*Ab his via sterniture ad maiora.*

In about 1820 the local monarch ordered Carl Friedrich Gauss to carry out a survey of the Kingdom of Hanover. The great mathematician toiled away on the survey for about four years. While physically difficult and stressful, it's nature gave Gauss something interesting to think about.

Halfway through he realized you could chop a flat map up into small triangles and get an approximation for the topography, but it could never be perfect. The Euclidian geometry we tend to think of where parallel lines never meet and the sum of the angles of a triangle is always 180° just doesn't work.^{1} He set his mind to consider the geometry of curved spaces. It undoubtedly seemed nutty to anyone but a mathematician at the time, but he pushed on and developed the Theorema Egregium - a masterpiece of thought. At a high level it shows you can determine the curvature of a surface with just local measurements. You don't need to consider the space the surface is embedded in. Among other things it tells you why we hold pizza the way we do and that the sum of the angles on a sphere is greater than 180° and changes on an egg and the border of Wyoming isn't a rectangle.. Here I link to a great explanation by the wonderful Cliff Stoll.

Gauss realized this was fundamental, but only a beginning. At the beginning of his paper describing the discovery was this phrase:

* Ab his via sterniture ad maiora* - 'From here the path to something more important is prepared'

Indeed it was. Thirty or so years later Bernhard Riemann generalized what Gauss had started. Its beauty was appreciated and enhanced by a few mathematicians until Albert Einstein needed a tool to describe the curvature of spacetime. And there it was - a beautiful, but fairly obscure, mathematical result from the mid 19^{th} century revolutionized physics 70 years later. Our Universe is not Euclidian .. that's only an illusion, albeit a very good approximation most of the time, dictated by where we live and our senses. Among mathematicians Gauss is a great GOAT candidate.^{2}

We didn't have Latin in high school and I probably wouldn't have taken it anyway. Since then I've learned a little on my own, but am very rusty. Still, there are phrases that seem more useful than their English equivalents. Encountering one you pause and think a bit. This is one I use encouraging people working on long term goals where much of the day to day grind to major accomplishments seem like small steps on the way to the goal. It is a reminder to keep pushing ahead.

__________

^{1} Think of lines of lines of latitude on the Earth. They intersect the equator at right angles added to 180°. The angle they subtend at the pole is greater than 0°, so the sum of all three is greater than 180°.

^{2} The story of a school master telling the seven year old Gauss to add the integers from 1 to 100 to occupy him for an hour appears in a summation of his life shortly after his death. Given the problem, he thought for awhile and answered 5050. He wrote the integers 1 through 100, folded the series and added .. so 1+100, 2+99 and so on. Each pair sums to 101 and there are 50 such pairs so 50*101 = 5050. He had shown the sum of integers from 1 to n = n(n + 1)/2.

I don't know if it was apocryphal, but he was doing serious math a few years later.

## Comments

You can follow this conversation by subscribing to the comment feed for this post.