Artist M.C. Escher used swans in flight to suggest infinity in this 1956 drawing.  All M.C. Escher works © the M.C. Escher Company B.V.- Baarn- the Netherlands.

Are there an infinite number of stars? Does the universe have infinite volume? Does space “go on forever”? These are open questions for cosmologists. But mathematicians, physicists, computer scientists, and artists have found valuable ways to use the idea of the infinite.

In a 3:30 p.m.  presentation on Wednesday (March 7) , Professor Martin E. Flashman will discuss some of the visual approaches to the infinite with points, lines, and curves from ancient to modern times. His talk is entitled “The Infinite: Visualizing What is Often Hard to Imagine.”

Perspective artwork utilizes the concept of vanishing points, roughly corresponding to mathematical points at infinity, located at an infinite distance from the observer. This allows artists to create paintings that realistically render space, distances, and forms. Artist M. C. Escher is specifically known for employing the concept of infinity in his work in this and other ways.

Flashman gave a lecture at the ASA in December in which he used Escher’s work to explain visual mathematics. In his upcoming talk, Flashman will give audience members an opportunity to experience visually some of the different types of the infinite—both small, large and in between—that surround us.

Martin E. Flashman

Flashman received his mathematics degrees from Brandeis University and a law degree from New York University School of Law. He taught six years at Bard College before arriving at Humboldt State in 1981 from which he is now retired as Professor Emeritus of Mathematics.

For 2017-18 he is visiting the University of Arizona while he works on several projects related to visualization in making sense of mathematics. An active presenter at national meetings and conferences, he will be giving four sessions this April at the British Congress of Mathematics Education related to his current projects.

Written by Mike Maharry, Academy Village Volunteer

More Info on attending an event
Academy Village is an active-adult community located off Old Spanish Trail six miles southeast of Saguaro National Park East. Its residents support the Arizona Senior Academy, a non-profit charitable organization whose mission includes offering free concerts and lectures to the public.

These events are held in the Great Room of The ASA Building adjacent to the Academy Village Community Center. Due to the popularity of cultural events, non-residents who wish to ensure priority seating are advised to make reservations by email at or by phone at (520) 647-0980. To learn more about the Academy, go to

Parking for visitors is in the lot behind the Community Center. All parking spaces in front of the Academy building are reserved.

Visualizing the Infinite: March 2018