Gauss is the subject of Google's latest Doodle, celebrating influential figures and movements from science and the arts.
He is known for his groundbreaking contributions to a huge variety of fields, from number theory, geometry and probability to planetary astronomy and electromagnetism.
A child prodigy, Gauss was raised in the Duchy of Brunswick-Wolfenbuttel (now Lower Saxony) to a working-class family and quickly distinguished himself by correcting his father's calculations of the household bills.
At just eight, he could add up all numbers from one to 100, noticing that by adding numbers from the opposite ends of the sequence he could always achieve a total of 101 (1 + 100 = 101, 2 + 99 = 101, 3 + 98 = 101 etc.), a virtuoso display that stunned his schoolteachers.
His talent was such that he was commended to the Duke of Brunswick in 1791, who became Carl Friedrich's patron and would pay for him to continue his education and study mathematics at the University of Gottingen between 1795 and 1798.
Gauss impressed with his discovery in 1792 that a regular 17-sided polygon could be drawn with a ruler and compass, a finding made by analysing the factorisation of polynominal equations. He would later request that a stonemason engrave a heptadecagon on his tombstone.
The young man completed a doctoral thesis in 1797 breaking down the fundamental theorem of algebra, boldly critiquing long-accepted principles, before publishing his influential Disquitiones Arithmeticae in 1801, which would set the pace for the study of number theory throughout the 19th century.
Gauss's next feat was the rediscovery of Ceres, a dwarf planet first spotted by Italian astronomer Guiseppe Piazzi in 1800 that had disappeared behind the sun before observers could chart its orbit. Gauss predicated the precise point of the planetoid's reemergence from the glare using comprehensive approximation methods to determine its speed and the arc of its trajectory.
His success saw him made Professor of Astronomy and director of the astronomical observatory in Gottingen, a position he would hold for the remainder of his life.
In 1818, he began a geodetic survey of the Kingdom of Hanover at the region's monarch's request - a task simplified thanks to Gauss's invention of the heliotrope, an instrument for measuring the sun's rays over great distances.
The polymath went on to produce further works on number theory and cartography before occupying himself with the study of the earth's magnetic field in the 1830s.
He died of a heart attack in Gottingen on 23 February 1855.
Known as a somewhat remote and even aloof figure, Gauss was said to have met the news that his wife was dying while he was busy in his study with the words: "Tell her to wait a moment till I'm done". The anecdote was a favourite of science fiction writer Isaac Asimov but is commonly dismissed as apocryphal.
Gauss's extraordinary contribution to "the queen of the sciences" is in no doubt, however.
Victorian mathematician Henry John Stephen Smith summarised his influence accordingly:
"If we except the great name of [Sir Isaac] Newton it is probable that no mathematicians of any age or country have ever surpassed Gauss in the combination of an abundant fertility of invention with an absolute rigorousness in demonstration, which the ancient Greeks themselves might have envied."
In addition to a number of monuments and prizes named in his honour, Gauss has been commemorated with an asteroid, a crater of the moon, an extinct volcano and an Antarctic expedition ship all christened in tribute.
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