Timeline for History of powers beyond squares and cubes
Current License: CC BY-SA 3.0
8 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Sep 26, 2015 at 18:09 | comment | added | Amir Asghari | @LeeMosher Please see my comment above | |
| Sep 26, 2015 at 18:08 | comment | added | Amir Asghari | @René Indeed, my conclusion was not just based on a few paragraphs I mentioned above. It was based on my previous reading of Khayyam. Tying algebra to geometry costed him and progress of mathematics a lot (about five hundred years for the latter). | |
| Sep 26, 2015 at 17:27 | comment | added | R.P. | I think we must not dismiss beforehand the possibility that philosophical beliefs can stand in the way of mathematical progress. It is also not really a forceful argument that Khayyam's way of thinking somehow lines up with modern-day topology: after all, Khayyam wasn't doing topology, he was doing algebra. But other than that I agree with you: the above does not convince me that Khayyam's meta-mathematical thinking prevented him from making progress that he might "otherwise" have made. | |
| Sep 26, 2015 at 16:33 | comment | added | Lee Mosher | I do not necessarily agree with the concluding sentence of this answer nor with the comment of @Joël. Instead, Khayyam's intelligence led him to pose and to seriously ponder an extremely important mathematical/geometric question which is quite close to issues we discuss in modern geometry and topology: What is the product of a surface with itself? It is rather ahistorical to suggest that his philosophical beliefs impeded the solution. What future historians might laugh at our "philosophical" inability to solve the P=NP conjecture? | |
| Sep 26, 2015 at 13:21 | comment | added | R.P. | Indeed interesting. It is intriguing to see how long it took even the greatest minds to treat algebra as independent of geometry. Even in as late a mathematician as François Viète (late 16th century), we find a very determined attempt to reconcile a sophisticated algebraic theory with a "dimensionalized" number system. I guess that, for a long time, what we call the number line was the most powerful source for producing numbers, and then of course the numbers did come with their own specific dimension. | |
| Sep 26, 2015 at 12:16 | history | edited | Amir Asghari | CC BY-SA 3.0 |
Complete the answer.
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| Sep 26, 2015 at 3:22 | comment | added | Joël | Interesting. Especially in comparison with René's post, which shows that Diophantus' point of view is closer to the modern one. | |
| Sep 25, 2015 at 22:49 | history | answered | Amir Asghari | CC BY-SA 3.0 |