Christopher Hanusa
Interview by Kate Schwarting, Programs Intern
Interview by Kate Schwarting, Programs Intern
KS: As a mathematical artist, how do you interpret the relationship between math and art?
CH: Mathematics and art are both very creative disciplines and are more alike than most people think. Mathematicians think deeply about all sorts of problems we've learned to be at peace with not knowing an answer and being unsure of the way forward. We understand the need to think about a problem in many ways, bringing in ideas from different angles, and exploring what is possible. This is all in a quest to understand what it is that we can know for certain.
The creation of art has been a similar process. While I may start with a blank canvas (in reality an empty computer file), there is some seed of an idea that is waiting to be teased out. Building on this seed, through experimentation, trial and error, dead ends, and happy accidents, a piece of art takes form, exploring what is possible in the medium of choice.
A misconception about mathematics is that you are always looking for The Answer, and that once It has been found then that is the end of the process. Perhaps that is true when your goal is to add a list of numbers, but it is not at all true for mathematical research. While it makes your day when you've vanquished a question that you've been thinking about for months (or years!), this is just a brief pause; one answer always leads to more questions. I see this as an exact parallel when an artist completes a piece of art. There are always variations on the theme that can lead to fruitful avenues to explore and new frontiers that open up with the gained experience.
CH: Mathematics and art are both very creative disciplines and are more alike than most people think. Mathematicians think deeply about all sorts of problems we've learned to be at peace with not knowing an answer and being unsure of the way forward. We understand the need to think about a problem in many ways, bringing in ideas from different angles, and exploring what is possible. This is all in a quest to understand what it is that we can know for certain.
The creation of art has been a similar process. While I may start with a blank canvas (in reality an empty computer file), there is some seed of an idea that is waiting to be teased out. Building on this seed, through experimentation, trial and error, dead ends, and happy accidents, a piece of art takes form, exploring what is possible in the medium of choice.
A misconception about mathematics is that you are always looking for The Answer, and that once It has been found then that is the end of the process. Perhaps that is true when your goal is to add a list of numbers, but it is not at all true for mathematical research. While it makes your day when you've vanquished a question that you've been thinking about for months (or years!), this is just a brief pause; one answer always leads to more questions. I see this as an exact parallel when an artist completes a piece of art. There are always variations on the theme that can lead to fruitful avenues to explore and new frontiers that open up with the gained experience.
KS: Your work fuses design and functionality with theory and experimental math. What is your process for creating work that combines these elements?
CH: I'm not sure everyone is aware that mathematics can also be experimental! My research is in combinatorics, which is the area of mathematics that involves understanding families of discrete objects like permutations, graphs, and polyhedra. I use technical mathematical software to encode these objects in the computer. I then generate all instances of these objects and collect some mathematical data about them to give me intuition about what theorems can be proved about the objects.
This informs how I create mathematical art. I get inspired by a mathematical concept or some found math, which may include an idea from a research seminar, an image from a book, a captivating pattern, or even a doodle on a page. This starts an investigation. What is the mathematics hiding behind the concept? How can I generate it algorithmically? How can I generalize the idea further? What makes it visually appealing? From these questions, I aim to determine what is possible to create using code-based mathematical software. After I create a computer model of my work, I use the 3D printers at Queens College to prototype my work, getting the virtual objects into my hands to play with, critique, and refine. I then meticulously adjust and perturb parameters to finalize the piece.
CH: I'm not sure everyone is aware that mathematics can also be experimental! My research is in combinatorics, which is the area of mathematics that involves understanding families of discrete objects like permutations, graphs, and polyhedra. I use technical mathematical software to encode these objects in the computer. I then generate all instances of these objects and collect some mathematical data about them to give me intuition about what theorems can be proved about the objects.
This informs how I create mathematical art. I get inspired by a mathematical concept or some found math, which may include an idea from a research seminar, an image from a book, a captivating pattern, or even a doodle on a page. This starts an investigation. What is the mathematics hiding behind the concept? How can I generate it algorithmically? How can I generalize the idea further? What makes it visually appealing? From these questions, I aim to determine what is possible to create using code-based mathematical software. After I create a computer model of my work, I use the 3D printers at Queens College to prototype my work, getting the virtual objects into my hands to play with, critique, and refine. I then meticulously adjust and perturb parameters to finalize the piece.

KS: What mathematical topics are you most drawn to when developing a new project?
CH: I am drawn to the beauty of mathematics, the elegance of precision and the aesthetics of randomness. An especially attractive subject is generative art, which involves writing an algorithm incorporating randomness to create a piece of art. While I guide the process by authoring the code, the final result is something that I did not precisely specify. I can rerun the code over and over to generate related but different works.
With my interest in mathematical research, I am drawn to topics where I will learn something new. A theme that has been percolating in my mind is the idea of creating three-dimensional analogs of two-dimensional designs. This area is especially ripe for mathematical investigation and research, since the jump from two to three dimensions often requires new, complex ideas.
CH: I am drawn to the beauty of mathematics, the elegance of precision and the aesthetics of randomness. An especially attractive subject is generative art, which involves writing an algorithm incorporating randomness to create a piece of art. While I guide the process by authoring the code, the final result is something that I did not precisely specify. I can rerun the code over and over to generate related but different works.
With my interest in mathematical research, I am drawn to topics where I will learn something new. A theme that has been percolating in my mind is the idea of creating three-dimensional analogs of two-dimensional designs. This area is especially ripe for mathematical investigation and research, since the jump from two to three dimensions often requires new, complex ideas.

KS: As a Professor of Mathematics, what do you see as the impact of this type of work?
CH:As an educator, I see that creating better visualizations increases the understanding of students. Certain topics in the mathematics curriculum are three-dimensional, which are hard to convey on a two-dimensional blackboard. Bringing hands-on mathematical art into the classroom gives students with visual learning styles more language and more ability to express their creativity. I love sharing knowledge so I have designed tutorials for people who want to learn how to do 3D Design in Mathematica to make their own creations. I have written a series of blog posts giving step-by-step explanations of the algorithmic design of some of my work.
Furthermore, I feel that mathematics brings a new flavor of possibility to the art world. By creating and discussing the art, this brings more mathematical ideas into the mainstream. I was very much inspired by a talk by George Hart and Elisabeth Heathfield that I attended at the mathematical art Bridges Conference held last summer in Waterloo, Ontario. They spoke about how in most classrooms throughout the country there are inspirational quotations from writers on the walls, while there is a lack of inspirational mathematics on the walls. Why isn't there be a fascinating piece of mathematical art in each classroom to immerse children in higher-level mathematical ideas at a young age which may lead them to question, investigate, and enjoy mathematics? It is within the realm of possibility that the creation and popularization of mathematical art would help reduce math anxiety in the general population.
KS:What current projects are you working on?
CH: This fall I have been creating generative pottery working with Matt Greco (Queens College Art) in a way that that mixes processes of old and new. We start by designing a 3D model of a bowl in a Computer Aided Design program and print it out on a 3D printer. We then create a plaster mold of the 3D print, and use a slipcasting technique to turn a virtual model into a ceramic bowl. I am very excited to see how they turn out!
An ongoing project is designing mathematical jewelry using these same algorithmic techniques and skills. It has been fun to design jewelry that highlights mathematical concepts and a joy to bring these virtual objects into the real world through the process of 3D printing. My Mathematical Jewelry is available to be 3D printed in a wide variety of materials through my production partner Shapeways.
A long-term goal is to collaborate with artists who would like to fuse their work with mathematical processes and ideas. I would also like to create public art installations. This would be an ideal platform to popularize mathematical art on a larger scale. I invite readers who are interested in collaborating to reach out by email.
Thank you! It's been a pleasure to share my story.
CH:As an educator, I see that creating better visualizations increases the understanding of students. Certain topics in the mathematics curriculum are three-dimensional, which are hard to convey on a two-dimensional blackboard. Bringing hands-on mathematical art into the classroom gives students with visual learning styles more language and more ability to express their creativity. I love sharing knowledge so I have designed tutorials for people who want to learn how to do 3D Design in Mathematica to make their own creations. I have written a series of blog posts giving step-by-step explanations of the algorithmic design of some of my work.
Furthermore, I feel that mathematics brings a new flavor of possibility to the art world. By creating and discussing the art, this brings more mathematical ideas into the mainstream. I was very much inspired by a talk by George Hart and Elisabeth Heathfield that I attended at the mathematical art Bridges Conference held last summer in Waterloo, Ontario. They spoke about how in most classrooms throughout the country there are inspirational quotations from writers on the walls, while there is a lack of inspirational mathematics on the walls. Why isn't there be a fascinating piece of mathematical art in each classroom to immerse children in higher-level mathematical ideas at a young age which may lead them to question, investigate, and enjoy mathematics? It is within the realm of possibility that the creation and popularization of mathematical art would help reduce math anxiety in the general population.
KS:What current projects are you working on?
CH: This fall I have been creating generative pottery working with Matt Greco (Queens College Art) in a way that that mixes processes of old and new. We start by designing a 3D model of a bowl in a Computer Aided Design program and print it out on a 3D printer. We then create a plaster mold of the 3D print, and use a slipcasting technique to turn a virtual model into a ceramic bowl. I am very excited to see how they turn out!
An ongoing project is designing mathematical jewelry using these same algorithmic techniques and skills. It has been fun to design jewelry that highlights mathematical concepts and a joy to bring these virtual objects into the real world through the process of 3D printing. My Mathematical Jewelry is available to be 3D printed in a wide variety of materials through my production partner Shapeways.
A long-term goal is to collaborate with artists who would like to fuse their work with mathematical processes and ideas. I would also like to create public art installations. This would be an ideal platform to popularize mathematical art on a larger scale. I invite readers who are interested in collaborating to reach out by email.
Thank you! It's been a pleasure to share my story.

About the Featured Art
"Snub Cube Terrarium" (2017) is a terrarium based on the geometry of the Snub Cube, a fascinating polyhedron with chirality. This is a rendering of a the terrarium in 3D printed porcelain. I've written a blog post about its construction.
“Abstract Line Pendant” (2017) and“Bubble Pendant” (2017) are two pieces of generative jewelry designed in Mathematica and 3D printed by Shapeways. Bubble Pendant is printed in Raw Bronze and Abstract Line Pendant is printed in Gold Plated Brass.
"The New Normal” (2017) and “Tortoise Torus” (2017) are pieces of generative art. They are sculptures that have been 3D Printed in Full Color Sandstone. The New Normal is based on the two-dimensional normal probability distribution and a random Voronoi decomposition of the base. Tortoise Torus seeks to emulate the patterns of a tortoise shell on the surface of a torus. The height function on each scute is based on the distance to the boundary. Learn more and interact with 3D renderings at hanusadesign.com.
"Snub Cube Terrarium" (2017) is a terrarium based on the geometry of the Snub Cube, a fascinating polyhedron with chirality. This is a rendering of a the terrarium in 3D printed porcelain. I've written a blog post about its construction.
“Abstract Line Pendant” (2017) and“Bubble Pendant” (2017) are two pieces of generative jewelry designed in Mathematica and 3D printed by Shapeways. Bubble Pendant is printed in Raw Bronze and Abstract Line Pendant is printed in Gold Plated Brass.
"The New Normal” (2017) and “Tortoise Torus” (2017) are pieces of generative art. They are sculptures that have been 3D Printed in Full Color Sandstone. The New Normal is based on the two-dimensional normal probability distribution and a random Voronoi decomposition of the base. Tortoise Torus seeks to emulate the patterns of a tortoise shell on the surface of a torus. The height function on each scute is based on the distance to the boundary. Learn more and interact with 3D renderings at hanusadesign.com.
You can find Christopher Hanusa's mathematical art portfolio at hanusadesign.com and his Queens College website at qc.edu/~chanusa. Follow @hanusadesign on instagram, facebook, twitter, and pinterest. Reach out to Christopher Hanusa by email or on Facebook.