More than any other art or science, the 20th-century mathematician G.H. Hardy wrote, mathematics is a young person’s game.
Isaac Newton, Hardy noted in A Mathematician’s Apology, “gave up mathematics at fifty…he had recognized no doubt by the time he was forty that his great creative days were over.”
Other famous mathematicians died prematurely: Evariste Galois not yet 21, Niels Abel at 27, Srinivasa Ramanujan at 33 and Bernhard Riemann at 40.
Hardy himself died at 70 in 1947 without meeting one exception to his rule—Billy E. Rhoades, who earned a Ph.D. from Lehigh in 1958 and continues to conduct research at the age of 82.
Rhoades has published more than 340 articles, including nine in 2010. In October he presented a paper at the Conference on Summability and Applications at the University of North Florida.
On March 30, he returned to Lehigh to give a talk titled “Hausdorff Matrices” at the mathematics department’s colloquium series.
Rhoades estimates he works 18 hours a week at the University of Indiana, where he is professor emeritus.
The good fortune of still having work to do
Of his longevity as a researcher, Rhoades says, “I’ve been blessed with good health and I’m fortunate to work in a field where there are open questions that I can solve.”
While teaching at Lafayette College, Rhoades became the first of 20 students at Lehigh to earn a Ph.D. in mathematics under the supervision of Albert E. “Tommy” Wilansky, professor emeritus of mathematics.
“Wilansky was a magnificent instructor. He encouraged me to select the problems I wanted to work on.”
Rhoades taught 10 years at Lafayette before moving to Indiana. His many honors include citations from the Mathematical Association of America and from his alma mater, Ohio Northern University, as well as the Jones Award for Superior Teaching from Lafayette.
Keep an open mind and build vertically
A misperception exists, says Rhoades, that mathematics is accessible only to a select few.
“Anyone can learn to do mathematics, but it’s much harder than English or history. Mathematics builds vertically; if you miss something, it’s very difficult to catch up.
“Also, with mathematics, everyone hits the wall. For the first time in your life, you don’t understand something the first time it’s presented. You turn to memorization, but that carries you only so far. A lot of people drop out of calculus because they have to synthesize and that’s a skill they don’t have much experience with.”
The key, says Rhoades, is to keep an open mind.
“At 17 or 18 years of age, just as you come to college, your brain is learning to reprocess information. If you keep your mind open, you can do things that you might not have been able to do in high school.
Good training for the heart
“But if you tell yourself you can’t do it, that’s a crutch to lean on. It’s not a valid excuse.”
The rewards are well worth the effort, he says.
“Much of mathematics is deterministic; you’re not dealing with people’s opinions but with factual material. Also, if something is true, it remains true, not like computer science or engineering, where the technology is constantly changing.
“And there’s a side benefit to studying mathematics whether or not you go on. When you approach any situation, you know how to get to the heart of the matter and focus on what’s important.
“That’s a very valuable skill, especially if you serve on a committee.”