A Personal Perspective on Mathematics Research in Industry Robert Calderbank

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Why should a corporation such as AT&T invest more than simply the sum of the constituent de- in fundamental research in the information sci- partments. ences? At a national level, why should the fed- Scientific curiosity that bridges different dis- eral government support research in mathe- ciplines is a great spur to innovation in indus- matics? We might look at the troubles of the try, but it also has a broader educational value. National Endowment for the Arts and conclude Mathematics education is essential to an in- that beauty alone may not be enough to guar- formed understanding of many aspects of so- antee taxpayer support. Indeed the common ciety, including fairness in voting and the means wisdom is that leadership in mathematics is es- that guarantee individual privacy in the infor- sential to the nation’s competitiveness in science mation age. It is important to the long-term fu- and technology. This chain of reasoning might ture of the profession that college students leave start from, say, fundamentals of probability and mathematics departments with an appreciation lead first to Shannon’s Information Theory, then of the different ways that mathematics touches to the capacity of particular channels, and finally their everyday experience. It is not enough to to the modes of transmission that approach stop at reforming the teaching of calculus. these limits. Within industry, the challenge facing Research Within industry it is essential that an Infor- Centers in the Information Sciences (which in- mation Sciences Center have a strategic influence clude mathematics, statistics, computer science, on the development of products and services. A and communication theory) is to breathe life center with about fifty researchers costs $10–$15 into these chains of reasoning. To be success- million per year, and this is difficult to justify ful a center needs to be a community where fun- on grounds of good public relations. Moreover, damental research and systems innovation draw it is not enough to wait for someone else to de- strength and inspiration from each other. This fine the application and to provide a technically is not so very different from the challenge fac- difficult mathematical analysis in support of ing university science and engineering faculties: that vision. Bricklaying is essential to building, how to fashion a community of scholars that is but architects are of greater value. Within acad- emia it is important that research in mathematics have a strategic influence on research in Robert Calderbank is a department head responsible other disciplines. For example, where mathe- for fundamental research in mathematics and communication theory at AT&T Research, Murray Hill, NJ. matics and physics connect it is important not His e-mail address is [email protected]. only to explore the equations that physicists

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have written down but to aspire to surprise the Within industry it falls to research to imag- physics community. ine the future. For example, telephony today in- volves synchronous transmission of speech and What constitutes fundamental research in in- limited volumes of data at kilobit rates. The ex- dustry? It would be foolish to attempt a list of pectation is that the network that prevails in the criteria, and any list is less interesting than a sin- next millennium will come to resemble more gle example. So let us consider the work of Peter Shor at AT&T Research on quantum computers the Internet with asynchronous transmission of and cryptanalysis. The problem of factoring in- sound and video as well as text files at megabit tegers is generally believed to be difficult to rates. The impact on society is likely to be enor- solve on classical computers, and this presumed mous; for instance, the retail industry is likely intractability is the basis for the RSA cryp- to be transformed as electronic commerce calls tosystem, which is in wide the economics of the shopping mall into ques- use. Shor has discovered fast tion. Mathematics research can play a strategic algorithms for solving this role in the definition of the next network. Algo- problem on a hypothetical rithms and optimization are essential to net- Within industry machine called a quantum work design; even a 5 percent improvement in computer. This machine, the layout of a new $3 billion network pays the it falls to originally proposed by the- rent on an Information Sciences Research Cen- research to oretical physicists, is de- ter for more than a decade. Probability, large de- signed to exploit quantum viations, and queueing theory are critical to fig- imagine the mechanical principles such uring out how to quantify quality of service and as superposition of states, how to charge for variable bandwidth—in short, future...It is also and nothing in the laws of to the design of new services. The mathematics physics seems to make of cryptography is essential to any guarantee of prudent for quantum computing impos- individual privacy and to the feasibility of elec- sible. Shor’s work has pro- tronic commerce. And most important of all, in mathematics vided the first example of telecommunications the penalty for failing to an important problem that a imagine the future is that you go out of business. research to quantum computer can Even companies such as Microsoft, which in contribute to solve much faster than a their early days prospered without investing in classical computer. This dis- research, are now forming research divisions. products and covery has energized the Of course it is also prudent for mathematics many research groups research to contribute to products and services services that around the world that are that will appear before the next millennium. attempting to discover Again we consider a particular example, the V.34 will appear whether a quantum com- modem standard for point transmission over puter can be built. Mathe- telephone lines at rates up to 34kb per second. before the next maticians work on problems Here data is encoded by a finite-state machine millenium. like this because of the that selects points from a finite-dimensional lat- magic of discovery, and tice, and mathematics also enters the algorithms quantum computing is as for shaping the signal constellation and for mit- imaginative and creative as igating intersymbol interference. Modem patent any piece of mathematics. revenue may amount to $10–$15 million after However, quantum computing also has ramifi- all the lawsuits have played out, but there can cations that need to be explored for the good of be more important strategic reasons for estab- society. If integer factorization can be done fast, lishing a standard. Here it created a new com- then one of the pillars supporting electronic modity market for modem chip sets, and AT&T- commerce will have been destroyed and new ME (Microelectronics) was able to significantly cryptosystems will have to be deployed. Appli- increase its market share. cations notwithstanding, scientific research of Fifteen years ago high-speed implementation this caliber does contribute to a corporate rep- of complex signal processing algorithms was utation for technical leadership, but in general impractical. Today it is an imperative, and there it is hard to put a dollar value on scientific rep- are great opportunities, for example, in personal utation. What, for example, was the value in the communication systems and wireless local ac- past of the Bell Labs name to AT&T? Neverthe- cess. Here classical analysis has a great deal to less, public perception of scientific leadership is contribute, since parts of harmonic analysis are important not just to marketing and standards only a small step away from these applications. activity within North America but to doing busi- There are also mass-market opportunities for ness in countries like China and India where sci- companies that combine strength in signal pro- entific partnership is often required. cessing with strength in integrated circuit design.

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One example is magnetic recording, which AT&T- ME has grown into a $250 million business over the last three years. In this case, the chief technical officer of AT&T-ME, Mark Melliar Smith, wanted to create a strategic partnership involv- ing AT&T-ME, selected hard disk manufacturers, and research in the mathematical sciences. The business advantage derived from sharing inno- vations in coding and signal processing with these customers is that of a preferred supplier. It is impossible to imagine a successful Re- search Center in the Mathematical Sciences that does not include statistics. Important applications include statistical methods for improving the yield of manufacturing processes. Here statistical analysis of patterns of defective chips on silicon wafers or of particle count data in clean- rooms can expose the root cause of manufacturing problems. The fact that companies are in- credibly secretive about yield is a good indicator of its importance. Within the telecommunications industry, a new challenge for statistics research is to make sense of massive data sets— for example, the 200 million telephone calls carried every day by the AT&T network. How to visualize this data, how to compute with it in real time—in short to understand how customers are using the network. The strategic purpose here is to contribute to the design of new services. Another purpose is early recognition of telephone fraud, which can save customers sig- nificant aggravation and the corporation tens of millions of dollars each year. Statistics research on large data bases is a truly interdisciplinary endeavor that requires leadership in both statistical methodology and computer science. The scarcity of students who can demonstrate leadership in both these fields is something we hope will improve with time. Industry and government have sound business reasons for investing in research in the mathematical sciences. The value of this in- vestment is strongly coupled to interdisciplinary research. It would benefit the profession as a whole and graduate students in particular if this idea were to take root in more university mathematics departments.

Acknowledgment I would like to thank Don Lewis and Andrew Odlyzko for their extensive and valuable com- ments on earlier drafts of this article.

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