Degrees of Difficulty
The toughest nut to crack in five already tough fields.

What is the most difficult language to learn?

Rachel Hayes-Harb, Ph.D.
Assistant Professor, Department of Linguistics

Reading and writing aside, for much of the world the answer is probably Mandarin, according to Hayes-Harb, a specialist in second-language acquisition. “Mandarin Chinese is an extremely difficult language for native English speakers to learn to produce, because words have at least four different tones,” she says. “I’ve been teaching phonetics and phonology for a while, and I can’t tell the difference.”

To illustrate, she plays four audio files. A female voice repeats the word ma. Depending on the intonation—higher pitch, lower pitch, even an almost musical version—one might use this word to address one’s mother, or call her a horse. The hardest thing is learning to decipher these tones. “Speech perception is all about knowing what acoustic stuff to pay attention to, and what acoustic differences should be ignored,” says Hayes-Harb. “If you can’t hear the difference between two sounds, you have no information to use to produce them.”

Hayes-Harb compares human speech to blowing across the top of glass bottles filled with different levels of water; the tongue, jaw, and other moving parts shape the output. “In phonetics and phonology, the first thing we study is aerodynamics,” she says. Language pairs like Spanish and English use similar movements, so they feel familiar. An English speaker studying Mandarin feels like a left-handed baseball player learning to swing the bat right-handed.

The mind is shaped by the structure of one’s mother tongue, so remembering sound associations in the new language requires additional memory architecture—especially with Mandarin’s four tones. “Unfortunately, we just don’t know what it means to build new architecture,” Hayes-Harb says. “We don’t know how to quantify that. Not all new sounds are created equal.” Clearly.

Who is the most difficult philosopher to fathom?

Stephen Downes, Ph.D.
Professor, Department of Philosophy

How do you get into the deep thinking when you don’t even understand the words? You can’t, and that’s why Downes picks German philosopher Martin Heidegger (1889-1976). Born in rural Germany, Heidegger studied as a Jesuit before switching to philosophy. He favored pre-Socratic thinkers, and wrote abstract, labyrinthine tracts on the nature of being. “Part of my state of affairs is that I literally can’t understand the guy,” Downes says. “I’ve been told it helps if you can read German, but I’m not completely convinced.”

In fairness, Downes is an analytic philosopher, a descendant of those in the U.S. and U.K. who, in the early 20th century, rejected the continental idea that interpretation is the key to reading philosophical texts. “They would say that the work of continental philosophers was simply impossible to understand and therefore irrelevant,” says the British native, who earned his bachelor’s and master’s degrees in England. “Why can’t you just tell us what you mean?”

Grabbing a thick text off his bookshelf, Downes flips to an essay by another German philosopher, Rudolf Carnap (1891-1970), who cites Heidegger’s work as “bad metaphysics”: “What is to be investigated is being only and—nothing else; being alone and further—nothing; solely being, and beyond being—nothing. What about this Nothing? ... The Nothing itself nothings.” Whatever that means. “I can’t imagine that Heidegger actually thought that it was a good idea to make his work inaccessible,” Downes says.

Heidegger’s followers believe his problematic prose obscures more lucid concepts, but his past as a member of Germany’s National Socialist Party in the 1930s (which allowed him to keep his university position) may also make it easier to reject him. “Why don’t I work harder,” askes Downes, rhetorically. “I can come up with lots of reasons. The guy was in the Nazi Party. I don’t do metaphysics. I mean, I don’t have to understand every philosopher on the planet.”

What is the most difficult math problem to solve?

Aaron Bertram, Ph.D.
Chair, Department of Mathematics

Seven great open math problems remain, Bertram says (one, the Poincare Conjecture, was probably solved over the past few years). But the Riemann Hypothesis, which predicts the distribution of prime numbers, is the most irksome—because it works. “We all believe the Riemann Hypothesis is true, and much of mathematics is built on it,” Bertram says. “But we don’t have a proof, and that is profoundly disturbing.”

In ancient Greece, Bertram explains, Euclid first discovered the unlimited supply of prime numbers, each an integer that can only be divided by itself. But how are they spaced out? In 1859, Bernhard Riemann, the shy second son of a poor Lutheran pastor in Prussian Hanover, intuited a connection. “He turned a question about how prime numbers are distributed into a question about a particular function, and where this function has its zeroes,” Bertram says. “If this hypothesis is true, then we know an awful lot about prime numbers.”

But it was practically an afterthought, a conjecture used to support another argument, so Riemann didn’t even attempt a proof. The “zeta function” — ζ(s) = 1 + 1/2s + 1/3s + 1/4s + ... —has been tested for billions of imaginary prime numbers, like 1/2 + 6i. So far, so good. “Suppose you ask me how many prime numbers there are that are less than a trillion,” Bertram says. “This would get us very, very close to the correct answer. Shockingly close.”

Knowing that it works is not enough, though. And nobody has found a proof to support Riemann’s intuition. “Interesting problems in math are like this,” Bertram says. “They establish some kind of remarkable link that turns one problem into another problem that looks quite different. Maybe something you can solve.” But until that proof is found, there remains an element of doubt. “Who says the billionth one is not going to stray off this line? We need to know that.”

What is the most difficult surgical procedure to perform?

Sean J. Mulvihill, M.D.
Anderson Professor and Chair, Department of Surgery

Mulvihill calls this “a vain exercise,” because, he notes, today’s surgeons have little or no experience outside their specialty. But within Mulvihill’s specialty—treating pancreatic cancer—the most challenging is probably the Whipple procedure, used to remove tumors from the small, slippery pancreas, whose consistency “is a little bit stronger than Jell-O,” he says.

Cancer of the pancreas kills 98 percent of newly diagnosed patients within five years. And only 10 percent of newly diagnosed cases are found early enough to justify the Whipple procedure. Formally called a pancreaticoduodenectomy, the procedure requires the surgeon to dig through a pile of organs to the back of the abdomen, where the pancreas lies behind the colon, attached to a section of the small intestine. That piece is removed along with the tumor, leaving intact only about half of the pancreas, which is subsequently in need of a new drainage for the 3 mm duct through which it secretes its juice. “Imagine taking this quivering soft organ and putting stitches into it so that it’s held in a watertight way to the intestine,” Mulvihill says.

Further complicating matters, the pancreas makes enzymes that assist digestion by breaking down proteins. “You’ve heard of Adolph’s Meat Tenderizer? Those are enzymes from the pancreas,” Mulvihill says. These enzymes can attack new proteins formed as part of the healing process, causing leaks that can lead to fatal infections. “Eighty-five percent of the time, it heals properly. This 15 percent of the time is really disappointing.”

Fortunately, the situation is improving. “We’ve gotten better technically at sewing this thing together,” Mulvihill says, citing specialized suture materials and magnification loupes. “And we’ve gotten a lot better at discovering the problems post-operatively, with better CT scans to detect the leaking fluid, instead of letting [patients] languish and die from a bad infection.”

Mulvihill is careful to point out that there is an equivalent to the Whipple procedure in every field, from trauma to neonatal heart surgery, such as correcting congenital defects on a walnut-sized heart in a 2-3 kg newborn. “Pancreas surgery is hard, but there are many other things that are just as difficult, or more,” he says.

What is the most difficult cosmological conundrum to crack?

David Kieda, Ph.D.
Professor, Department of Physics

"Until about 1995, the big thing was dark matter,” says Kieda, who specializes in experimental high-energy astrophysics. “It’s part of a bigger puzzle now.” Dark matter refers to an unknown mass that explains unexpected gravitational behavior in single galaxies. But technological advances like the Hubbell Space Telescope have allowed scientists to track clusters of hundreds of distant galaxies, revealing behaviors that can only be explained by another unknown force: dark energy.

Streaming the lingo of his field with vague echoes of Star Trek, Kieda explains how the consistent light output of Type I-A Supernovas—white dwarves approaching the threshold to collapse into neutron stars—were cross-calibrated with the Hubbell’s red-shift line to show that the universe is not only expanding, but is also accelerating. “If you throw a ball up in the air, it slows down as it moves away,” he says. “The universe was thrown up in the air, but then it starts to actually accelerate. So something else is pushing those distant galaxies. That’s dark energy.”

Where does it come from? What are its characteristics? The only way to find out is by developing new technologies to look farther into the past. “The effects of dark energy get more pronounced as you move farther back in time, back toward the Big Bang,” Kieda says. “You can look at finer detail in the supernova that are appearing. So there’s a push to build bigger infrared telescopes to extend these supernova surveys.”

The more we learn, the less we know. About 75 percent of the universe is composed of dark energy; another 21 percent is dark matter. But only about 4 percent is made of the luminous matter we are aware of—and that’s more than we knew we were aware of. “One percent is missing,” Kieda says. “Maybe it’s just massive objects, Jupiter-sized things that we haven’t found yet. That’s a minor problem.”