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