Scientists Say: Topology

algebra: A field of mathematics that describes a way to think about certain relationships that will involve numbers. And not just any particular number, usually, but abstract expressions involving numbers. For instance, instead of saying “1 + 2 = 3” or “3 – 1 = 2,” algebra gives each number a letter to take its place. So it now reads something like a “a + b = c” or “c – a = b.” But any number can substitute for those letters as long as the values on each side of the equal sign are still true. In other words, “a” can be 100 and “b” can be 101 — as long as “c” = 201. Such expressions with different things on either side of an equals sign are known as algebraic equations.

clay: Fine-grained particles of soil that stick together and can be molded when wet. When fired under intense heat, clay can become hard and brittle. That’s why it’s used to fashion pottery and bricks.

computer model: A program that runs on a computer that creates a model, or simulation, of a real-world feature, phenomenon or event.

cosmologist: A scientist who studies the origin and development of the cosmos, or universe.

engineer: A person who uses science and math to solve problems. As a verb, to engineer means to design a device, material or process that will solve some problem or unmet need.

field: An area of study, as in: Her field of research is biology.

focus: (in behavior) To look or concentrate intently on some particular point or thing.

geometry: The mathematical study of shapes, especially points, lines, planes, curves and surfaces. Geometry can also refer to the defined shape of something (such as it had a very spherical geometry).

insight: The ability to gain an accurate and deep understanding of a situation just by thinking about it, instead of working out a solution through experimentation.

matter: Something that occupies space and has mass. Anything on Earth with matter will have a property described as “weight.”

model: A simulation of a real-world event (usually using a computer) that has been developed to predict one or more likely outcomes. Or an individual that is meant to display how something would work in or look on others.

morph: (in non-living systems) It refers to a thing, policy or activity that has undergone change, becoming something that looks or seems new and different.

Möbius strip: A famous “surface” in mathematics that has two sides but appears to have just one (because you can trace your finger from the outside to the inside and then continue on ending up on the outside again). Such a strip can be made by cutting a long, thin strip of paper, putting a half twist in it, and then attaching the ends together.

physicist: A scientist who studies the nature and properties of matter and energy.

theory: (in science) A description of some aspect of the natural world based on extensive observations, tests and reason. A theory can also be a way of organizing a broad body of knowledge that applies in a broad range of circumstances to explain what will happen. Unlike the common definition of theory, a theory in science is not just a hunch. Ideas or conclusions that are based on a theory — and not yet on firm data or observations — are referred to as theoretical. Scientists who use mathematics and/or existing data to project what might happen in new situations are known as theorists.

topology: (in math) The study of the properties of shapes and their relationships to each other. Shapes are related when they have similar properties even after deformation (such as bending, stretching, shrinking). They will not be similar if cut, torn or have had some pieces glued (or otherwise patched) onto it.

universe: The entire cosmos: All things that exist throughout space and time. It has been expanding since its formation during an event known as the Big Bang, some 13.8 billion years ago (give or take a few hundred million years).

warp: A change in the shape, usually due to some twisting or curving in a normally flat surface or plane. A piece of wet lumber may warp as it dries unevenly, causing it to bow or show a slight twist.