This section concerns contributions to the development of information science and technology at its logical (as opposed to its hardware) level.  Specifically, this section deals with areas such as computation theory, artificial intelligence, the statistical theories of information, communication, and systems control, cryptography, operations research, computer and network architectures, and algorithm and software design.  The general level of this contribution is reflected in the current ~45% Jewish membership in the Computer and Information Sciences division of the US National Academy of Sciences and in the percentages of Jewish recipients shown below for several of the most prestigious awards in the field.  Two of the four individuals generally recognized to have been the principal architects of the Information Age were the Jewish mathematicians Norbert Wiener and John von Neumann.¹

• Jewish Computer and Information Scientists
  
• Jewish Recipients of the ACM A.M. Turing Award in Computer Science (30% of recipients)
• Jewish Recipients of the IEEE C.E. Shannon Award in Information Theory (33% of recipients)
  
• Jewish Recipients of the John von Neumann Theory Prize in Operations Research (40% of recipients)
• Jewish Recipients of the EATCS/ACM Kurt Gödel Prize in Theoretical Computer Science (44% of recipients)
• Jewish Recipients of the ACM/IEEE Donald Knuth Prize in the Foundations of Computer Science (45% of recipients)
  
• Jewish Recipients of the ACM Paris Kanellakis Theory & Practice Award in Computer Science (54% of recipients)
• Jewish Recipients of the IMU Abacus Medal (Rolf Nevanlinna Prize) in Computer & Information Science (55% of recipients)

Some of the more notable Jewish contributions are listed below.  (The names of non-Jewish scientists and engineers mentioned in the accompanying discussion have been denoted with the superscript "+" in order to avoid confusion.)

• The interpretation of thermodynamic entropy as an information metric by Leo Szilard.  Szilard's 1929 analysis of the Maxwell's demon paradox "is now considered to be the earliest known paper in what became the field of 'information theory' in the 1950s and 1960s." ²  Other important information metrics were formulated by John von Neumann,  Alfréd Rényi, Solomon Kullback, and Richard Leibler.  The von Neumann entropy, e.g., is the quantum generalization of Szilard's classical information measure and is one of the fundamental concepts in quantum information theory.

• The introduction of the diagonal argument proof method by Georg Cantor*.  This method is central to the derivation of the incompleteness and noncomputability results of Gödel⁺, Turing⁺, Church⁺, and Post that lie at the foundation of theoretical computer science.  In a 1936 paper, Emil Post described a mechanical definition of computation, known as the Post machine, which is equivalent to the Turing machine introduced by Alan Turing⁺ in a paper that appeared several months later.  Post had understood the undecidability implications of such a definition as early as 1921, but had hesitated to publish and lost priority to Gödel⁺, who approached the problem from a very different perspective in his 1931 paper.  Post was also one of the four principal founders of the theory of recursive functions, which is of immense importance in theoretical computer science.³

• The design of Colossus, the first all-electronic, digital, programmable computer by Max Newman*.  Although Colossus was not a general purpose computer and had only limited programmability, it represented an important milestone.  Newman, a Cambridge University professor of mathematics, headed the "Newmanry," a special code-breaking unit at Bletchley Park in England during World War II.  Colossus was designed and built to break the German Lorenz cipher, which was used by the Nazi high command to encrypt its highest priority communications.  The Colossus machines (whose physical design and construction was carried out by a team working under the electrical engineer Tommy Flowers⁺) played a critical role in securing Allied victory in Europe and were influential in the post-war development of computers in England.⁴  (Contrary to what is sometimes claimed, Alan Turing⁺, who was Newman's protégé, had relatively little direct involvement with Colossus, although his ideas were extremely influential.  Newman later declined to become "Sir Max Newman" in protest against the treatment accorded Turing⁺ by the postwar British government.)
  

• The design of the logical architecture employed in virtually all modern computers by John von Neumann.  The von Neumann architecture was incorporated into the design of EDVAC, the first all-electronic, binary, stored-program, general purpose computer.⁵  Von Neumann's 1946 paper "Preliminary Discussion of the Logical Design of an Electronic Computing Instrument" has been described as "the most influential paper in the history of computer science ... the ideas it contains, collectively known as the von Neumann machine, have provided the foundation for essentially all computer system developments since that date." ⁶  Von Neumann also invented the theory of system fault tolerance and the cellular automata  model of computation.  The universal von Neumann constructor, a generalization of the universal Turing machine that emerged out of von Neumann's theory of self-reproducing automata, is one of the foundational concepts in the field of molecular nanotechnology.

• The invention of parallel supercomputing architectures by Stephen Unger, Daniel Slotnick, David Schaefer, and Włodzimierz Holsztyński.  Unger, Slotnick, Schaefer, and Holsztyński are four of the "eight men [who] dominate the history of SIMD computer architectures." ⁷  SIMD (single instruction, multiple data) refers to the basic parallel processing technique employed in the earliest supercomputers.⁸  Unger was the first to propose and explore such architectures in the late 1950s.  Slotnick designed SOLOMON in the early 1960s and built the first parallel processing prototypes.  He was later the architect of Illiac IV, the first important parallel supercomputer, which had up to 256 processing elements.  Built with 64 processing elements in the early 1970s with ARPA (now DARPA) funding and operated by NASA, Illiac IV remained the world's fastest computer until its shutdown in 1981.  In the late 1970s and early 1980s, Schaefer initiated and managed the development of NASA's Massively Parallel Processor (MPP), the first truly massively parallel supercomputer, with 16,384 processing elements.  Holsztyński designed the Geometric-Arithmetic Parallel Processor (GAPP) in 1981.  GAPPs with hundreds of thousands of processing elements are used today in real-time video image processing applications such as image enhancement and noise reduction, video data compression, and format and frame rate conversion.
  

• The co-discovery of NP-completeness by Leonid Levin.  Levin  and Stephen Cook⁺ independently discovered and proved what is now referred to as the Cook-Levin theorem, the central result concerning the P = NP? question, which is the major open problem in theoretical computer science.  Richard Karp introduced the terms "P" and "NP" and defined NP-completeness (although not the term itself) in its present form.  He also identified the decision problem formulations of many well-known, combinatorially intractable problems as being NP-complete.  Levin, Karp, and Manuel Blum are considered to be three of the six founders of the field of computational complexity theory.

• The invention of context-free languages by Noam Chomsky.  This work was based on Emil Post's theory of production systems in mathematical logic.  It is the basis of the BNF notation widely used to specify the syntax rules of programming languages.  Chomsky's hierarchical classification of formal languages initiated the field of formal language theory in computer science.

• The co-invention of BASIC by John Kemeny.  Kemeny and Thomas Kurtz⁺ developed this popular programming language.  At least one-third of the nine-person team that developed FORTRAN under John Backus⁺ at IBM were Jewish.  Also at IBM, Adin Falkoff collaborated with Kenneth Iverson⁺ on the design and development of the array processing language APL (acronym for "A Programming Language").  Four of the six principal designers of COBOL, Howard Bromberg, Norman Discount, Jean Sammet, and William Selden, were Jewish.  COBOL was used to run an estimated 80% of the world's business systems at the turn of the century.  Although its usage has been in gradual decline since then, it is still widely employed in business, financial, and government systems.  Ada, an advanced programming language adopted by the US Department of Defense as its standard high-level computer programming language in the 1980s and 1990s, was designed by Jean Ichbiah.  LISP, the second-oldest high-level programming language still in use (primarily in artificial intelligence research), was invented by John McCarthy* in 1958.  Barbara Liskov was awarded the 2008 ACM Turing Award for fundamental advances in programming language design.  The ACM press release noted that her innovations "are now the basis of every important programming language since 1975, including Ada, C++, Java, and C#."
  

• The invention of the MINIX operating system by Andrew Tanenbaum.  MINIX was the precursor to, and inspiration for, the widely used Linux operating system.
  

• The invention of the computer spreadsheet by Dan Bricklin and Robert Frankston.  Bricklin and Frankston's VisiCalc spreadsheet was the first "killer app."  The Lotus 1-2-3 spreadsheet program, the most successful software product of its time, was developed by Jonathan Sachs and Mitchell Kapor.

• The invention of the computerized word processor by Evelyn Berezin.  Berezin, who was inducted into the National Inventors Hall of Fame in 2022, invented the Data Secretary, the first computerized word processor, in 1971.  She is also credited with developing the first office computer, the first computerized banking system, and the United Airlines computerized reservation system, the largest data processing system of its time.  Other important word processors were designed by Charles "Nick" Corfield (Adobe FrameMaker) and Richard Brodie* (Microsoft Word).
  

• The co-founding of the field of artificial intelligence by Marvin Minsky, Herbert Simon*, and John McCarthy*.  (Allen Newell⁺ is considered to have been the other one of its  four founders.⁹)  Six of the ten inductees into the IEEE Computer Society's Intelligent Systems Magazine AI Hall of Fame are, or were, Jewish or of Jewish descent (Noam Chomsky, Edward Feigenbaum, John McCarthy*, Marvin Minsky, Judea Pearl, and Lotfi Zadeh*).  Major approaches to machine learning, the now dominant approach to artificial intelligence, were pioneered by Jews, including Bayesian Networks (Judea Pearl), Support Vector Machines (Vladimir Vapnik and Alexey Chervonenkis), Deep Learning (Frank Rosenblatt and Yoshua Bengio, together with Geoffrey Hinton⁺ and Yann LeCun⁺), Evolutionary Computing (Lawrence Fogel), and the Probably Approximately Correct (PAC) Model (Leslie Valiant).¹⁰  Minsky, Simon, McCarthy, Feigenbaum, Pearl, Bengio, and Valiant have received  seven of the eleven Turing Awards given thus far for work in artificial intelligence.

• The development of computer algebra (symbol manipulation) programs by Jean Sammet (FORMAC), Carl Engelman (MATHLAB), Joel Moses (MACSYMA), and Stephen Wolfram (Mathematica).

• The invention of reversible computation theory by Rolf Landauer.  Reversible computation circumvents the thermodynamic limits on irreversible computation established by John von Neumann, and is one of the foundations of quantum computing.  The ballistic architecture, or Fredkin gate, model of reversible computation was introduced by Edward Fredkin.

• The invention of quantum computing by Paul Benioff, Richard Feynman, Yuri Manin,* and David Deutsch.

• The invention of DNA computing by Leonard Adleman.

• The invention of fuzzy logic by Max Black and Lotfi Zadeh* (independently).

• The invention of algorithmic complexity by Ray Solomonoff.  Also termed Kolmogorov complexity or algorithmic information theory, Solomonoff's 1964 work was later arrived at independently by Andrei Kolmogorov⁺ (1965) and Gregory Chaitin (1969).
  

• The invention of the Monte Carlo method by Stanislaw Ulam and John von Neumann.  This statistical numerical method is one of the cornerstones of computer simulation science.  Von Neumann invented the first computer-based random number generator for use in Monte Carlo simulations.  The so-called Metropolis Monte Carlo algorithm, widely used in statistics and computational physics, was largely devised by Marshall Rosenbluth, based in part on ideas from Edward Teller and John von Neumann. 
  

• The invention of nondeterministic algorithms by Michael Rabin.  Such algorithms employ Monte Carlo methods to provide efficiently computable solutions that are correct with high (but less than one hundred percent) probability to many problems whose exact solution is computationally intractable.  Rabin's probabilistic primality testing, e.g., is essential to the practical implementation of RSA public-key cryptography.
  

• The invention of the SIMPLEX linear programming algorithm by George B. Dantzig.   Linear programming (LP), invented independently by Dantzig and Leonid Kantorovich, is a powerful optimization technique that is widely used in economics and engineering.  It has been estimated that, aside from database operations such as sorting and searching, LP consumes more computer time than any other mathematical procedure.¹¹  The SIMPLEX algorithm remains LP's fundamental numerical solution technique.

• The invention of the ellipsoid method of convex optimization by Naum Shor and, independently, by Arkadi Nemirovski and David Yudin.  This technique, which was successfully employed by Leonid Khachiyan⁺ to prove the polynomial-time complexity of linear programming, underlies most modern results concerning the computational complexity of convex optimization programs.  The ellipsoid method provided the first effective solver for semidefinite programs (which are encountered in many engineering applications) and has led to significant advances in combinatorial optimization.
  

• The invention or co-invention of five of CiSE's "Top Ten Algorithms of the Century" by Stanislaw Ulam, John von Neumann, Marshall Rosenbluth, George Dantzig, Cornelius Lanczos, I. J. Good, Leslie Greengard, and Vladimir Rokhlin.   The January/February 2000 issue of Computing in Science & Engineering, a joint publication of the American Institute of Physics and the IEEE Computer Society, assembled a list of "the ten algorithms with the greatest influence on the development and practice of science and engineering in the 20th century."  In addition to the Monte Carlo method and the SIMPLEX algorithm discussed above, the top ten algorithms included the Krylov subspace iteration method for the solution of large systems of linear equations (Lanczos, together with Magnus Hestenes⁺ and Eduard Stiefel⁺), the Fast Fourier Transform (FFT) (Lanczos, together with G. C. Danielson⁺ in 1942, and independently by I. J. Good in 1958 and by James Cooley⁺ and John Tukey⁺ in 1965),¹² and the fast multipole algorithm for the solution of many-body problems (Greengard and Rokhlin).

• The invention of the Wiener filter by Norbert Wiener.  The Wiener filter is an optimal filter for extracting signals from noise in stationary stochastic systems and is one of the central results in statistical communication theory, a field pioneered by Wiener.  (A version of the Wiener filter was also formulated independently by Andrei Kolmogorov⁺.)  The nonlinear, recursive Wiener filter, or Kalman filter, its extension to nonstationary systems for use in tracking and guidance was first formulated by Peter Swerling in 1959.¹³  Wiener and Alexander Khinchine independently derived the Wiener-Khinchine theorem, another central result in statistical communication theory.
  

• The invention of statistical decision theory by Abraham Wald.  Among other applications, statistical decision theory plays an important role in radar, control, and  communication.  Its minimax decision rules derive from John von Neumann's theory of optimal strategies (theory of games).

• The invention of dynamic programming by Richard Bellman.  This procedure solves sequential, or multi-stage, decision problems and is one of the foundations of modern control theory.  It also constitutes the basis for many powerful algorithms, including the backpropagation algorithm used to train neural networks in machine learning and the Viterbi algorithm, invented by Andrew Viterbi, that is used to decode convolutional codes employed in error correction and in CDMA and GSM digital cellular telephony.
  

• The co-invention of public-key cryptography by Martin Hellman.  Hellman and Whitfield Diffie⁺ devised the Diffie-Hellman algorithm for secure key distribution over nonsecure channels.
  

• The co-invention of RSA by Adi Shamir and Leonard Adleman.  RSA (which is named for its three co-inventors, Shamir, Adleman, and Ronald Rivest⁺) is the most widely used public-key algorithm.

• The invention of elliptic curve cryptography (ECC) by Neal Koblitz and Victor S. Miller (independently).  Based on concepts rooted in algebraic geometry, ECC is widely deployed as the leading successor to RSA.  Relative to RSA, it provides greater cryptographic strength with much smaller cryptovariables.  (It does, however, share the same potential vulnerability to quantum computational attack.)

• The formulation of the learning with errors (LWE) problem by Oded Regev.  The application of LWE, a computationally "hard" problem, has led to revolutionary developments in cryptography.  CRYSTALS-Kyber, the recent finalist in the US National Institute of Standards and Technology’s six-year international competition to find a quantum-resistant, or "post-quantum," algorithm standard for general encryption, is based on LWE.  CRYSTALS-Dilithium, one of the three algorithms selected to become quantum-resistant digital signature standards, is also based on LWE.  (FALCON, one of the other two digital signature finalists, is based on the NTRU cryptographic system, which was invented by Joseph Silverman, Jeffrey Hoffstein, and Jill Pipher.⁺)   LWE is also the basis for the recent breakthrough in the construction of efficient, fully homomorphic encryption (FHE) schemes by Zvika Brakerski, Craig Gentry,⁺ and Vinod Vaikuntanathan.⁺  FHE techniques permit the processing of encrypted data without the need to first decrypt it, thus permitting the secure processing of sensitive data on non-secure computing platforms.  

• The invention of quantum cryptography by Stephen Wiesner.  Although quantum key distribution was invented in the mid-1980s by others, it was specifically acknowledged to have been inspired by Wiesner's circa 1970 work that established the basic principles underlying the use of quantum mechanics to achieve information security.

• The development of mathematical and statistical cryptanalysis by William Friedman.  Friedman's innovations are ranked amongst the greatest in the history of cryptology; he supervised the breaking of the Japanese diplomatic code PURPLE in 1940 and directed US cryptanalysis during World War II.  Other important World War II cryptologists included Solomon Kullback, Leo Rosen, and Abraham Sinkov in the US and Max Newman*, I.J. Good, and Leo Marks in England.  Newman and Good were instrumental in the design of Colossus, which was used to break the Lorenz cipher employed by the German high command.  Marks, the chief cryptologist of the Special Operations Executive (SOE) of MI6, revolutionized the one-time pad.

• The invention of cryptocurrency by David Chaum.  In his seminal 1982 paper, Chaum established the concept of secure digital cash, the first cryptocurrency.  Chaum's invention anticipated by several decades the now widespread recognition of the issue of electronic privacy in financial and other transactions.
  

• The co-invention of blockchain by David Chaum and, independently, by Stuart Haber (together with W. Scott Stornetta⁺).  Chaum gave the first full technical description of a blockchain in his 1982 doctoral dissertation, but never published the concept in a journal or conference proceeding.  It, therefore, went largely unnoticed.  In a 1991 paper, Haber and Stornetta⁺ introduced another embodiment of this concept for a shared, tamper-proof, decentralized transaction ledger.  Their company Surety Technologies, founded in 1994, created the first and longest running commercial blockchain.  Blockchain technology is widely claimed to have the potential to revolutionize e-commerce (and more) by greatly increasing the efficiency, confidentiality, and trust with which online transactions are conducted and recorded.    

• The invention of convolutional codes by Peter Elias.  Important decoding algorithms for these error correction codes were invented by Barney Reiffen, Robert Fano, and Andrew Viterbi.

• The co-invention of the Reed-Solomon error correction code by Gustave Solomon.  Reed-Solomon and Viterbi- or Fano-decoded convolutional codes, or hybrid concatenations of the two, are probably the most widely used error correction techniques at present.

• The invention of the LZ data compression algorithm by Jacob Ziv and Abraham Lempel.  Although LZ coding was not the first data compression technique (the first such technique having been invented, independently, by Robert Fano and Claude Shannon⁺), it is today the most widely used in commercial systems.  It underpins PDF, GIF, TIFF, ZIP, and other widely used file formats.
  

• The development of automated, electronically switched telephone networks by Amos Joel.  Joel received both the 1989 Kyoto Prize ("Japan's Nobel Prize") and the 1993 US National Medal of Technology for work that revolutionized telephone switching systems worldwide.  Joel's 1972 US Patent No. 3,663,762, "Mobile Communication System," is the basis of the switching technology that made cellular telephone networks possible. 
  

• The co-invention of spread spectrum communications by Hedy Lamarr.  Lamarr (the Hollywood actress) and George Antheil⁺ (a Hollywood composer) received US Patent No. 2,292,387, "Secret Communication System," in 1942 for the invention of frequency-hopped spread spectrum.  The digital form of spread spectrum that is widely used in cellular communications (CDMA) was developed by Qualcomm, a company founded by the information theorists Irwin Jacobs and Andrew Viterbi.  Jacobs received the US National Medal of Technology in 1994 and Viterbi received the US National Medal of Science in 2007.  Both were recognized for their pioneering innovations in digital wireless communications.  Joel Engel also received the Medal of Technology in 1994 as one of the two "fathers of the cellular phone" for his work on the development of the basic network architecture used worldwide in cellular telephony.
  

• The co-invention of the Internet by Leonard Kleinrock, Paul Baran, Vinton Cerf,* and Robert Kahn.  Together with Kleinrock, Baran, Cerf, and Kahn, Donald Davies⁺ and Lawrence Roberts⁺ are the six individuals most frequently cited as principal inventors of the Internet.  Kleinrock, Cerf, Kahn, and Roberts⁺ were awarded the US National Academy of Engineering's half-million dollar Draper Prize in 2001 "for the development of the Internet."  Baran, Kleinrock, Davies⁺, and Roberts⁺ received the first IEEE Internet Award in 2000 for "their early, preeminent contributions in conceiving, analyzing and demonstrating packet-switching networks, the foundation technology of the Internet."  Cerf, Kahn, and Baran received US National Medals of Technology, the former two in 1997 and the latter in 2007.  Kleinrock was awarded the US National Medal of Science in 2007.  Cerf and Kahn co-invented the TCP/IP protocol for integration of heterogeneous networks, which is the basis of the Internet's "inter-networking" architecture.  They shared the 2004 ACM Turing Award for this work, and in 2005 each received the US Presidential Medal of Freedom.
  

• The invention of Alohanet (precursor to Ethernet) by Norman Abramson.  Alohanet was a packet-switched research network that solved the major problem of packet interference, or "packet collision."  Alohanet was further developed by Robert Metcalfe,⁺ working at the Xerox Palo Alto Research Center, into Ethernet (which Metcalfe⁺ originally called the Alto Aloha network), the standard method used in local area computer networking.  Radia Perlman's spanning tree protocol, which solved the problem of broadcast storms due to network switching loops, was the critical enabler that allowed Ethernet to realize high levels of robust network complexity.
  

• The invention of Google by Sergey Brin and Larry Page*.  The algorithm employed by Google, the most powerful and widely used search engine on the Internet, employs an adaptation of the citation frequency "impact factor" metric originally invented in the 1950s by Eugene Garfield to rank the relative influence of scientific researchers, articles, and journals.  A search algorithm very similar to Google PageRank, called HITS (Hypertext Induced Topic Search), was devised almost simultaneously by Jon Kleinberg at IBM.  In his papers, Kleinberg credited the 1976 mathematical work of Gabriel Pinski and Francis Narin, as does the PageRank patent.  Pinski and Narin had shown how to formulate and compute Garfield's relative influence in terms of a graph theoretic matrix eigenvalue problem.  Similar mathematical techniques for calculating the relative influence of individuals in social networks or of production sectors in national economies can be found, respectively, in the 1953 work of statistician Leo Katz and in the 1941 work on input-output analysis by the Nobel Prize winning economist Wassily Leontief.*  

NOTES
1. According to the prominent historian of technology George Dyson, "there were four essential prophets whose mathematics brought us into the Information Age: Norbert Wiener, John von Neumann, Alan Turing and Claude Shannon."  See "The Elegance of Ones and Zeroes," by George Dyson in The Wall Street Journal, 21 July 2017.
2. See  Genius in the Shadows: A Biography of Leo Szilard, by William Lanouette (Scribner's, New York, 1992, p. 63).
3. See  "Emil Post and His Anticipation of Gödel and Turing," by John Stillwell in Mathematics Magazine (Mathematical Association of America, Washington, DC, Vol. 77, No. 1, Feb. 2004, pp. 3-14).  See also http://www-gap.dcs.st-and.ac.uk/~history/Mathematicians/Post.html.
4. See "Max Newman: Mathematician, Codebreaker and Computer Pioneer," by William Newman in Colossus: The First Electronic Computer, edited by Jack Copeland (Oxford, Oxford and New York, 2004).
5. See http://www.nationmaster.com/encyclopedia/EDVAC.
6. Encyclopedia of Computer Science (Fourth Edition), edited by Anthony Ralston, Edwin D. Reilly, and David Hemmendinger (Wiley, Chichester, England, 2003, p. 1841).
7. Parallel Supercomputing in SIMD Architectures, by R. Michael Hord (CRC Press, Boca Raton, FL, 1990).
8. Although most supercomputers are now based on MIMD (multiple instruction, multiple data) architectures, their individual processing nodes generally embody small-scale SIMD capabilities.  The still largely hypothetical quantum computer can be thought of as an SIMD machine with exponentially many virtual processors.
9. See  AI: The Tumultuous History of the Search for Artificial Intelligence, by Daniel Crevier (Basic Books, New York, 1993, p. 26), or Encyclopedia of Computer Science (Fourth Edition), edited by Anthony Ralston, Edwin D. Reilly, and David Hemmendinger (Wiley, Chichester, England, 2003, p. 91).
10. The 2019 IEEE Xplore article “Who Is the Father of Deep Learning?” states: “We conclude that Frank Rosenblatt developed and explored all the basic ingredients of the deep learning systems of today, and that he should be recognized as a Father of Deep Learning, perhaps together with Hinton, LeCun and Bengio who have just received the Turing Award as the fathers of the deep learning revolution.”  Lawrence Fogel initiated the field of evolutionary computing in 1960 and is considered to be the “father of evolutionary programming,” the first of four basic approaches that were eventually formulated and subsequently merged into the field of evolutionary computing.
11. See http://www-gap.dcs.st-and.ac.uk/~history/Mathematicians/Dantzig_George.html.
12. Cooley and Tukey are generally credited with invention of the "modern" FFT.   Their 1965 paper only referenced the prior work of I. J Good, whose FFT algorithm was both somewhat different and less efficient.  In a January 1992 paper in IEEE SP Magazine, entitled "How the FFT Gained Acceptance," Cooley reviewed other prior work and concluded that "it appears that Lanczos had the FFT algorithm" in 1942.  He holds out the possibility that Gauss may have had it as early 1805, however.  Gauss's work was not published until after his death and was in Latin and employed somewhat archaic notation, which made it difficult to decipher.  It was only published in 1866 in his collected works. An analysis by Michael Heideman, Don Johnson, and C. Sidney Burrus has concluded that Gauss did indeed have the basic elements of the modern FFT in 1805, but due to its obscurity, his formulation appears to have had no influence on subsequent work.  
13. See the next-to-last paragraphs in https://archive.siam.org/news/news.php?id=526 and in the obituary published in the November 2000 issue of Physics Today (pp. 75-76).  See also the  discussion in the Appendix to Tracking and Kalman Filtering Made Easy, by Eli Brookner (Wiley, New York, 1998, pp. 383-387).
 
*  Georg Cantor and Herbert Simon had  Jewish fathers; Simon's mother was of partial Jewish descent, which was also the case, at a minimum, for the mother of Georg Cantor.  Max Newman and Vinton Cerf had Jewish fathers and non-Jewish mothers, while Richard Brodie, Wassily Leontief, Yuri Manin, John McCarthy, Larry Page, and Lotfi Zadeh have, or had, Jewish mothers.  For more information, see the footnotes to these and other listings in Jewish Computer and Information Scientists, or in the cases of Leontief and Manin, in Jewish Economists and Jewish Mathematicians, respectively.

+ Non-Jewish.

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