What kind of mathematical "discoveries" have enabled mankind to build modern computers?After studying the very thrilling Examples of mathematical discoveries which had been saved as a mystery I got here to think of something: maximum math discoveries appear to had been made centuries ago, and with Pascal and Leibniz we already had machines that would add and multiply (a few don't forget them as the first computer systems). Of direction modern computer systems needed energy and electric signals that can be transformed to at least one's and zero's, but those we've since the 19th century. First computer systems were also built with transistors, however we've the ones since the 1940's.current computers are, at their center, not so extraordinary from the primary computer systems that followed the Von Neumann structure (with its arithmetic-logic unit). this is: they understand how move information from one place to any other, the way to upload and a way to multiply, in addition to perform logical operations (and, or, xor, now not), and from that they get all of the other operations (some can substract, divide and do some different stuff, however it is all very primitive in that sense). Of path, current computers paintings at a miles better level than their predecessors: while inside the beginning programming needed to be accomplished the use of commands composed of zero's and 1's or, in the event that they were lucky, the usage of meeting language, now we have high stage programming languages that (to say it kind of) enclose a group of these single commands into one high stage command.And when I see pretty graphics in video-games, programs like photoshop, 3D rendering, CAD programs and such, I always think of all the calculus stuff I learned and how it must be applied to achieve those wonderful results.And this is where my question arises: all of this mathematical knowledge has been available to us for way longer than computers existed. So, are there any modern mathematical discoveries that enabled the giant leap we took from the first computers we had in the 40's to what we have now? Or maybe old math started being applied in a different way at some point in time?

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What kind of mathematical &quot;discoveries&quot; have enabled mankind to build modern computers?After studying the very thrilling Examples of mathematical discoveries which had been saved as a mystery I got here to think of something: maximum math discoveries appear to had been made centuries ago, and with Pascal and Leibniz we already had machines that would add and multiply (a few don&#039;t forget them as the first computer systems). Of direction modern computer systems needed energy and electric signals that can be transformed to at least one&#039;s and zero&#039;s, but those we&#039;ve since the 19th century. First computer systems were also built with transistors, however we&#039;ve the ones since the 1940&#039;s.current computers are, at their center, not so extraordinary from the primary computer systems that followed the Von Neumann structure (with its arithmetic-logic unit). this is: they understand how move information from one place to any other, the way to upload and a way to multiply, in addition to perform logical operations (and, or, xor, now not), and from that they get all of the other operations (some can substract, divide and do some different stuff, however it is all very primitive in that sense). Of path, current computers paintings at a miles better level than their predecessors: while inside the beginning programming needed to be accomplished the use of commands composed of zero&#039;s and 1&#039;s or, in the event that they were lucky, the usage of meeting language, now we have high stage programming languages that (to say it kind of) enclose a group of these single commands into one high stage command.And when I see pretty graphics in video-games, programs like photoshop, 3D rendering, CAD programs and such, I always think of all the calculus stuff I learned and how it must be applied to achieve those wonderful results.And this is where my question arises: all of this mathematical knowledge has been available to us for way longer than computers existed. So, are there any modern mathematical discoveries that enabled the giant leap we took from the first computers we had in the 40&#039;s to what we have now? Or maybe old math started being applied in a different way at some point in time?

Zoe Andersen · Accepted Answer

The mathematical foundations of modern-day computer science commenced to be laid by Kurt Gödel along with his incompleteness theorem (1931). in this theorem, he showed that there have been limits to what could be proved and disproved within a formal device. This caused paintings with the aid of Gödel and others to outline and describe these formal structures, inclusive of ideas consisting of mu-recursive features and lambda-definable capabilities.In 1936 Alan Turing and Alonzo Church independently, and additionally collectively, brought the formalization of an set of rules, with limits on what can be computed, and a &quot;simply mechanical&quot; model for computing. This became the Church–Turing thesis, a hypothesis approximately the character of mechanical calculation gadgets, such as electronic computer systems. The thesis claims that any calculation that is feasible may be finished by an algorithm strolling on a pc, supplied that enough time and storage area are to be had.In 1936, Alan Turing also posted his seminal work on the Turing machines, an summary virtual computing machine that&#039;s now certainly referred to as the standard Turing gadget. This machine invented the principle of the cutting-edge computer and become the birthplace of the saved application concept that the majority contemporary day computers use. those hypothetical machines were designed to officially determine, mathematically, what may be computed, taking into consideration obstacles on computing potential. If a Turing machine can complete the task, it is taken into consideration Turing computable or greater typically, Turing entire.up to and all through the 1930s, electric engineers had been able to construct digital circuits to resolve mathematical and logic problems, but maximum did so in an ad hoc manner, lacking any theoretical rigor. This changed with Claude Elwood Shannon&#039;s guide of his 1937 master&#039;s thesis, A Symbolic evaluation of Relay and Switching Circuits. even as taking an undergraduate philosophy class, Shannon were uncovered to Boole&#039;s paintings, and recognized that it is able to be used to set up electromechanical relays (then used in smartphone routing switches) to remedy good judgment issues. This idea, of utilizing the properties of electrical switches to do good judgment, is the basic idea that underlies all digital virtual computers, and his thesis became the muse of practical digital circuit layout while it have become well known a few of the electric engineering community for the duration of and after international warfare II.Shannon went on to found the field of data concept along with his paper titled A Mathematical theory of communication, which applied probability idea to the problem of how to excellent encode the statistics a sender wants to transmit. This paintings is one of the theoretical foundations for many regions of look at, together with records compression and cryptography.

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