Query: Note that computer models are just concatenations of calculations you could do on a hand-held calculator, so they are theoretical and cannot be part of any evidence."

Relevant passages:
Computer science <=SEP=> Computer science deals with the theoretical foundations of information and computation , together with practical techniques for the implementation and application of these foundations .   Computer science is the study of the theory , experimentation , and engineering that form the basis for the design and use of computers . It is the scientific and practical approach to computation and its applications and the systematic study of the feasibility , structure , expression , and mechanization of the methodical procedures ( or algorithms ) that underlie the acquisition , representation , processing , storage , communication of , and access to information . An alternate , more succinct definition of computer science is the study of automating algorithmic processes that scale . A computer scientist specializes in the theory of computation and the design of computational systems .   Its fields can be divided into a variety of theoretical and practical disciplines . Some fields , such as computational complexity theory ( which explores the fundamental properties of computational and intractable problems ) , are highly abstract , while fields such as computer graphics emphasize real-world visual applications . Other fields still focus on challenges in implementing computation . For example , programming language theory considers various approaches to the description of computation , while the study of computer programming itself investigates various aspects of the use of programming language and complex systems . Human -- computer interaction considers the challenges in making computers and computations useful , usable , and universally accessible to humans .

Mathematics <=SEP=> Mathematics ( from Greek μάθημα máthēma , `` knowledge , study , learning '' ) is the study of topics such as quantity ( numbers ) , structure , space , and change . There is a range of views among mathematicians and philosophers as to the exact scope and definition of mathematics .   Mathematicians seek out patterns and use them to formulate new conjectures . Mathematicians resolve the truth or falsity of conjectures by mathematical proof . When mathematical structures are good models of real phenomena , then mathematical reasoning can provide insight or predictions about nature . Through the use of abstraction and logic , mathematics developed from counting , calculation , measurement , and the systematic study of the shapes and motions of physical objects . Practical mathematics has been a human activity from as far back as written records exist . The research required to solve mathematical problems can take years or even centuries of sustained inquiry .   Rigorous arguments first appeared in Greek mathematics , most notably in Euclid 's Elements . Since the pioneering work of Giuseppe Peano ( 1858 -- 1932 ) , David Hilbert ( 1862 -- 1943 ) , and others on axiomatic systems in the late 19th century , it has become customary to view mathematical research as establishing truth by rigorous deduction from appropriately chosen axioms and definitions . Mathematics developed at a relatively slow pace until the Renaissance , when mathematical innovations interacting with new scientific discoveries led to a rapid increase in the rate of mathematical discovery that has continued to the present day .   Galileo Galilei ( 1564 -- 1642 ) said , `` The universe can not be read until we have learned the language and become familiar with the characters in which it is written . It is written in mathematical language , and the letters are triangles , circles and other geometrical figures , without which means it is humanly impossible to comprehend a single word . Without these , one is wandering about in a dark labyrinth . '' Carl Friedrich Gauss ( 1777 -- 1855 ) referred to mathematics as `` the Queen of the Sciences '' . Benjamin Peirce ( 1809 -- 1880 ) called mathematics `` the science that draws necessary conclusions '' . David Hilbert said of mathematics : `` We are not speaking here of arbitrariness in any sense . Mathematics is not like a game whose tasks are determined by arbitrarily stipulated rules . Rather , it is a conceptual system possessing internal necessity that can only be so and by no means otherwise . '' Albert Einstein ( 1879 -- 1955 ) stated that `` as far as the laws of mathematics refer to reality , they are not certain ; and as far as they are certain , they do not refer to reality . ''   Mathematics is essential in many fields , including natural science , engineering , medicine , finance and the social sciences . Applied mathematics has led to entirely new mathematical disciplines , such as statistics and game theory . Mathematicians also engage in pure mathematics , or mathematics for its own sake , without having any application in mind . There is no clear line separating pure and applied mathematics , and practical applications for what began as pure mathematics are often discovered .

Computer <=SEP=> A computer is a device that can be instructed to carry out an arbitrary set of arithmetic or logical operations automatically . The ability of computers to follow generalized sequences of operations , called programs , enable them to perform a wide range of tasks .   Such computers are used as control systems for a very wide variety of industrial and consumer devices . This includes simple special purpose devices like microwave ovens and remote controls , factory devices such as industrial robots and computer assisted design , but also in general purpose devices like personal computers and mobile devices such as smartphones . The Internet is run on computers and it connects millions of other computers .   Since ancient times , simple manual devices like the abacus aided people in doing calculations . Early in the Industrial Revolution , some mechanical devices were built to automate long tedious tasks , such as guiding patterns for looms . More sophisticated electrical machines did specialized analog calculations in the early 20th century . The first digital electronic calculating machines were developed during World War II . The speed , power , and versatility of computers has increased continuously and dramatically since then .   Conventionally , a modern computer consists of at least one processing element , typically a central processing unit ( CPU ) , and some form of memory . The processing element carries out arithmetic and logical operations , and a sequencing and control unit can change the order of operations in response to stored information . Peripheral devices include input devices ( keyboards , mice , joystick , etc. ) , output devices ( monitor screens , printers , etc. ) , and input/output devices that perform both functions ( e.g. , the 2000s-era touchscreen ) . Peripheral devices allow information to be retrieved from an external source and they enable the result of operations to be saved and retrieved .