Cornell professor reconstructs ancient canoe using mathematics

MOUNT VERNON, Iowa – Cornell Associate Professor of Mathematics Fabiàn Candelaria used mathematics to study a fragment of a colonial canoe that floated ashore on the west coast of Puerto Rico after sitting underwater for hundreds of years.

Candelaria joined a diverse team of researchers, including an archeologist, an artist, and an archaeobotanist to study the fragment, which they concluded was as much as 370 years old. The canoe washed up after large sea swells in February 2021 and was the first of its kind documented on the island.

The results of the study were published in a Spanish scholarly journal, Patrimonio, in October of 2024, an issue focused on archeological studies. 

Candelaria, a professor of mathematics who is originally from Puerto Rico, says he’s never published in an archeological journal–only math and applied math journals. 

“This was a first for me, but it was very fulfilling because I contributed to the scientific community in Puerto Rico and the Caribbean,” Candelaria said. “These types of navigation devices were used in other islands around Puerto Rico, and they connected people. This research connected me to where I came from.”

Candelaria met archeologist Reniel Rodríguez Ramos, who led the canoe research project at the University of Puerto Rico, during a different study where he used mathematics to create maps of caves. When the canoe surfaced, Rodríguez asked Candelaria if he would take part in the study. 

“I used this opportunity to explore some of the relations between mathematics and archaeology,” Candelaria said. 

During the summer of 2022, they collected data on the fragment using a LiDAR, or a Light Detection and Ranging instrument.

“It’s kind of like a laser ruler, but instead of taking one distance, it takes thousands, sometimes millions, depending on how long you use it. This one was handheld, and they walked around it and collected data on every single surface, which we later cleaned up.”

Their goal was to use applied mathematics to figure out what the full canoe looked like since they only had a small portion of the boat. 

“I used 3D LiDAR data from the fragment to create elliptical projections that modeled the canoe’s interior dimensions and reconstructed its possible shape.”

But it wasn’t an easy process. 

He realized he was missing a big piece of data, the length of the canoe, to create the model. They were able to find a single drawing of a similar canoe in a book by a Spaniard who visited Puerto Rico during the period. The picture showed the canoe was an estimated 15 feet long.

“There were no records. We didn’t have anything,” Candelaria said. “So we took the new information and added it into the model. That allowed us to fix the lines and the data and get a better shape.”

Candelaria enjoyed working on this project because he worked with other experts who studied what tree the canoe was made out of, how people would have crafted it, how old it was, and an artist who made a rendering of the canoe. It was all the same project, the same history–but examined from different angles. 

“I hope my students at Cornell look at this and see how interesting it is that math can be related to other topics in nontraditional ways,” Candelaria said. “We tend to think about math as algebra and solving equations for the unknowns. We were solving equations for the unknowns, but it was related to the geometry of this piece of an artifact. I want them to think outside the box and see all the ways that they can connect what we know to what we can do.”