In Part 3 of his series, Coach K highlights Carl Friedrich Gauss, the "Prince of Mathematicians." Gauss’s groundbreaking work, from predicting planetary paths to developing the normal distribution, shaped modern science and actuarial practices.
This is part 3 of a 4-part series where I'm exploring how math has changed my career and my life. I’m sharing three heroes of mine who have impacted actuarial science, mathematics, and many parts of our lives.
I discussed my first hero, Leonhard Euler, in my last blog. My second hero is Carl Friedrich Gauss, who was born in Germany on April 30, 1777, and who died on February 23, 1855.
Meet Carl Friedrich Gauss
To give you context, Gauss was born 70 years after Euler and 6 years before Euler passed away. Like Euler, Gauss had challenges to overcome. He was born to a poor family, and pursuing a career in math and science was not a guaranteed way to make a living. However, being poor didn’t slow Gauss’s pursuit of excellence.
Gauss became well-known when he calculated where the newly discovered dwarf planet Ceres would reappear. A true data scientist, he predicted where the planet would appear within 0.5 degrees of accuracy despite having data for less than 3 degrees.
Gauss’s Contributions to Mathematics
Actuaries benefit directly from Gauss’s development of the normal distribution and method of least squares. But, let’s start at his beginnings. Gauss is a giant in number theory as he is credited for making modular arithmetic real math and proving the law of quadratic reciprocity.
A key part of number theory are the prime numbers. The order of prime numbers was an unsolved mystery for mathematicians before Gauss. Gauss found a key clue to this mystery by identifying the probability that a random number between 1 and N is prime equals 1/ln(N). That means the expected number of primes between 1 and N is N/ln(N). This was a major breakthrough in understanding primes.
I mentioned in the previous blog that Euler defined i to represent √-1. √-1 was defined as the imaginary number by Rene Descartes centuries before Euler used the letter i. √-1 was not considered an important concept until Euler and Gauss uncovered its value, hence the term “imaginary.” Ironically, almost all of our modern conveniences can be traced back to this number.
Why did the Industrial Revolution and modern inventions like the light bulb and telephone emerge in the late 18th and 19th centuries? This progress was driven by advancements in mathematics, with the imaginary number and complex analysis playing key roles. The concept of the imaginary number began around 1572, but it took roughly 200 years for mathematicians to realize its potential.
What makes mathematicians like Gauss and Euler remarkable is their ability to find “diamonds in the rough” of math. They developed the imaginary number into a powerful tool by expanding real numbers into complex numbers. Once this math was established, scientists used it to transform the world.
Lessons from the Prince of Mathematicians
Some consider Gauss as the greatest mathematician of all time, or at least the “prince of mathematicians.” This is not because of the number of papers he published. Gauss was the opposite of Euler, who published nonstop. Even though Gauss was a great mathematician, he was not confident about publishing his work until he was absolutely sure it was perfect.
So much of Gauss’s work was found unpublished after his death. Gauss' discovery of non-Euclidean geometry is a famous example of work he chose not to publish. For 2,300 years, Euclid’s geometry was the dominant framework. Imagine the pressure Gauss felt when he uncovered an equally elegant way to define geometry, where the sum of a triangle’s angles can be less than or greater than 180 degrees.
While Gauss may not have seen its full potential, other mathematicians built upon his idea, making it one of history’s most important breakthroughs. I learned two important lessons from Gauss here.
1. Don't be afraid to share your work.
I often doubt my work, even when I strive for professional quality. Maybe it’s the actuary in me imagining worst-case scenarios, like someone finding major mistakes. But if I don’t publish, others miss out. So, I’m working on overcoming those doubts.
I had similar fears about publishing this 4-part series on mathematicians. The history and importance of math aren’t typical topics for actuaries, and some might question their relevance. Still, these concepts have deeply impacted my life, and perhaps they can help others too. That’s why I publish.
2. Encourage others to publish.
A second lesson for me is to encourage others to publish as well. This means fostering a culture where they feel comfortable taking that step. This applies not just to actuaries but also to other professionals, such as programmers, who must move their code to production.
The Story Continues
We’ll continue this story in our next blog where we’ll meet my third hero, Bernhard Riemann. Now that we’ve digested the published and unpublished work of Gauss, we admire his mathematical genius. However, perhaps his greatest contribution was the impact he had on Riemann. Gauss mentored Riemann and convinced him to pursue a career in mathematics.
Just like Gauss took Euler’s work to new heights, Riemann took Gauss’s work to a whole new world. So one final lesson from Gauss is the importance of mentoring others. Society reaps exponential gains when we invest our time mentoring others. Or, in Gauss’ own words, “Mathematicians stand on each others’ shoulders.”