Keep trying to solve harder and harder problems...

Professor Mladen V. Wickerhauser - mathematician inside Green's Cave along the Meramec River in Missouri, 2006.

Mladen V. Wickerhauser is Croatian American mathematician working at Washington University St. Louis, Missouri. His field of professional interestes is in the wavelet analysis and signal processing. In March 2009 he visited his native Zagreb and delivered a lecture at the Department of Mathematics, PMF, University of Zagreb. Dr. Željko Hanjš recently made an interview with him.

Q. Dear Professor Wickerhauser, please, tell us something about your family. We know that your great-uncle Teodor was distinguished Croatian surgeon, one of the founders of the Zagreb Medical Faculty, and honorary citizen of the city of Zagreb.

A. My great-uncle Teodor not only helped found the Zagreb Medical School in 1919, he also brought the first X-ray machine to Zagreb, so it seems he appreciated medical technology. He is listed in the Zagrebački Leksikon and of course in any history of the Medical School. What many may not know is that he was a famous amateur hunter. I share his love of the outdoors and go camping and canoeing whenever I can.

Dr. Teodor Wickerhauser (Zagreb, September 4 1858 - Zagreb, March 13 1946), and his street existing in Zagreb since 1968.

Wickerhauser street is quite near the Faculty of Medicine and not far from the Mathematics Department in Zagreb. Photo by Dr. Željko Hanjš.

My grandfather was Teodor's younger brother Victor, who served in the Austro-Hungarian navy and rose to the rank of Admiral. He is mentioned in the Pomorska Enciklopedia. He saw action in China during the Boxer Rebellion and commanded the Danube Flotilla during the First World War, protecting food shipments coming from Romania and Ukraine. See Lawrence Sondhaus, "The naval policy of Austria-Hungary, 1867-1918." Later he taught classes and was the assistant commander at the Naval Academy in Rijeka. I still have his ceremonial sword and portrait.

A Lecture Hall of the Faculty of Medicine of the University of Zagreb, bearing the name of Teodor Wickerhauser. Photo by the courtesy of Eugen Divjak, student of the faculty.

Because he traveled so much, my grandfather did not have as great an influence on Zagreb as my great-uncle Teodor nor my great-aunt Nathalie, who in 1892 founded the Agramer Mädchen-Lyzeum in Gornji Grad. My father's twin brother, Professor Teodor Wikerhauser, prolongs this tradition as a current member of the Croatian Academy of Sciences and Arts (HAZU)[1].

My parents met and married in Zagreb, where I was born in 1959. They moved to the United States in 1963, intending to stay only one year. After living in the USA for 43 years, they finally did move back to Zagreb. From their apartment it is a short uphill walk to Wickerhauserova ulica, named after my great-uncle the surgeon. Unfortunately, the houses there may be too expensive for any current Wickerhauser to buy!

Mladen V. Wickerhauser biking with his daughter.

Q. At your early age you went with your parents to live in the USA. Can you describe your schooling there from the primary school till the University. What do you remember best from that period?

A. I was four years old when my family moved to the United States in 1963. I naturally spoke Croatian, and could even read a little. We first came to Chicago, then moved to Los Angeles. It took me about one month to learn enough English to play with the neighborhood kids. I started kindergarten in North Hollywood, California, at Toluca Lake Elementary School. There was a table full of puzzles and magnets and gyroscopes in the classroom, and the teacher, Mrs Grace, allowed us the freedom to play with such things all we wanted, once we had completed the basic lesson.

Toluca Lake stayed open during the Summer so that children would have a safe place to play. One thing I remember fondly is a huge barrel of wooden dominos that we would use to make vast structures with built-in self-destruct mechanisms.

In second grade I took an aptitude test and was advanced one year into third grade. However, since second graders were dismissed earlier than third graders, I and another lucky pupil were allowed to leave in the middle of arithmetic, the last class of the day. As a result, we escaped much of the tiresome, repetitive practice calculation then used to teach multiplication and division. But we never became really good at arithmetic, either.

My family moved to the Washington, DC area in the middle of third grade, and I started attending Catholic elementary school. The mathematics classes were taught from little pamphlets with almost no content, so after a while I was excused from the classes and allowed to read whatever I wanted in the school library. I liked books on games and puzzles and "How Things Work" plus plenty of science fiction and adventure stories.

In seventh grade, the Catholic school's mathematics curriculum was greatly improved by the introduction of new books sponsored by the Mathematical Association of America (MAA). I also had excellent seventh and eighth grade teachers who made good use of the better books. We learned to solve linear and quadratic equations and to reason with inequalities. This required my full attention and thus, unfortunately, ended my little vacations in the library.

Concentration... paying close attention at a lecture in 2007.

My parents put me back into public school for ninth through twelfth grades because public schools had more money and consequently better instruction in advanced subjects. Our calculus teacher at Walter Johnson High School, for example, had a Ph.D., as did the senior French language teacher. Many other teachers had Masters degrees, and there were well-equipped chemistry, physics, and biology laboratories. Some of the students were highly motivated children of researchers at the National Institutes of Health, the Goddard Space Flight Center, the IBM Corporation, and so on, so there was plenty of academic competition.

Walter Johnson gave its students a free hour in the middle of the day to do independent work. A few friends and I would spend it in the mathematics laboratory where there were puzzles, games and some advanced high-school-level books published by the MAA. It also had a computer terminal and programmable calculators. It was the beginning of the computer age and we were taught FORTRAN programming on a local company's computers when they were not predicting satellite orbits. I was very lucky to have such opportunities so early.

After high school I went to the California Institute of Technology, a very expensive private college, with the help of scholarships and government loans. Such money was easier to get in the late 1970s than it is today, when private colleges are even more expensive. I also worked part time as a computer programmer during my last year. It is good to have a marketable skill. I was paid well, but it still took me ten years to pay off my college debts.

Although my major subject was pure mathematics, I was required by Caltech to take courses in physics, chemistry, and engineering. Those courses proved very useful later when I started to work in applied mathematics. It may seem unimaginable today, but I was also one of the few mathematics Ph.D. students at Yale University who could write a computer program.

Q. What attracted you to study mathematics? Who incited you most to be interested in it. Did you participate in mathematical competitions during primary and secondary education?

A. Success on mathematics tests in seventh and eighth grades, when the revised curriculum actually contained some theorems and proofs, definitely drew me into the subject. In high school there were other kinds of competition as well: Math Team problem-solving races between schools, with trophies as prizes; an annual national test (the "MAA test") on which I once received the highest regional score; and the USA Mathematical Olympiad test on which I did not do so well. I also wrote a paper on "Pythagorean triples" for the Westinghouse (now Intel) Science Talent Search and received an honorable mention. I was already the strongest mathematics student in my high school, but these outside competitions motivated me to advance further. Winning them also earned me extra money for college tuition and books.

Mladen V. Wickerhauser, professor of mathematics at Washington University St. Louis, Missouri, born in Zagreb

The most important factor in my decision to study mathematics as a career was a Summer mathematics camp, HCSSiM[2], sponsored by the USA National Science Foundation (NSF) and held in 1975 at Hampshire College in Amherst, Massachusetts. About 50 high school juniors and seniors spent six weeks living with college mathematics professors, postdocs and graduate students, learning some number theory, non-Euclidean geometry, combinatorics, and other subjects accessible with only high school preparation. We mainly solved problems, but also socialized, ate lots of ice cream, played frisbee and did normal teenager stuff together to soften the stress of competition. There were International Mathematical Olympiad medalists among both students and faculty, so I got to meet some really strong problem solvers. Many of my campmates are now professors of mathematics and physics; some are very well known.

Q. Is the rest of your family interested in mathematics?

A. I have a maternal cousin Višnja who teaches mathematics but there is no one in my immediate family besides me. My sister Olga was also a very strong mathematics student in elementary and high school, but she studied languages in college instead. She later earned a Master's degree in horticulture and now teaches college chemistry. Both of my parents are chemical engineers, so pure mathematics must seem rather strange to them, but they never objected to my choice of career. My father appreciates the practical applications and the patents, at least. My ten-year-old daughter, Natalie, is pretty good at geometry and logic but dislikes arithmetic just as I did at her age.

Q. You are the author of several books, you have several patents, and you delivered numerous lectures. What are the most important achievements in your research and where are they applied? Who did you collaborate most successfully with?

A. My most significant collaboration has been with my mentor, Professor Ronald Coifman of Yale University. After I completed a doctoral dissertation on the existence and uniqueness of solutions to a nonlinear partial differential equation from fluid dynamics, he encouraged me to consider numerical solution methods based on wavelet Fourier analysis. This resulted in many joint papers and two patents. Our 1992 paper Entropy-based Algorithms for Best Basis Selection[3] is perhaps our most important work. It led to a custom image compression algorithm, called WSQ, used by the FBI to encode fingerprint images. The general design of such algorithms is described in my 1992 survey article, High-resolution Still Picture Compression[4]. But our fast algorithm for best basis selection has many other applications and has been cited in almost 400 later articles, a very large number for a mathematics result.

My most enjoyable "pure" result is published in a short 1993 note in the Comptes Rendus, Smooth Localized Orthonormal Bases[12]. It resulted from a flash of insight that occured while I was traveling from Paris to Beijing by way of Helsinki. I wrote the manuscript on the airplane and faxed it to the journal from the Helsinki airport, feeling like the hero in one of my elementary school adventure stories. Still, despite its "purity," one of my collaborators has used this idea in speech recognition software.

Q. In 2002 you obtained a very prestigious "Wavelet Pioneer Award" from the International Optics Society SPIE (Society of Photo-Optical Instruments Engineers, [18]) in Orlando, Florida. For what kind of achievements is it assigned?

A. The "Wavelet Pioneer Award" was established in 1997 with the first one going to Professor Stephane Mallat of Ecole Polytechnique. Since then it has been awarded annually at the SPIE meeting in Orlando, Florida, to an applied mathematician whose published results have proven especially useful in optical engineering. It comes with a plaque and a small honorarium. The selection committee consists of previous recipients plus some society officials. The SPIE is a huge society with many well-funded researchers working on some extremely difficult signal and image processing problems. The creation of such an award shows that our little branch of applied mathematics has grown strong enough to support more than its own weight.

I was greatly honored by the award in 2002, which cited the Entropy[3] and Smooth[12]papers plus my book, Adapted Wavelet Analysis from Theory to Software[13], as particularly pioneering contributions. Afterwards, being in Orlando, I visited Walt Disney World.

Q. Despite many obligations you keep contacts with your homeland and with our University, in particualr with Mathematics Departemnt of the Faculty of Natural Sciences and Mathematics in Zagreb. Recently you delivered a very interesting and well attended lecture. You are a memeber of several well known journals, including our scientific mathematical journal Glasnik Matematički, published in Zagreb. With which institutions, and in particular, with which professors do you have especially successful collaboration?

A. Being, speaking and understanding Croatian has made it easy for me to maintain ties with Croatian institutions. Besides Professor Hrvoje Šikić of PMF, with whom I have a joint publication, I have worked with Professors Ante Graovac and Tomislav Živković of the Ruđer Bošković Institute, and have been invited by Professor Mladen Kos to speak at the Fakultet elektrotehnike i računarstvo (FER) in Zagreb. As an associate editor of Glasnik Matematički, I have solicited manuscripts that I think would be of interest to the readership, including one from my very strong former Ph.D. student, Professor Morten Nielsen of the University of Aalborg, who is now collaborating with Professor Šikić.

My institution, Washington University in Saint Louis, has a research grant jointly with PMF, supported by both the NSF and the Croatian Ministry of Science. This has paid for international travel and conferences in Saint Louis and Zagreb. We were also pleased to host a Fulbright Scholar from PMF, Professor Damir Bakić, for one year. He and my two colleagues Professors Guido Weiss and Edward Wilson have several joint papers in wavelet analysis as a result. I am pleased that the ties between Saint Louis and Zagreb have grown though many common intellectual and personal interests besides just my own.

Q. Can you provide any advices for our secondary school students that are interested in mathematics and informatics?

A. First of all, keep trying to solve harder and harder problems. You earn the freedom to choose intellectual challenges in your career, a freedom that is the soul of our subject, by constant application of brain power and bold imagination. Get used to competition, too. Read the USSR Olympiad Problem Book by Shlarsky, Chentzov, and Yaglom, for example, or visit the American Mathematics Competitions[14] web site.

For the engineers: learn as much pure mathematics as you can. Even very abstract ideas are tools that fit some practical problems. Also, there is great satisfaction in completely solving a pure mathematics problem, something rarely achieved with messy applications. Pick a good, challenging book and thoroughly understand every theorem in it. One especially challenging example in English is Emil Artin's Galois Theory[15].

For the purists: learn how to use a computer well. It is not hard, and even if you find programming tedious, like arithmetic, knowing how to do it will help you communicate your ideas and keep you connected to the real world. Learn TeX[16] and use it for homework; set up a website for your math club; learn how to use Maxima[17] to compute indefinite integrals.

Finally, remember that all professional scientists collaborate. Make friends with others with whom you can work and study productively. Create a culture that you can enjoy.

Editorial Board Service of professor Wickerhauser: International Journal of Wavelets, Multiresolution and Information Processing (2002- ) Birkhauser "Applied Harmonic Analysis" book series (1996- ) Glasnik Matematički (1995- ) - Croatian scientific journal Journal of Fourier Analysis and Applications (1994- ) Journal of Applied and Computational Harmonic Analysis (1993- ) SIAM Journal on Mathematical Analysis (1993-97)

Professor Mladen V. Wickerhauser touring the downtown of Chongqing during a conference in May, 2004, with one of the student organizers from the National Logistical University.

Professor Mladen V. Wickerhauser awarding the 2004 SPIE "Wavelet Pioneer Award" to Dr. Henrique Malvar in Orlando, April, 2004.

We express our gratitude to professor Mladen V. Wickerhauser for permission to publish this interview for the readers of the CROWN. The Croatian translation of the article will appear in Matematičko-fizički list, Zagreb. Editor in chief of this journal specialized in mathematics and physics, and intended for secondary school students in Croatia, is Dr. Željko Hanjš from the University of Zagreb.

Formated for CROWN by prof.dr. Darko Žubrinić Distributed by www.Croatia.org . This message is intended for Croatian Associations/Institutions and their Friends in Croatia and in the World. The opinions/articles expressed on this list do not reflect personal opinions of the moderator. If the reader of this message is not the intended recipient, please delete or destroy all copies of this communication and please, let us know!