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I read Charles Babbage invented the first mechanical computer (the Analytic Engine) and that Ada Lovelace devised the first computer programs.

Also I realize John Von Neumann invented the first electronic programmable digital computer and had actually invited Alan Turing to work with him on devising computer programs after reading about Turing's Universal Turing machine. Yet another programmable computer?

Are these all manifestations of the same principles in digital computers or is each a separate distinct invention building on the others. Thank you.

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    $\begingroup$ According to wikipedia Colossus Computer "Colossus is thus regarded as the world's first programmable, electronic, digital computer, although it was programmed by switches and plugs and not by a stored program." Babbage's colleague and programmer was Ada Lovelace, the daughter of romantic poet, Lord Byron. $\endgroup$ – Nick May 18 '18 at 3:00
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    $\begingroup$ What are you really asking? Babbage computer was "programmable" and "digital". What else? $\endgroup$ – Alexandre Eremenko May 18 '18 at 3:21
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    $\begingroup$ You can try with some books : Martin Davis, Engines of logic : Mathematicians and the Origin of the Computer, WWNorton&Co (2000), page 139-40 for Babbage. $\endgroup$ – Mauro ALLEGRANZA May 18 '18 at 6:43
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    $\begingroup$ I think the crux of the question is "programmable". Many "computers" of the era 1930-1960 (such as IBM accounting machines and tabulators) were programmable by patch cords and switch settings. If by "programmable" you mean electronically stored program in the modern sense, the Manchester "Baby" (en.wikipedia.org/wiki/…) of 1948 wins. The much more useful Eniac got its stored program memory later that year. $\endgroup$ – kimchi lover May 18 '18 at 13:03
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    $\begingroup$ We should absolutely not forget (Admiral?!) Grace Hopper, who did also/independently invent "programming". She was so valuable to the Navy that she was not allowed/required to retire at the "mandatory" retirement age... ! And so on. $\endgroup$ – paul garrett May 18 '18 at 22:19
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To answer your title question, the first "programmable, digital computer" was designed by Charles Babbage and Ada Lovelace, known as the Analytical Engine. Turing, von Neumann, and other computer scientists and mathematicians approached the concept of a programmable computer both independently and building on the work of Babbage, Lovelace and their contemporaries. Turing devised the concept of a general-purpose computer in the 1930s, which the Analytical Engine was theorized to be. A quote exists from the second link which illustrates how the modern computer was theorized through Babbage's engine:

"Charles Babbage started work on his Analytical Engine in the mid-1830s, with the idea of creating a new calculating machine that could “eat its own tail”, by which he meant that it could modify its calculation while it was running. It would do this by pausing during a calculation, and using the values it had already determined to choose between two possible next steps. Babbage listed the basic operations that such a machine, with a large enough memory, would need if it were to execute “the whole of the developments and operations of analysis”, in other words any calculation that could be conceived of at the time. We now know that the basic operations that he described are what are needed to compute anything that can be calculated by any modern computer. This means that the Analytical Engine would have been, in modern terms, a general-purpose computer, a concept first identified by Alan Turing in the 1930s."

Many mathematicians and computer scientists interpreted this concept through their distinct vision, and they also built on it through various manifestations.

Hope this helps!

Helpful links:

https://www.computerhistory.org/babbage/engines/ https://blogs.bodleian.ox.ac.uk/adalovelace/2018/07/26/ada-lovelace-and-the-analytical-engine/

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