1. Introduction. Why am I writing on this topic? Partly because picturing of data is important. Partly because, if present trends continue, an increasing fraction of all mathematicians will touch—or come close to touching—data during the next few decades. Mathematicians have many advantages in approaching data—and one major disadvantage. Those mathematicians who might come close to data need to know their advantages from their disadvantages. Experience and facility with clear thinking—and with varied sorts of calculi that lead step-by-step from start to conclusion—knowledge of a variety of mathematical structures—even some of the more abstract are sometimes relevant to data—these are great advantages. The habit of building one technique on another—of assembling procedures like something made of erector-set parts—can be especially useful in dealing with data. So too is looking at the same thing in many ways or many things in the same way; an ability to generalize in profitable ways and a liking for a massive search for order. Mathematicians understand how subtle assumptions can make great differences and are used to trying to trace the paths by which this occurs. The mathematician's great disadvantage in approaching data is his—or her—attitude toward the words" hypothesis" and" hypotheses". I must diverge for a moment to tell a story, dating to about 1946. The late Walter Mayer, then a member of the School of Mathematics at the Institute for Advanced Study, and I were chatting at the AMS annual meeting at Rutgers. He was surprised that I was going to stay with Bell Laboratories, as well as with Princeton University. He explained how he had become involved with applied matters in Germany during World War I, and how happy he was to get back where," and I