Blue & Yellow
Blue & Yellow: Georgiy Voronyi revolutionized computer graphics and AI.
January 27, 2023

Introduction: Uncovering Ukraine is a series of short stories about Ukrainians who’ve advanced technology, art, and science to new heights. Check out our other articles in this series.

Georgiy Voronyi was an outstanding Ukrainian scientist, and professor at the University of Warsaw, and served as Dean of the Faculty of Mechanics of the Warsaw Polytechnic Institute.

Voronyi is a co-founder of a new branch of mathematics — the geometry of numbers — and his work is widely used in modern research, computer graphics, and more. 

Voronyi was born in the village of Zhuravka, Pyriatyn, in the Poltava Governorate, on April 28, 1868. Voronyi graduated from high school at the Gymnasium of Priluki in 1885, where he demonstrated a strong aptitude for mathematics and particularly algebra.

While attending school in Priluki, he solved a mathematical challenge set by professor Ermakov of Kyiv University on factorizing polynomials. Despite his young age, his solution was eventually published in the Journal of Elementary Mathematics.

In 1885, Voronyi entered St. Petersburg University and set number theory as his main field of research. Poor health forced the young scientist to return to his native Zhuravka, where he continued to work on his research. In the fall of 1889, Georgiy Voronyi passed his final exams and defended his thesis on Bernoulli’s numbers.

Shortly after, he prepared for the master’s exams on the basis of a submission signed by the leading professors of mathematics, Markov, Korkin, Sohotsky, and Posse. At the same time, he was appointed a part-time teacher at the Peterhof secondary school.

During his short life — only 40 years — Voronyi wrote extensively and produced six large memoirs and six articles published between 1890 and 1908. Voronyi’s work helped change modern number theory and he is considered among the greatest arithmeticians of his era. His research is now used in a wide variety of fields, including crystallography, physics, astronomy, chemistry, microbiology, computer graphics, artificial intelligence, pattern recognition, and ophthalmology.

He introduced the concept of what is now known as Voronyi diagrams or tessellations. This concept is used in many areas of science, such as the analysis of spatially distributed data, and it has helped shape modern geophysics, condensed matter physics, and meteorology.

The concepts of tessellations are also used in many areas of computer graphics, including architecture, filmmaking, and even video games. For example, Blender 3D — an open-source 3D computer graphics software too — uses a Voronyi texture generator as one of its main sources of randomly generated images. This graphical generator can be applied as textures for many different uses.

By the 1990s, such terms as “Voronyi diagram”, “Voronyi cell,” “Voronyi partition,” and the “Voronoi mosaic” were widely-used in scientific terminology. In England, the concept of the Voronyi diagram is even included in the school curriculum.

In addition to works on number theory, Voronyi has a single work on mathematical analysis. It is devoted to generalized sums of numerical series. This is his report at the congress of Russian naturalists and doctors in St. Petersburg, and it was published in the journal of the congress in 1902. In this publication, Voronyi introduces for the first time a variety of methods for summing divergent series.

Voronyi diagrams are used in engineering structures and a variety of design projects. The Voronyi method of dividing a certain volume into parts makes it possible to create the strongest structures using the minimum amount of material.

A few examples of design projects incorporating three-dimensional Voronyi diagrams include a Chinese yacht called “Voronyi yacht and a Voronyi-inspired “mushroom lamp,” designed by the Portuguese architect Andre Coelho.

After health complications, Voronyi died on November 20, 1908, at the age of 40. 


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