Cantor's Tower of Infinities

Math / Fantasy Illustration • Quanta Magazine • 2020
Stylized painting: Georg Cantor standing on a clieff, pondering an ever-rising, infinite tower in a fantastical landscape.

Quanta Magazine, 2021. Reuse prohibited.

Art direction, concepts, digital painting

C4D, Clip Studio Paint

Art direction and fantasy architecture design / environment painting for a mathematics article: Georg Cantor pondering an ever-rising, infinite tower. For an article about a new infinity proof by Natalie Wolchover: How Many Numbers Exist? Infinity Proof Moves Math Closer to an Answer.

In 2020-21, I was just barely getting back into painting after about a decade's hiatus (for part of which I'd stopped making art entirely). It was immensely frustrating; I'd forgotten things that used to be easy and intuitive. And even once I resumed, opportunities to create were rare, since my other duties as Art Director took priority and overtook most of my time. But in a couple of years I learned, re-learned, and improved a ton, especially in my process. I'm now a bit embarassed by how much time and effort the process below took, and there's quite a bit I'd change. And that's great thing!

Sketches: Gerog Cantor's infinite tower
Sketches: Gerog Cantor's infinite tower

Concept sketches, figuring out the tower's form while keeping it to spec. Specifically, its size had to grow with the height and along the way, Natalie suggested that discrete towers, more like my later attempts, were a better representation of the math. As with all Quanta art, we put a lot of thought into details like this, even if the average viewer wouldn't notice them.

Sketches: towers with infinity symbols

Some tower concepts, unused

© Olena Shmahalo