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Much of the argument is the same as for the initial push to formalize mathematics in the late 19th century. Formalisms allow for precision and help reduce error
by constantcrying 1y ago
Much of the argument is the same as for the initial push to formalize mathematics in the late 19th century. Formalisms allow for precision and help reduce errors, but the most important change was in how mathematicians were able to communicate, by creating a shared understanding.
Computerized mathematics is just another step in that direction.
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- dboreham 1y agoImho it was always "computerized", they just didn't have a computer. To me the approaches used in the early 20th century look like people defining a simple VM then writing programs that "execute" on that VM.
- zozbot234 1y ago> Imho it was always "computerized", they just didn't have a computer. They had a whole lot of computers, actually. But back then the "computers" were actual people whose job was to do computations with pen and paper (and a few very primitive machines).
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- constantcrying 1y agoExactly. The step to formalize mathematics through computation is just the logical consequence of the program of the formalizers. The idea actually goes back to Leibnitz, who was very much overoptimistic about computability, but already conceived of the idea of a logic machine, which could deter the truth value of any statement.
- ljlolel 1y agoWhich fell apart in shambles under Gödel
- jojomodding 1y agoIncredible, you managed to mention Gödel's incompleteness theorem on HN without wildly mis-stating what it's about ;)