Algorithms

Algorithms are instructions for accomplishing a goal and typically take the form of a step-by-step procedure. Given the conditions, these procedures can take various paths, increasing an algorithm's complexity. While traditional computer algorithms are programmed to account for all possible scenarios within a given process, machine learning systems build their own rules from data-driven patterns.

These include search algorithms to quickly process and find important information, cryptographic algorithms to secure communications, randomized algorithms—such as Monte Carlo simulations for estimating probabilities of outcomes—and greedy algorithms, which make optimal choices based on available data in a step-by-step fashion, as seen in navigation apps.

Muhammad ibn Mūsā al-Khwārizmī was a 9th-century mathematician whose works introduced Arabic numerals and the decimal-based numeral system to Europe. The term "algebra" came from the name of his mathematical treatise, "Al-Jabr," and the term "algorithm" came from his Latinized name, Algoritmi.

When translating a description of the Analytical Engine—a machine designed by English mathematician Charles Babbage to handle data entered via punch cards—Lovelace added her own notes, which included a procedure for calculating a sequence of values called Bernoulli numbers. She believed such a device could one day perform computations on non-numeric quantities and even compose music.

The device reads data, overwrites or ignores it, and then moves on to the next piece of data based on a set of programmed rules. By imagining this data as zeros and ones—binary that makes up computer code—Turing machines became the theoretical models for how any algorithm could be run on a computer if the procedure could be coded into a set of digital rules.

In 1956, Dutch programmer Edsger Dijkstra spent about 20 minutes developing an algorithm to demonstrate how computers could quickly determine the shortest route between Rotterdam and Groningen. Since then, modified versions of Dijkstra's formulation comprise the processing backbone of systems such as Google Maps and Apple Maps.

Algorithms can be designed to achieve a specific goal and gradually iterate on themselves based on how well they achieve it. Over time, these iterations transform the original algorithms as they become increasingly efficient, sometimes to the point where the optimized code is too complex to understand.

Found in search engines, hiring and college admissions tools, facial recognition systems, and other software, algorithms act on the rules they are programmed with, which may be authored by individuals unaware of their own biases. Algorithms based on limited, incomplete, or inaccurate data are more likely to inherit and propagate existing biases.

Secure communications rely on numeric keys generated by multiplying two enormous prime numbers together, and it is computationally impractical to determine these primes by trying every possible prime number. While Shor's algorithm can provide better guesses for this brute-force approach, it relies on a number that is difficult to determine on classical computers but easier to calculate using the simultaneous computations enabled by quantum superposition.

This interactive shows how different algorithms shift elements in a randomized set to order them from smallest to largest. By comparing the different procedures and their corresponding functions, users can explore how runtimes vary across algorithms that complete the same task.