Telephones and mathematics

Summary: Mathematicians have played key roles in efficiently managing telecommunication networks and developing newer and more powerful phones and wireless networks.

Inventors Elisha Gray and Alexander Graham Bell independently designed devices to electrically transmit speech in the 1870s; however, Bell patented his device first. The American Bell Telephone Company created the first telephone exchange in 1877. A subsidiary company, American Telephone and Telegraph (AT&T), was incorporated in 1885 to develop and implement long-distance telephone service, and Bell Laboratories was founded in 1925 for research and development. Later, the labs would be managed by both AT&T and Lucent Technologies. The telecommunications industry has long relied on the contributions of mathematicians for its success and hundreds of companies continue to employ mathematicians to address the increasingly complex problems of twenty-first-century communication. They develop technology and algorithms for wired and wireless communication, which facilitate speed and efficiency for a variety of applications. They also research ways to increase security and prevent unauthorized listening or wiretaps. Some create business models or study issues such as customer satisfaction.

Finite Phone Numbers in an Expanding Communication Network

One notable mathematical problem of the early twenty-first century is assignment of phone numbers. In 2007, the Federal Communications Commission stated that 582 million of 1.3 billion available phone numbers in the United States were already assigned, increasingly to cell phones. Some mathematical models have suggested that exponential growth would exhaust the supply. Similar concerns have been raised about social security numbers and Internet addresses, since the number of digit permutations for any given string length is finite.

Cell Phones and Smartphones

Mathematical methods were also important in the development of cell phones and smartphones. In 1947, Bell Labs engineer W. Rae Young suggested a hexagonal tower arrangement for cellular mobile telephone systems, which was expanded upon by engineer Douglas Ring—though the technology did not exist to implement the idea until the 1970s. The Motorola DynaTAC 8000x, released in 1983, was the first truly portable cell phone. Cellular technology proliferated rapidly, and society has widely embraced smartphone technology. Described as a new generation of telephone, smart phones are, essentially, computers small enough to fit in a palm or pocket. The IBM Simon Personal Communicator, created by IBM and BellSouth and sold beginning in 1994, is cited as the first smartphone, while at the start of the twenty-first century, Apple’s iPhone and the Motorola Droid are very popular. The Android open-source operating system, which forms the basis for the Droid smartphones, was invented by computer scientist Andrew Rubin. It has been compared to Lego system building blocks because of the structure of its software solution stack, which many consider to be more compatible than the discretely packaged and isolated programs of some other operating systems.

Mathematics has played an increasingly large role in cell phone and smartphone service. Smartphones not only serve as cell phones for verbal or textual communication, they also play media, provide access to the Internet, serve as GPS and navigation devices, and run various other software. Electronic signals from smartphones carry digitized speech and data, requiring mathematical algorithms to construct and compress information, as well as to correct errors. Mathematicians and information theorists, such as David Huffman and Jorma Rissanen, developed compression techniques using concepts from probability theory and entropy. Mathematical methods from signal processing and graph theory prevent interference between multiple callers and help to establish networks that provide uninterrupted coverage. The International Mobile Telecommunications-2000 or 3G (third generation) is a global standard for mobile telecommunications introduced in 2000. It addresses critical issues such as data rates, bandwidth, frequencies, broadband compatibility, and issues of authentication, confidentiality, and privacy. As of 2010, scientists and mathematicians were developing further standards for mobile networks and devices, including a next generation 4G network. The Open Handset Alliance is a group of companies that develops and advocates for open standards for mobile devices.

Apps

As smartphone popularity booms, so do the tools developed for smartphones by computer scientists and others. Downloadable mobile applications (commonly called “apps”) are readily accessible for free or for purchase.

Many of them are aimed at education or academic subject areas, including mathematics. One set of apps offers the opportunity to practice with mathematics concepts and skills, like Math Flash Cards and Advanced Mental Math. Gamer-style apps like Math Ninja require players to answer challenge questions to advance. Other apps are electronic versions of mathematically based board games, like Mancala and Dominoes, while the popular game Tetris involves performing geometric transformations quickly to stack variously shaped objects, which is related to classical packing problems.

Bibliography

Horak, Ray. Telecommunications and Data Communications Handbook. 2nd ed. Hoboken, NJ: Wiley-Interscience, 2008.

Mercer, David. The Telephone: The Life Story of a Technology. Westport, CT: Greenwood Press, 2006.

Thompson, Richard. Telephone Switching Systems. Norwood, MA: Artech House Publishers, 2000.

Whitfield, Diffie, and Susan Landau. Privacy on the Line: The Politics of Wiretapping and Encryption, Updated and Expanded Edition. Cambridge, MA: MIT Press, 2010.