HMC Department of Mathematics

Quod Erat Ars

April 24 - May 14, 2023

Sprague Gallery

Hannah Friedman (HMC ’23), Zooey Meznarich (HMC ’23), Jasper Bown (HMC ’24), Peter Kagey, David Bachman, Yoni Maltsman (HMC ’23), Ming Chen

View of a sculpture which is a skull. It appears as though non-figurative, decorative pattern is carved into the surface of the skull.
David Bachman, BZ Reaction Skull, 2022, 3D printed “sandstone” (binder-infused gypsum powder), 4 x 5 x 6 inches.
Photo courtesy of the HMC Department of Mathematics.

And each man hears as the twilight nears, to the beat of his dying heart,
The Devil drum on the darkened pane: "You did it, but was it Art?"

Rudyard Kipling, The Conundrum of the Workshops

Mathematicians postulate certain self-evident statements (axioms) and then use logical reasoning to create new mathematical truths (theorems). These new truths arise from sound deductive arguments for the conclusion from the premise (proof). As if to emphasize the timeless nature of these mathematical conclusions, mathematicians are fond of ending their proofs with QED, for the latin phrase “quod erat demonstrandum” (“that which was to be demonstrated”).

But whose truth are we speaking of in mathematics? And who are we demonstrating to? Does mathematics connect us with eternal truths from an underlying Platonic reality or is mathematics not really about anything and we are merely among the faithful in the Church of Pythagoras? This ambiguity for meaning in mathematics underscores the necessity for mathematics to be shareable if it is to stand the test of time. Through sharing, mathematicians create meaning and open the door to new interpretations, new insights, and ultimately new truths.

What creates meaning in art? Must art be shared to exist? Noted logician Edward Nelson writes that meaning in mathematics is not found in a cold, abstract, static world of Platonic ideas, but rather in the human, historical, collegial world of mathematicians and their work. It is discovered in the beauty and depth of patterns, unsuspected relationships between structures that seemed unrelated, the fierce struggle to bring order to seemingly insurmountable complexity and, above all, the awe in confronting the potential infinity that is the world of mathematics (Edward Nelson, Mathematics and Faith, 2000).

The works shared in Quod Erat Ars expand our sense for what has meaning and invite us to explore beauty and depth in pattern, see relationships between seemingly unrelatable structures, and embrace attempts at finding order from infinite complexity.  Mathematics and art have been interconnected for centuries, from the use of the golden ratio and linear perspective to modern fractal geometry, but the works in this exhibition go beyond these conventional connections to define new ways in which mathematical beauty, wonder, inspiration, and comfort can connect and unite us. Ultimately, these works inspire awe for the infinite potential that lies in the synthesis of math and art. QEA.

Artist Notes

Hannah Friedman, Piecewise Puzzles, 2021: I started this project very shortly after becoming a math major. I was so excited about mathematics that I wanted to put some of my favorite ideas into a blanket. Each hexagon is a visual interpretation of a mathematical concept I learned about in my first two years at Mudd. This blanket tells a piece of my math story, but I like to think of it as a puzzle with multiple correct answers. What mathematical ideas do you see in this blanket?

Zooey Meznarich, metamorphosis, 2023: My love for mathematics grew most during some of the most difficult years of my life. This work represents my journey as a student of mathematics and as a student of life – from curiosity, to comfort, to confidence. It is also an epilogue for my time in college, and a prelude to what the future may hold. I hope this work may resonate with those who also find refuge in beautiful things, in mathematics and beyond.

Peter Kagey, Truncated Trihexagonal Truchet Tiling, 2023: This piece combines two ideas that I think a lot about: polygonal tilings of the plane and Truchet tiles, which are related to ideas in statistical mechanics such as fully packed loop models. The piece starts with a truncated trihexagonal tiling, which consists of squares, hexagons, and 12-gons, and draws circular arcs from pairs of midpoints of edges in such a way that (a) the arcs intersect the edges of the polygons at right angles and (b) no arcs intersect each other. The number of ways to draw arcs on a tile in this way is given by the Catalan numbers. These arc configurations are chosen at random in such a way that highly symmetric configurations are relatively more likely to be drawn. The resulting structure has some interesting emergent properties, and leads to a number of open mathematical questions.

Jasper Bown, Elevated Spikey, 2023: I was inspired by the wolfram alpha and mathematica logo. Nicknamed Spikey, the rhombic hexecontahedron has 60 sides (though I only had to make 50 for this sculpture). Several of my ceramic pieces use the technique of creating geometric forms using laser cut templates for surfaces and 3D printed or machined templates for angles, so I was able to use that technique to create this piece, placing holes in order to create the hanging structure.

Jasper BownCoded Entwinement, 2023: Dodecahedrons and icosahedrons are mathematically interrelated since each shape has the same set of symmetries. If you take the center of the faces of a dodecahedron, you get an icosahedron, and vice versa. This piece explores how the tension of working with multiple materials can mirror the tension of engaging deeply with different passions and identities. Understanding the whole piece and process takes multiple perspectives.

David Bachman, BZ Reaction Skull, 2022: The Belousov–Zhabotinsky reaction is a nonlinear chemical oscillator with no stable equilibrium. It is modeled by a set of 3 very simple equations with 3 unknown variables that oscillate chaotically over time, giving rise to beautiful complex patterns. To create BZ Reaction Skull, these equations are adapted to a triangular mesh coming from a 3D scan of a human skull. Additional constraints are added to enforce symmetry across the two sides of the skull (even though the underlying model was not symmetric).

Yoni Maltsman, Programming Knitting Machine, 2023, Playground, 2023, Stay Back, 2023: These works were created with the help of bugs, or mistakes. Each work is generated with a mathematical rule that dictates how something's position and color should change over time, given its current position and color. Throughout my time at Mudd I've been indoctrinated for better or for worse that pretty much everything in the world follows some mathematical rule. Maybe if we consider the possibility that these rules are bugs, mistakes in an almost intelligent design of the universe, then it can take some of the pressure off our lives.

Ming Chen, n1 sin Θ1 = n2 sin Θ2, 2023: Inspired by the mathematical formula n1 sin θ1 = n2 sin θ2 (Dispersion and Scattering of Light). This equation makes you nostalgic for Newton and the scene when he picked up a prism to capture monochromatic light. The index of refraction for each color is unique in non-vacuous materials. These unique indices cause each wavelength to follow a different path. Why the sky is blue, why love is rose red, why you just happen to see that double rainbow over the mountains, and mathematics gives you the answers of certainty and consistency.

HMC Department of Mathematics – Quod Erat Ars opens on April 24 and continues through May 14, 2023. Gallery hours are Monday through Friday, 8AM to 5PM. The exhibition is open to the public. The Covid-19 guidelines will be updated as new information becomes available.

The exhibition is curated by the HMC Department of Mathematics.

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