"Mathematics is an aspect of culture as well as a collection of algorithms." (Carl B Boyer, "The History of the Calculus and Its Conceptual Development", 1959)
"An algorithm must be seen to be believed, and the best way to learn what an algorithm is all about is to try it." (Donald E Knuth, The Art of Computer Programming Vol. I, 1968)
"Scientific laws give algorithms, or procedures, for determining how systems behave. The computer program is a medium in which the algorithms can be expressed and applied. Physical objects and mathematical structures can be represented as numbers and symbols in a computer, and a program can be written to manipulate them according to the algorithms. When the computer program is executed, it causes the numbers and symbols to be modified in the way specified by the scientific laws. It thereby allows the consequences of the laws to be deduced." (Stephen Wolfram, "Computer Software in Science and Mathematics", 1984)
"Algorithmic complexity theory and nonlinear dynamics together establish the fact that determinism reigns only over a quite finite domain; outside this small haven of order lies a largely uncharted, vast wasteland of chaos." (Joseph Ford, "Progress in Chaotic Dynamics: Essays in Honor of Joseph Ford's 60th Birthday", 1988)
"In brief, an algorithm is a systematic way of performing a certain task. […] The algorithmic complexity of a problem depends therefore on the availability of efficient algorithms to handle the problem." (David Ruelle, "Chance and Chaos", 1991)
"On this view, we recognize science to be the search for algorithmic compressions. We list sequences of observed data. We try to formulate algorithms that compactly represent the information content of those sequences. Then we test the correctness of our hypothetical abbreviations by using them to predict the next terms in the string. These predictions can then be compared with the future direction of the data sequence. Without the development of algorithmic compressions of data all science would be replaced by mindless stamp collecting - the indiscriminate accumulation of every available fact. Science is predicated upon the belief that the Universe is algorithmically compressible and the modern search for a Theory of Everything is the ultimate expression of that belief, a belief that there is an abbreviated representation of the logic behind the Universe's properties that can be written down in finite form by human beings." (John D Barrow, New Theories of Everything", 1991)
"Algorithms are a set of procedures to generate the answer to a problem." (Stuart Kauffman, "At Home in the Universe: The Search for Laws of Complexity", 1995)
"Let us regard a proof of an assertion as a purely mechanical procedure using precise rules of inference starting with a few unassailable axioms. This means that an algorithm can be devised for testing the validity of an alleged proof simply by checking the successive steps of the argument; the rules of inference constitute an algorithm for generating all the statements that can be deduced in a finite number of steps from the axioms." (Edward Beltrami, "What is Random?: Chaos and Order in Mathematics and Life", 1999)
"Heuristics are rules of thumb that help constrain the problem in certain ways (in other words they help you to avoid falling back on blind trial and error), but they don't guarantee that you will find a solution. Heuristics are often contrasted with algorithms that will guarantee that you find a solution - it may take forever, but if the problem is algorithmic you will get there. However, heuristics are also algorithms." (S Ian Robertson, "Problem Solving", 2001)
"The vast majority of information that we have on most processes tends to be nonnumeric and nonalgorithmic. Most of the information is fuzzy and linguistic in form." (Timothy J Ross & W Jerry Parkinson, "Fuzzy Set Theory, Fuzzy Logic, and Fuzzy Systems", 2002)
"Knowledge is encoded in models. Models are synthetic sets of rules, and pictures, and algorithms providing us with useful representations of the world of our perceptions and of their patterns." (Didier Sornette, "Why Stock Markets Crash - Critical Events in Complex Systems", 2003)
"Swarm Intelligence can be defined more precisely as: Any attempt to design algorithms or distributed problem-solving methods inspired by the collective behavior of the social insect colonies or other animal societies. The main properties of such systems are flexibility, robustness, decentralization and self-organization." ("Swarm Intelligence in Data Mining", Ed. Ajith Abraham et al, 2006)
"The burgeoning field of computer science has shifted our view of the physical world from that of a collection of interacting material particles to one of a seething network of information. In this way of looking at nature, the laws of physics are a form of software, or algorithm, while the material world - the hardware - plays the role of a gigantic computer." (Paul C W Davies, "Laying Down the Laws", New Scientist, 2007)
"An algorithm refers to a successive and finite procedure by which it is possible to solve a certain problem. Algorithms are the operational base for most computer programs. They consist of a series of instructions that, thanks to programmers’ prior knowledge about the essential characteristics of a problem that must be solved, allow a step-by-step path to the solution." (Diego Rasskin-Gutman, "Chess Metaphors: Artificial Intelligence and the Human Mind", 2009)
"Programming is a science dressed up as art, because most of us don’t understand the physics of software and it’s rarely, if ever, taught. The physics of software is not algorithms, data structures, languages, and abstractions. These are just tools we make, use, and throw away. The real physics of software is the physics of people. Specifically, it’s about our limitations when it comes to complexity and our desire to work together to solve large problems in pieces. This is the science of programming: make building blocks that people can understand and use easily, and people will work together to solve the very largest problems." (Pieter Hintjens, "ZeroMQ: Messaging for Many Applications", 2012)
"These nature-inspired algorithms gradually became more and more attractive and popular among the evolutionary computation research community, and together they were named swarm intelligence, which became the little brother of the major four evolutionary computation algorithms." (Yuhui Shi, "Emerging Research on Swarm Intelligence and Algorithm Optimization", Information Science Reference, 2014)
"Again, classical statistics only summarizes data, so it does not provide even a language for asking [a counterfactual] question. Causal inference provides a notation and, more importantly, offers a solution. As with predicting the effect of interventions [...], in many cases we can emulate human retrospective thinking with an algorithm that takes what we know about the observed world and produces an answer about the counterfactual world." (Judea Pearl & Dana Mackenzie, "The Book of Why: The new science of cause and effect", 2018)
"Algorithms describe the solution to a problem in terms of the data needed to represent the problem instance and a set of steps necessary to produce the intended result." (Bradley N Miller et al, "Python Programming in Context", 2019)
"An algorithm, meanwhile, is a step-by-step recipe for performing a series of actions, and in most cases 'algorithm' means simply 'computer program'." (Tim Harford, "The Data Detective: Ten easy rules to make sense of statistics", 2020)
"Big data is revolutionizing the world around us, and it is easy to feel alienated by tales of computers handing down decisions made in ways we don’t understand. I think we’re right to be concerned. Modern data analytics can produce some miraculous results, but big data is often less trustworthy than small data. Small data can typically be scrutinized; big data tends to be locked away in the vaults of Silicon Valley. The simple statistical tools used to analyze small datasets are usually easy to check; pattern-recognizing algorithms can all too easily be mysterious and commercially sensitive black boxes." (Tim Harford, "The Data Detective: Ten easy rules to make sense of statistics", 2020)
"Each of us is sweating data, and those data are being mopped up and wrung out into oceans of information. Algorithms and large datasets are being used for everything from finding us love to deciding whether, if we are accused of a crime, we go to prison before the trial or are instead allowed to post bail. We all need to understand what these data are and how they can be exploited." (Tim Harford, "The Data Detective: Ten easy rules to make sense of statistics", 2020)
"Many people have strong intuitions about whether they would rather have a vital decision about them made by algorithms or humans. Some people are touchingly impressed by the capabilities of the algorithms; others have far too much faith in human judgment. The truth is that sometimes the algorithms will do better than the humans, and sometimes they won’t. If we want to avoid the problems and unlock the promise of big data, we’re going to need to assess the performance of the algorithms on a case-by-case basis. All too often, this is much harder than it should be. […] So the problem is not the algorithms, or the big datasets. The problem is a lack of scrutiny, transparency, and debate."
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