As of 2020, Cheng is a scientist in residence at the School of the Art Institute of Chicago, where she teaches mathematics to arts students. Cheng formerly held academic appointments at the University of Nice Sophia Antipolis, the University of Sheffield and the University of Chicago. She has published over a dozen research papers across several journals within her area of category theory. Former doctoral students include Nick Gurski and Thomas Cottrell.
Mathematics and baking
Cheng's research interests are in category theory, which she has written about for a general audience by using analogies from baking. Her vision is to rid the world of mathematics phobia. In How to Bake Pi, published on May 5, 2015, each chapter begins with a recipe for a dessert, to illustrate the commonalities in the methods and principles of mathematics and cooking. The book was well received and has since been translated into French. Cheng has also written a number of papers with similar themes, such as On the perfect quantity of cream for a scone and On the perfect size for a pizza. Cheng has presented similar topics through YouTube in a light-hearted manner and has explored mathematics in other ways such as in her speech Mathematics and Lego: the untold story.
Cheng is a pianist who specialises in lieder and art song. She was awarded the Sheila Mossman Memorial Award from the Associated Board of the Royal Schools of Music and was the first recipient of the Brighton and Hove Arts Council Award for the Musician of the Year. In Chicago, she gave a recital in the Pianoforte Chicago recital series; she performed Schwanengesang and Winterreise with Paul Geiger at Schubertiade Chicago in 2005 and 2006 respectively, and Die Schöne Müllerin with Ryan de Ryan at Schubertiade Chicago 2007. She performed lieder with tenor Nicholas Harkness in the Noontime Recital Series at the University of Chicago, the Salon Series at the Tower Club, and the Maxwell Recital Series, and she gave recitals for the Auxiliary Board Chapter of the Lyric Opera; she also performed La Traviata at the Oak Park Village Players. In 2013, Cheng founded the Liederstube as an oasis for art song in the Fine Arts Building, in downtown Chicago. The mission of the Liederstube is to present and enjoy classical music in an intimate and informal setting. The Liederstube is a Not For Profit 501 organisation.
How to Bake Pi: An Edible Exploration of the Mathematics of Mathematics ; Cakes, Custard and Category Theory: Easy recipes for understanding complex maths ; How to Bake Pi: Easy Recipes for Understanding Complex Maths
Beyond Infinity: An Expedition to the Outer-Limits of the Mathematical Universe; Beyond Infinity: An Expedition to the Outer Limits of Mathematics
The Art of Logic: How to Make Sense in a World that Doesn't ; The Art of Logic in an Illogical World