The Seven Secrets of a Beautiful Mind

The mathematician who dared compete with Fourier, aeronautical engineer, M.D., philosopher and teacher, Athanassios “Thanasis” Fokas wrestles with mathematical juggernauts

First Secret

“Do not solve a problem that someone else can solve.  After all, what is important is for science to advance. If someone else can solve it, science does not need you.”

“Thanasis Universalis,” as his closest friends call him, wrestles with math that has universal consequences.   From his time as an undergraduate student in aeronautics at Imperial College (1975) to his Ph.D. in applied mathematics from the California Institute of Technology (1979) and his M.D. from the University of Miami School of Medicine (1986), Fokas has done groundbreaking work in mathematics, mathematical physics, fluid mechanics, medical imaging and protein folding. 

These days, he divides his time between USC, the Academy of Athens and the University of Cambridge where he holds the Chair of Nonlinear Mathematical Science at the Department of Applied Mathematics and Theoretical Physics. At USC Viterbi, he is a visiting professor in the Ming Hsieh Department of Electrical Engineering.

What is it about Fokas that makes him such a unique thinker? A man whose computer-based algorithms in medical imaging can construct powerful images of the brain much faster and more accurately than commercial machines, but who does his work with pen and paper to the sound of Verdi’s Requiem.

Second Secret

“Choose problems based on aesthetics and universal importance, always seeking quality, using the deep interplay between beauty, simplicity and complexity as a criterion.”

In 1997, Fokas added an indispensable armament to the arsenal of tools that scientists and engineers can use to solve an entire class of problems. The Fokas Method has completely supplanted transform methods discovered in the 18th century and used for over 250 years to solve linear partial differential equations. Today, professors teach it at a growing number of universities, including USC. His lifelong friend, USC Viterbi Dean Yannis Yortsos, calls Fokas “the ultimate interdisciplinary scientist.”

Third Secret

“Conventional mathematical wisdom says compete with your contemporaries, but never, ever compete with the classics, for nothing escapes the classics. But that is conventional wisdom.”

“Dr. Fokas is a good example of how deep thinking and deep thinkers rise above their basic disciplines and contribute to the common intellectual good,” said neuroscientist Antonio Damasio, director of the Brain and Creativity Institute at USC and the author of “Self Comes to Mind: Constructing the Conscious Brain.”

Take Fokas’s collaboration with his mentor, Israel Gelfand, one of the giants of 20th-century mathematics whose research laid the framework for the imaging abilities of MRI and CT scanners. While working with Gelfand on protein folding, Fokas discovered unexpected topological properties in an important class of proteins called beta proteins. Following their seminal works, scientists can now predict the 3-D structure of these proteins with a success rate of 80 percent, accelerating more effective, targeted drug designs. 

Fourth Secret

“Explore different areas. The statement that one cannot be both deep and broad is a myth.  It allows one to make remote associations, and thus to understand the deeper essence
of things.”

The work with Gelfand led Fokas to unearth the deep mathematics that play a crucial role in SPECT medical imagining technology and Magnetoencephalography (MEG) used to map brain activity.  After nearly 15 years of research, his group at the Academy of Athens can now reconstruct SPECT images faster and more accurately than existing commercial systems.

“He doesn’t care where one science ends and the other begins,” is the way Nicholas Protonotarios, of the Center for Mathematics and Medical Imaging at the Academy of Athens, described Fokas’s work. “He treats mathematics, physics, engineering, biology, medicine and neuroscience as a continuum. That is the beauty of Fokas.”

Fifth Secret

“Set aside two months in a year away from mathematics, but use this time productively. During this period, I only read books in four categories: neuroscience, music, painting, and the ancient Greeks.”

For Fokas working on one open problem in a particular field can surreptitiously lead to solving one in another. The result? Math beautifully reveals a hierarchy of imperatives in our understanding of the universe – each success buys an admission ticket to a more difficult problem.

While attempting to connect the Fokas Method to the Riemann Hypothesis — the most celebrated open problem in the history of mathematics — Fokas recently achieved a breakthrough for the Lindelöf Hypothesis, a slight variant of Riemann, a feat that would have compelled many mathematicians to trade their souls with Mephistopheles for a proof. But this does not satisfy Fokas.

Ten years ago, renowned physical chemist Costas Vayenas proposed that the force that keeps the three elementary particles in protons and neutrons together is actually relativistic gravity, not strong force as universally agreed. Fokas, in collaboration with experts in general relativity, is now attempting to derive Vayenas’s formula. If he succeeds, an alternative, simpler theory to two of the fundamental forces of nature, strong force and weak force, will emerge. It will represent one of the most spectacular breakthroughs in the history of natural sciences since Albert Einstein’s special relativity in 1905 and Niels Bohr’s model of the H atom in 1913.

Sixth Secret

“Be overly optimistic.  It is a moral obligation to enjoy the great gift of life. Be mentally resilient because failures are inevitable and crisis will come. The question is not what happens to you but what you do with what happens to you.”

Crisis did come to Fokas in the summer of 2017 when his heart literally came under the knife. Yet, with astonishing optimism and untapped reserves, he continued to work on open problems while recovering from a 7.5 hours heart surgery at Yale University. In Fokas’s mind, there is no requiem for an unsolved problem.

“There’s an unbelievable drive in him,” said his friend Evangelos Angelakos, shipping tycoon and former mayor of the island of Oinousses. “He won’t let go. He pulls from a reservoir of inspired knowledge that includes opera, painting and philosophy and he bases his life on truth and sharing. That is his secret.”

Seventh Secret

“Protect your creative time at all cost. I protect my time as I protect my three children.”

The work of a mathematician is monastic in nature. Fokas essentially does not watch TV and keeps his emails very short.  What remains of his time, he spends investing in people.  He’s classical in this way. In the expedition for knowledge, Fokas believes you can’t hold on to science with one hand and technology with the other so that you have no hand left to reach for the human spirit which he believes is “the greatest expedition.”