women-mathematicians-from-the-united-states

"I became kind of hooked on CS, but at that point I wasn’t contemplating jumping sideways into a CS career."

"It’s really [three- and four-dimensional shapes] that are exciting for me, but the study of these things is deeply linked with knot theory."

"I didn’t allow myself to work on it during the day,” she said, “because I didn’t consider it to be real math. I thought it was, like, my homework."

"“I think Brown is amazing in that people can put together different courses of study that reflect the kinds of things they’re interested in,Follow your instincts – you never know what you’re going to find.”."

"People don’t like to understand how systems work, particularly, I hope that in decision-making, people will use them as decision aids but not decision surrogates. This will require that our systems get much better at explanation."

"I noticed that they were talking about these cases the same way I talked about some examples."

"At some point, I wanted a break from being a student."

"I have had many wonderful students over the years. Many have gone on for their master's and doctorate degrees and that has been most rewarding for me."

"I used to prefer teaching to administrative work, but by the time I left teaching in 1995, the students cared about nothing but the grades and they didn't care how they got them. I believe in knowledge for knowledge's sake. But students now need a reason for everything. Everything has to be useful and entertaining. And they don't study."

"When the Library of Congress reached out to me, I was blown away…it was interesting to see that all the work that she had done was being recognized. It was really an honor…I never thought that someone in our family would be in the Library of Congress. And it’s just very exciting and I’m very grateful."

"I was always counting, weighing (measuring), locating items, and reasoning with customers."

"Ethnomathematics is the study of such mathematical ideas involved in the cultural practices of a people."

"Educators often overlook the importance of making emotional connection between students and the subject matter."

"Ultimately,” he adds, “if we are to maximize human potential, having a safe, welcoming environment is absolutely vital for knowledge generation and for learning. I’m certainly committed to making sure that the Swanson School and the University of Pittsburgh are the best places for individuals to come and do their best work"

"It was surreal watching the movie"

"Someone actually got what went on and how I felt"

"I could do a split, but another African American girl could do a flip,” she remembers. “There could only be one African American cheerleader, and I couldn’t do a flip, so that was that."

"Girls always come up here, but they never finish, and you won’t finish either.” Then he glanced at her hands and added: “Besides, you’re never going to be able to draw with those fingernails.”"

"Some of it may have been racial prejudice,” she says, “but they didn’t even have to get to racial because being a girl in engineering, being female, was enough"

"There’s always been magic in complex math calculations,” she says. “I used to think about problems all day long. Sometimes I solved the problems in my sleep. But then I would wake up and couldn’t think of what I did. So I trained myself to write down the solution immediately"

"As the first African American female graduate of the University of Pittsburgh School of Engineering in 1961, I did not have a role model,” she writes in part. “I understand that requests are not few, and her contacts must be very limited. If there is a way that a meeting can be arranged or a sighting, I am very interested. … Knowing of her has been an inspiration to me."

"Our first meeting in person took place at the IMU Congress in Nice in the summer of 1970. Together with my friend and collaborator András Hajnal we were eager to meet her, and this happened right after she arrived in Nice. Her first sentence to us was “I just proved that there is a Dowker space;” i.e., a normal space whose product with the unit interval is not normal. To appreciate the weight of this sentence, one should know that this meant she solved the most important open problem of general topology of the 1960s."

"A space has the shrinking property if, for every open cover {Va | a ∈ A}, there is an open cover {Wa | a ∈ A} with for each a ∈ A. lt is strangely difficult to find an example of a normal space without the shrinking property. It is proved here that any ∑-product of metric spaces has the shrinking property."

"Geometric topology was really the dominant new topological theme in the 1950's and differential topology in the 1960's. Algebraic topology did not take a back seat in either development. But something happened in the 1960's which had profound effect upon the part of topology we are concerned with. ... Paul Cohen proved that it is consistent with the usual axioms for set theory that the continuum hypothesis be false. In itself this theorem has few consequence in topology for there is very little one can do with not-CH alone. But the technique of proof, called forcing, has translations into Boolean algebra terms, into partial order terms, into terms which lead to remarkable combinatorial statements which are applicable to a wide variety of topological problems related to abstract spaces."

"The purpose of this paper is to construct (without using any set theoretic conditions beyond the axiom of choice) a normal Hausforff space X whose Cartesian product with the closed unit interval I is not normal. Such a space is often called a Dowker space. The question of the existence of such a space is an old and natural one ..."

"Souslin's conjecture sounds simple. Anyone who understands the meaning of countable and uncountable can "work" on it. It is in fact very tricky. There are standard patterns one builds. There are standard errors in judgement one makes. And there are standard not-quite-counter-examples which almost everyone who looks at the problem happens upon. S. Tennenbaum and others have shown that that it is consistent with the axioms of Zermelo-Fraenkel set theory that Souslin's conjecture be either true or false."

"We must include in any language with which we hope to describe complex data-processing situations the capability for describing data. We must also include a mechanism for determining the priorities to be applied to the data. These priorities are not fixed and are indicated in many cases by the data. Thus we must have a language and a structure that will take care of the data descriptions and priorities, as well as the operations we wish to perform. If we think seriously about these problems, we find that we cannot work with procedures alone, since they are sequential. We need to define the problem instead of the procedures. The Language Structures Group of the Codasyl Committee has been studying the structure of languages that can be used to describe data-processing problems. The Group started out by trying to design a language for stating procedures, but soon discovered that what was really required was a description of the data and a statement of the relationships between the data sets. The Group has since begun writing an algebra of processes, the background for a theory of data processing. Clearly, we must break away from the sequential and not limit the computers. We must state definitions and provide for priorities and descriptions of data. We must state relationships, not procedures."

"Admiral Hopper, ... is the first woman to receive America's highest technology award as an individual. The award recognizes her as a computer pioneer, who spent a half century helping keep America on the leading edge of high technology."

"From then on, when anything went wrong with a computer, we said it had bugs in it."

"At present, we're putting on paper a lot of stuff that never needed to be on paper. We do need to keep the records. But there isn't any reason for printing them. The next generation growing up with the computers will change that."

"I handed my passport to the immigration officer, and he looked at it and looked at me and said, "What are you?""

"In total desperation, I called over to the engineering building, and I said, "Please cut off a nanosecond and send it over to me.""

"At the end of about a week, I called back and said, "I need something to compare this to. Could I please have a microsecond?""

"There's something you learn in your first boot-camp, or training camp: If they put you down somewhere with nothing to do, go to sleep — you don't know when you'll get any more."

"I had a running compiler and nobody would touch it. ... they carefully told me, computers could only do arithmetic; they could not do programs."

"I've always been more interested in the future than in the past."

"I've received many honors and I'm grateful for them; but I've already received the highest award I'll ever receive, and that has been the privilege and honor of serving very proudly in the United States Navy."

"[The Computer] was the first machine man built that assisted the power of his brain instead of the strength of his arm."

"They're going right to building them bigger and bigger and faster and faster. They'd do much better to build a system of computers and have them operate in parallel. We'd get much more done, faster. (…) My analogy is that back in the early days of this country, when they moved heavy objects around, they didn't have any Caterpillar tractors and they didn't have any big cranes. They used oxen. And when they got a great, big log on the ground and one ox couldn't move it, they didn't try to grow a bigger ox. They used two oxen."

"It's just like planning a dinner. You have to plan ahead and schedule everything so it's ready when you need it. Programming requires patience and the ability to handle detail. Women are 'naturals' at computer programming."

"Life was simple before World War II. After that, we had systems."

"Humans are allergic to change. They love to say, "We've always done it this way." I try to fight that. That's why I have a clock on my wall that runs counter-clockwise."

"We're flooding people with information. We need to feed it through a processor. A human must turn information into intelligence or knowledge. We've tended to forget that no computer will ever ask a new question."

"You manage things, you lead people. We went overboard on management and forgot about leadership. It might help if we ran the MBAs out of Washington."

"The wonderful thing about standards is that there are so many of them to choose from."

"The most dangerous phrase in the language is 'We've always done it this way!'"."

"Unsourced: One accurate measurement is worth a thousand expert opinions."

"A ship in port is safe; but that is not what ships are built for. Sail out to sea and do new things."

"If in doubt – do it."

"This saying has been in print already 1957, in Gerald Kershs "Fowler's End", p. 23."