Johann Carl Friedrich Gauss was born in what is now northwestern Germany, to a mother who couldn’t read or write. Though she didn’t note the exact date, she recalled it was a Wednesday, eight days prior to the Feast of the Ascension, occurring 39 days post-Easter.

Subsequently, by determining the date of Easter and using mathematical methods to deduce historical and future dates, Gauss pinpointed his birthday. Remarkably, he identified it without any mistakes, concluding it was April 30, 1777.

By the time he accomplished this, he was 22. As a young genius, he had already made significant mathematical discoveries, penned a number theory textbook, and his journey was just beginning. Many might not recognize Gauss, but he’s a pivotal figure in mathematics.

Born to financially struggling parents, young Gauss showcased his outstanding computational abilities before he even turned three. E.T. Bell, who wrote Men of Mathematics, noted that while Gauss’s father, Gerhard, was handling laborers’ payroll, young Gauss keenly observed.

It wasn’t long before educators recognized his talent in math. Impressively, at the tender age of seven, he outpaced his 100 classmates in solving arithmetic problems. As a teenager, he was already on the path of groundbreaking mathematical revelations.

In 1795, 18-year-old Gauss started his education at the University of Göttingen. Although he was a mathematical genius, Gauss initially considered a career in philology, delving into language and its literature.

However, a month shy of turning 19, Gauss made a landmark mathematical discovery. Historically, mathematicians, including greats like Euclid and Isaac Newton, believed it was impossible to construct a regular polygon with prime number sides exceeding 5 (like 7, 11, 13, 17, etc.) using merely a ruler and compass.

Young Gauss challenged this belief. He demonstrated that a regular heptadecagon (17 equal-length-sided polygon) could be constructed using basic tools. Furthermore, he revealed that similar constructions were feasible for shapes whose sides were products of unique Fermat primes combined with powers of 2.

This revelation saw him fully commit to mathematics. By 21, he had written his masterwork, Disquisitiones Arithmeticae. Focusing on number theory, it remains a seminal piece in the field of math.

The year he identified his unique polygon, Gauss unveiled more findings. Shortly after his polygon revelation, he pioneered modular arithmetic and advanced number theory. He further contributed to the prime number theorem, shedding light on the spread of prime numbers.

He was also the pioneer to validate quadratic reciprocity laws, enabling mathematicians to assess the solvability of any quadratic equation within modular arithmetic.

Demonstrating his algebraic prowess, he jotted down “ΕΥΡΗΚΑ! num = Δ + Δ’ + Δ” in his personal journal. Through this, Gauss established that every positive integer can be depicted as the sum of, at most, three triangular numbers, influencing the later profound Weil conjectures.

Moreover, Gauss’s impact extended beyond pure math. In 1800, when astronomer Giuseppe Piazzi attempted to chart the dwarf planet Ceres, he consistently faced issues. After observing the planet for just over a month, it vanished in the sun’s brightness.

When it should have reappeared, Piazzi couldn’t locate it due to mathematical discrepancies. Fortunately, Gauss learned of this challenge. Rapidly, he applied his innovative mathematical techniques to project where Ceres might emerge in December of 1801, nearly a year post its discovery.

Gauss’s estimate was astonishingly accurate, deviating less than half a degree. Post this success in astronomy, Gauss delved deeper into planetary studies, elaborating on orbital patterns and hypothesizing the consistent orbital motion of planets through time.

In 1831, Gauss dedicated considerable time to exploring magnetism and its impact on aspects like mass, density, charge, and time. During this phase, he developed Gauss’s Law, a principle connecting electric charge distribution to the consequent electric field.

Throughout his life, Carl Friedrich Gauss committed himself to solving mathematical equations and took an interest in those initiated by his peers, aiming to complete them.

He was driven by the quest for knowledge rather than the allure of fame. Often, he’d jot down his findings in his personal diary instead of publicizing them, leading his peers to share similar discoveries before him.

Gauss’s meticulous nature meant he withheld from publishing anything he deemed below his ideal standard. This sometimes allowed other mathematicians to introduce findings before him.

This exacting nature wasn’t confined to his professional work but extended to his familial expectations too. Across two marriages, he had six children, with three being sons. For his daughters, he desired societal norms of the time – a prosperous marital alliance.

However, for his sons, his hopes were arguably more demanding and somewhat self-centered. He discouraged them from entering the realms of science or math, apprehensive they might not possess his prodigious talents. He wanted to preserve his family’s reputation from potential failures.

This stance strained his bond with his sons. Following the passing of his first wife, Johanna, and their infant son, Louis, a profound melancholy engulfed Gauss.

Many believe he never truly emerged from this gloom, immersing himself wholly in mathematical endeavors. In correspondence with mathematician Farkas Bolyai, Gauss conveyed sole joy in research and a general disinterest in other pursuits.

Even as he aged, Gauss’s intellectual fervor didn’t wane. He taught himself Russian at 62 and continued publishing academic papers throughout his 60s. At 77, in 1855, he succumbed to a heart attack in Göttingen, his final resting place. His brain was preserved and analyzed by Rudolf Wagner, a Göttingen-based anatomist.

While many might not recall Gauss’s name today, it remains iconic in mathematical circles: the standard bell curve in statistics is termed the Gaussian distribution. Furthermore, a prestigious mathematical accolade awarded quadrennially is named the Carl Friedrich Gauss Prize.

Though he may have come across as somewhat gruff, it’s indisputable that mathematics would be significantly different without the brilliance and commitment of Carl Friedrich Gauss.