Who is the greatest mathematician of all time?

This is a subjective question without a definitive answer, much like asking "who is the greatest artist of all time?" The "greatest" can be judged by different criteria: the breadth of their work, the depth of their insights, their influence on future generations, the number of problems they solved, or the new fields they opened up.

• Commonly Mentioned Figures (in no particular order):
• Archimedes (c. 287 – c. 212 BCE): For his foundational work in geometry, mechanics, and early calculus.
• Isaac Newton (1643-1727): For co-inventing calculus and his work on universal gravitation, optics, and laws of motion.
• Leonhard Euler (1707-1783): Incredibly prolific, he made fundamental contributions to almost every area of mathematics existing in his time, introducing much of modern mathematical notation.
• Carl Friedrich Gauss (1777-1855): Known as the "Prince of Mathematicians," he made profound contributions to number theory, algebra, statistics, differential geometry, and more.
• Euclid (c. 300 BCE): For systemizing geometry.
• Srinivasa Ramanujan (1887-1920): For his extraordinary natural genius and original contributions, especially in number theory.
• David Hilbert (1862-1943): For his broad influence on 20th-century mathematics, including his list of 23 unsolved problems that guided research.
• Why it's Hard to Choose:
• Different Eras: Comparing mathematicians from vastly different historical periods is challenging due to the different tools and knowledge available.
• Different Fields: Some mathematicians excelled in specific areas, while others had broader impact.
• Key Takeaway: There's no single "greatest mathematician." Appreciation of mathematical greatness often involves recognizing a group of exceptional individuals who fundamentally advanced the field and whose work continues to resonate. The names listed above are frequently cited in such discussions due to their monumental and lasting impact.