- #1
MatheusMkalo
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Who First Utilized Rigorous Proofs in Mathematics?
- Context: Undergrad
- Thread starter MatheusMkalo
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Discussion Overview
The discussion centers on the historical origins of rigorous proofs in mathematics, specifically exploring which ancient civilization first utilized them. Participants reference various cultures, including the Egyptians, Babylonians, and Greeks, and their mathematical knowledge and practices.
Discussion Character
- Historical, Debate/contested
Main Points Raised
- Some participants suggest that the ancient Greeks were the first to employ rigorous proofs in mathematics.
- Others propose that the Babylonians and Egyptians may have had knowledge of certain mathematical formulas, though it remains unclear if they used rigorous proofs.
- One participant mentions that the Babylonians likely knew formulas related to Pythagorean triples, indicating a level of mathematical understanding that could imply some form of proof.
- Another participant notes that while the Greeks had rigorous proofs, other civilizations may not have required proofs, relying instead on acceptance of mathematical concepts.
Areas of Agreement / Disagreement
Participants express differing views on whether the Greeks were the first to use rigorous proofs, with some arguing for the capabilities of earlier civilizations while others maintain that the Greeks stand out in this regard. The discussion remains unresolved regarding the extent of proof usage in non-Greek cultures.
Contextual Notes
There are limitations in the discussion regarding the definitions of "rigorous proofs" and the historical evidence for mathematical practices in ancient civilizations, which are not fully explored or agreed upon.
- #2
tiny-tim
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Welcome to PF!
Hi MatheusMkalo! Welcome to PF!
That's the same as (A + B)(A - B) = A2 - B2 …
Hi MatheusMkalo! Welcome to PF!
That's the same as (A + B)(A - B) = A2 - B2 …
I think that it was known to the ancient Greeks.
- #3
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There has reportedly been some discussion among scholars whether the Egyptians knew the formula [tex]a^3-b^3=(a-b)(a^2+ab+b^2)[/tex].
In fact, the Babylonians knew formulas like [tex]xy=\frac{(x+y)^2-(x-y)^2}{2}[/tex]. So it wouldn't seem unlikely that already the Babylonians and the Egyptians knew about [tex](a+b)(a-b)=a^2-b^2[/tex]. But, to my knowledge, there is no proof that they did.
But the Greeks almost certainly knew the formula. It seems like one of the things that Pythagoras liked to prove geometrically...
In fact, the Babylonians knew formulas like [tex]xy=\frac{(x+y)^2-(x-y)^2}{2}[/tex]. So it wouldn't seem unlikely that already the Babylonians and the Egyptians knew about [tex](a+b)(a-b)=a^2-b^2[/tex]. But, to my knowledge, there is no proof that they did.
But the Greeks almost certainly knew the formula. It seems like one of the things that Pythagoras liked to prove geometrically...
- #4
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This site: http://www.math.tamu.edu/~dallen/history/babylon/babylon.html explains that the Babylonians probably knew about the formula and used it to generate Pythagorean triples (yes, Pythagoras' theorem was also known to them!)
- #5
coolul007
Gold Member
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The Greeks had rigorous proofs, while other civilizations didn't require proofs, just acceptance.
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