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This remarkably general law allows mathematicians to determine the solvability of any quadratic equation in modular arithmetic.
The prime number theorem, conjectured on 31 May, gives a good understanding of how the prime numbers are distributed among the integers.
There are many other anecdotes about his precocity while a toddler, and he made his first groundbreaking mathematical discoveries while still a teenager.
He completed his magnum opus, Disquisitiones Arithmeticae, in 1798, at the age of 21—though it was not published until 1801.
Two religious works which Gauss read frequently were Braubach's Seelenlehre (Giessen, 1843) and Siissmilch's Gottliche (Ordnung gerettet A756); he also devoted considerable time to the New Testament in the original Greek.
Eugene shared a good measure of Gauss's talent in languages and computation. He did not want any of his sons to enter mathematics or science for "fear of lowering the family name", as he believed none of them would surpass his own achievements.
In connection to this, there is a record of a conversation between Rudolf Wagner and Gauss, in which they discussed William Whewell's book Of the Plurality of Worlds.
In this work, Whewell had discarded the possibility of existing life in other planets, on the basis of theological arguments, but this was a position with which both Wagner and Gauss disagreed.
In the days of his full strength, it furnished him recreation and, by the prospects which it opened up to him, gave consolation.
Toward the end of his life, it brought him confidence.
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For Gauss, not he who mumbles his creed, but he who lives it, is accepted.