## mathematics research

# Adding Up in Berlin

Mathematics is booming in the German capital. The city has a vibrant community of researchers and institutions, as well as companies that are finding highly lucrative commercial applications for the innovative research.

When Prince died suddenly in April last year, the Berlin research center Matheon issued a public statement. The mathematicians’ message was that the pop star’s life could have been saved. Yet that didn’t explain why a mathematics research group felt inclined to make the statement. Prince certainly didn’t die from a number.

However, Prince did die from a large dose of the painkiller fentanyl. The drug belongs to the family of opioids, and is similar to morphine but with devastating side effects. Its dangerous nature is very well known at the Zuse Institute in Berlin, perhaps better than anywhere else in the world. Over 10 years ago Marc Weber and his team began to work to free fentanyl of its detrimental side effects. Suddenly Prince’s death was very relevant to the work of a mathematics institute in Berlin.

The math boom in Berlin is very different from what is going on across the country in Bonn. While the Rhineland city is the stronghold of theoretical mathematics, Berlin thinks more in practical terms.

Nowhere else in the world do math institutions work so closely together. In the 1990s, the Matheon was founded to do the math research for key technologies. Later, additional centers were added, among them the Berlin Mathematical School, a globally unique graduate school which brings together researchers from all three of Berlin’s major universities. It attracts the best mathematicians from not only Germany but across the world.

While the Rhineland city is the stronghold of theoretical mathematics, Berlin thinks more in practical terms.

Even when the presidents of the universities weren’t getting along, the mathematicians maintained stimulating relations, regardless of which institute they represented. Applied mathematics developed in Berlin have been able to reach exceptional achievements, constructing whole new worlds. The magical worlds of “Harry Potter,” “The Matrix” and “Spiderman” were all computed in Berlin.

On a sunny morning, Mira Schedensack, is sitting at her computer with a pile of written notes spread out in front of her, enjoying one of her last days in Berlin. Her year as a guest lecturer at the Humboldt University’s faculty in Adlershof is almost up. Her next stop is Augsburg, but as she says goodbye to Berlin, her office door is open.

Her peers say 30-year-old Ms. Schedensack’s doctoral dissertation is worth four doctorates. And yet, her doctoral supervisor initially advised her against working on the subject of numerical approximation in computational mechanics, which hadn’t seen any groundbreaking innovations for decades. But Ms. Schedensack had a specific idea. She talks about it as if the audacity of her idea amused her more than anyone else.

To put it simply, she achieved what all mathematicians aspire to do: simplification. The streamlined solution. The way she thought about and tackled things, the computer models no longer drowned in parameters but were given a boost through a simpler language of algorithms. It is this optimization effect on which Berlin’s reputation is based.

Ms. Schedensack, born and raised in Hildesheim, a city in Lower Saxony, had not been considered a particularly exceptional mathematical talent. She was certainly good at math, but she initially majored in psychology at university in Freiburg. The surprise came in her second semester. It concerned multidimensional levels, and Ms. Schedensack found herself entering mathematical worlds beyond the power of imagination. For the first time in her life, she felt it was beyond her ability to think of things for which she had no mental image. She found herself entering a state of crisis. Half her fellow students dropped out.

Today, Ms. Schedensack says the experience was helpful. “It’s no longer surprising for me when I don’t understand something.” Especially since creating images from the abstract is an integral part of the inner workings of mathematics.

“You should imagine a bridge,” says Ms. Schedensack. To calculate the burden for every point of this bridge, mathematicians rely on differential equations that consistently only allow an approximation of the actual values. A body that buckles under stress can influence every point of the structure situated next to it, so that enormously high computing power results from these inter-dependencies.

Nevertheless, you never know exactly how the construction will behave in the end. There is no formula that tells engineers when the load limit has been reached.

Engineers first construct the bridges they dream of using a computer. Ms. Schedensack’s method now aims at creating the simples conditions possible for the simulations so that the computers don’t need to calculate endlessly to arrive at a realistic picture.

“There were no simple methods in this area, so I wanted to try something different.” She noticed when working with completely different mathematical problems that there was a trick to writing functions differently, with the so-called Helmholtz decomposition. The result would be the same, only the equation looked simpler. “No one had done that before.”

Günter Ziegle, a leading expert in geometry, tries to help explain Berlin’s particular position at the spearhead of mathematical research. Through his popular books, he has made a name for himself as someone who can explain mathematical problems in a way that is easily understood by the layman and also entertaining. He says that the traditional divide between theoretical and practical mathematics “was never taken seriously” in Berlin. For example, Mr. Ziegler’s institute, Matheon, focuses on interdisciplinary work and seeks to solve everyday problems. It positions itself as an ideas laboratory. Mr. Ziegler himself routinely answers the standard question, “can you explain that in two sentences?” with no.

Nevertheless, he is continually driven to those points of contact where computer technology changes people’s lives. Recently, Mr. Ziegler has taken an interest in social networks and how information can be gained from unstructured data flows for specific use in influencing buyer interest and viewing habits. It is, if you will, the mathematician’s campaign against the predominance of Facebook. After all, Mr. Zigler argues, Facebook is merely a mathematical construct.

Mr. Ziegler wishes to “separate pictures from the data,” to make visible people’s dependency on the algorithms operating behind the data. He is convinced that to see is to understand it.

The same thought motivated Hans-Christian Hege to form a company with three cohorts in 1986. Today the company, Mental Images, is considered one of the most important tech companies in Berlin. The physicist and mathematician wanted to make computer animation, which was still new at the time, available for scientists. The idea was to improve their ability to see what they were working on. “But that wasn’t financially viable,” Mr. Hege said. Mental Images switched to a more lucrative market, and produced animation for advertising films and Hollywood productions. Eventually, the co-founders had a falling out and the company became a subsidiary of Nvidia.

Soon after, Mr. Hege returned to the university to dedicate himself to his core interest, data visualization. Nothing is as complex as computing an image. The simple display of a leaf on a tree must take all physical conditions into account. The wind that causes it to rustle, the movement of light through the branches, the shadows of clouds. The huge cost and effort are “hardly justifiable,” says Mr. Hege, adding that in the end, it’s merely a picture. Nothing more.

There is the perception among some mathematicians that a picture is not needed for things we cannot imagine. Mr. Hege disagrees. He believes it makes sense to visually construct abstract things beyond our power of imagination, as it can lead to a harmonizing of scientific views. Although admittedly, he is already a step further.

A professor at the Zuse Institute, Mr. Hege is developing imaging techniques for medicine that would give surgeons a three-dimensional overview of the area of the body they are operating on, among other things. Anatomical corrections, such as to jaw structure, can also be modeled in advance. Data from ultrasound, CT and MRT images are fed into a simulation and put together into a complete spatial image. The computer is programmed so it can even learn to differentiate between bones and blood vessels, by recognizing qualitative discrepancy. It requires an enormous amount of work for people to learn to do this – and even then still are mistaken.

Mr. Hege’s research is unrivaled worldwide. He ascribes that to his PhD students, who are financed by Matheon, since “they do the work.” He himself, has founded three companies, through which he is preparing his findings for the market. Still, he adds, he is not the sort to push a thing to the point of being ready for marketing.

Which leads backs to the death of Prince and Marc Weber’s involvement. He is among that elite who can think things that do not exist. They must remain logical – a prerogative mathematicians have over futurists, although, as Albert Einstein once said, “If at first the idea is not absurd, then there is no hope for it.” That is a much quoted phrase among Berlin mathematicians. Their world, a world that is above all a completely inaccessible, abstract discipline for many people, revolves around ideas. And Mr. Weber had a really good one.

The mathematician made an intensive study of the dangerous nature of Prince’s painkiller, fentanyl, which is used as an anesthetic in emergency medicine. “It’s there,” says Mr. Weber, to “paralyze things.” That’s the reason, he says, more people die every year in the United States from prescribed painkillers than from heroin and cocaine.

Because paralyzing is what it “does everywhere,” says Mr. Weber. It affects the head, where it creates addiction, the stomach, which results in nausea, the circulatory system, which produces respiratory problems, and the intestine, which causes constipation. Many bodily functions are reset at a lower level, even though it is taken only as a way of numbing the pain.

10 years ago, that disparity deeply worried the Charité medical doctor Christoph Stein. The anesthesiologist had discovered that the suppression of pain was not only taking place in the head, but rather had docked in the inflammation site that was causing the pain. He was searching for a substance that lost its effect in areas not involved. He hoped that mathematicians could help.

Chemists have long been searching for a substance for suppressing pain that doesn’t cross the blood-brain barrier, without success. What was needed was a fentanyl whose molecules were modified in such a way that they dissolve in the PH-neutral area of the brain.

To find such a compound, Mr. Weber simulated several variations on the computer so the best ones could eventually be synthesized by a chemist. In this way, a suitable substance was found within a relatively limited time.

It has already worked magnificently on rats. Mr. Weber is waiting for the next step. But for Prince, it’s too late.

*This article originally appeared in Der Tagesspiegel. To contact the author: redaktion@tagesspiegel.de*

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