Applications
Problems and deep mathematical theories that, in the beginning, were studied without thought of practical applications, have shown themselves to be crucial in practical contexts many decades later.
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was, until the 1960s, presented as being purely theoretical, but is today the building block for all transmission of secure information, specifically, in the fields of and . This is used every time you use your bank card or send an email.
, developed purely abstractly by George Boole in 1854, has found practical applications in digital and automation technology.
A part of the geometry called , which deals with points and lines "in perpetuity", was developed in the 1800s and is today a cornerstone in , which, for example, is used to program the movements of robots.
Another type of geometry called is concerned with concepts such as distance and areas in curved space and was develop early in the 1800s in connection with land surveys and map production. Through the entire 1800s the field was developed further as a separate purely theoretical field and this was a crucial foundation of . Einstein's theories, which were based largely from ideas from (in short, "geometry in which straight lines are replaced by curved ones", as on the sphere), were developed in the 1800s.
The field called studies properties of "space" that are preserved by deformations. The famous mathematical problem of the is one of the problems that have shaped the field. solution from 1736 was further developed in the subsequent centuries and topology is now crucial for theories in theoretical physics such as and . Wormholes are what makes it theoretically possible to "jump" from one place to another in space. String theory is a mathematical physics theory that has as it's goal to explain all natural phenomena and all of our universe with a single theory. Here one begins by assuming that all elementary particles are not point-particles, but strings that vibrate in a 10-dimensional universe. Four of these are the -dimensions that we see every day, and the remaining six are microscopic curled-up dimensions that appear to be required to have very specific mathematical properties, namely the properties of certain types of spaces that pure mathematicians have been studying since the 1950s and which have the name . Strings moving in these hidden dimensions carve out surfaces that are called after the German mathematician and the study of Riemannian surfaces in Calabi-Yau manifolds is a central theme in the fields in pure mathematics called and .
