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Some mathematicians are considered the "greatest of their era". For instance, Archimedes is generally considered the greatest mathematician of Antiquity. Is there any mathematician who stood out similarly from the rest in that timeline?

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    $\begingroup$ Considered by whom? I am sure different people (mathematicians, historians, etc) have different opinions. AFAIK, there is nobody in that time period who is comparable to say, Archimedes or, Diophantus, or Euclid, but this is just my opinion. $\endgroup$ – Moishe Kohan May 9 at 15:42
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    $\begingroup$ For instance, somebody by the name James Allen (a programmer) lists here 100 greatest mathematicians of all times. Few people on his list (but pickings are slim), say, Muhammed al-Khowârizmi, fall into the time interval you are interested in. You can choose somebody else, say, Aryabhata.... $\endgroup$ – Moishe Kohan May 9 at 15:57
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    $\begingroup$ The problem with lists like Allen's is that they mostly reflect the background knowledge/awareness of the list-maker, aside from a few notables that everyone includes. For example, among his top 100 are Einstein, Turing, Polya, Littlewood, Maxwell, Galilei (note that 3 of these are not even mathematicians). Absent in his top 100 (and born before 1930) are Erdős, Steinhaus, and Wiener who surely should be above Turing, Polya, and Littlewood! And why Turing and ignore Church and Kleene, both far more influential in mathematics than Turing, although none should probably be on a top 100 list. $\endgroup$ – Dave L Renfro May 9 at 19:49
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    $\begingroup$ See mathshistory.st-andrews.ac.uk/Indexes/Full_Chron.html for a chronological list to choose from. E.g. Roger Bacon, Omar Khayyam, Guo Shoujing ... $\endgroup$ – Gerald Edgar May 9 at 22:38
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    $\begingroup$ @Madhava: Regarding Erdős, Steinhaus, and Wiener, I think I'd put Erdős and Wiener on an all-time top 100 list, but almost certainly not Steinhaus (this would open up whether Kuratowski and Sierpinski should be on the list for me, and I suspect if I spent enough time going over names, I would have to exclude all three), so my comment should mostly be taken to mean who surely should be above Turing, Polya, and Littlewood (a no-brainer in my opinion, and I could probably come up with a dozen more who would be above these three and also who are not on Allen's top 100 list). $\endgroup$ – Dave L Renfro May 13 at 7:54
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Al-Khwarizmi was a ninth-century mathematician who created many of the most basic techniques for how we perform calculations. His greatest contributions were in the realm of developing formal, systematic ways of doing arithmetic and solving equations.

His works mark the beginning of what we today understand as Algebra. One of his principal achievements in algebra was his demonstration of how to solve quadratic equations by completing the square, for which he provided geometric justifications. Indeed, the word "algebra" comes from part of the title of his book on solving equations (Al-jabr), and the word "algorithm," meaning a systematic set of rules used to solve a problem, descends from his name (in Latin, his name became ‘Algoritmi’ and his systematic calculating procedures were called algorisms — later, algorithms).

Al-Khwarizmi's "On the Calculation with Hindu Numerals", written about 820, was principally responsible for spreading the Hindu–Arabic numeral system throughout the Middle East and Europe.

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  • $\begingroup$ this idea of "completing the square, for which he provided geometric justifications" is already clearly present in Euclides. $\endgroup$ – Jean Marie Becker May 26 at 21:48
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    $\begingroup$ @Jean, Euclid had no notion of equations, but he solved problems using a geometrical approach. On the other hand, Al-Khwarizmi classified six types of quadratic equations and told how to solve them by completing the square while giving a geometrical proof. The critical point in my answer which you missed while quoting is the term "quadratic equations". $\endgroup$ – Big Brother May 27 at 6:27
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There are several prominent mathematicians of the medieval era, most notably Leonardo of Pisa, or more commonly called "Fibonacci". He developed the Fibonacci sequence and he also introduced the Hindu - Arabic numeral system to Europe in the 13th century. As a result, the Roman numeral system was discarded in favor of the former.

Link: https://www.storyofmathematics.com/medieval_fibonacci.html

Another notable mathematician is Aryabhata. Aryabhata was an astronomer and mathematician. He wrote the influential "Aryabhatiya", where he gave rules for square roots, quadratic equations, and predicting eclipses. He also gave an approximation for the irrational constant pi (π).

Link: https://www.britannica.com/biography/Aryabhata-I

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