>>11443987Whenever a power ranking of mathematicians is seriously considered, multiple factors are commonly considered: breadth (corpus of work), depth (importance of results) and longevity (lifetime productive capacity, closely related to but distinct from breadth). Euler and Gauss are commonly spoken of as the GOAT, or near GOAT status, Euler for the breadth and depth of his output (and influence on notation), and Gauss for depth (FTA, other stuff generally for which I admit ignorance OTTOMH, statistics I guess). Earlier, Newton and Leibniz are considered "deep" particularly for FTC, but don't take me as an authority on that. On the other extreme, Galois is a famous and uncharacteristic example of a mathematician whose life was cut very short, in dramatic fashion. In practice, most mathematicians lead long, dull lives, which is exactly what is needed to do mathematics, a slow, peaceful, contemplative activity. One can't do math very well when one is scraping for survival. I think this has much to do with why math only really got going in the past 500 years or so, whereas most of the preceding was just equations in at most two degrees, again and again.
In the history of mathematics, Gauss' Disquisitiones Arithmaticae is still useful and accessible, and Euler wrote an Elements of Algebra. Euclid remains relevant (pace moderns) in the sense that "doing" mathematics still entails much the same activity: definitions, state theorems, prove them, provide occasional illustrations, use theorems to prove more theorems. Theorem-proving is not the end-all be-all of math, but of course it's a central activity. The following is a suggested ranking based on a spotty undergrad education, talk to some actual smart people for more clarity:
Top tier: Euler, Gauss, Riemann, Newton, Leibniz
high-tier: Poincaré, Grothendieck, Hilbert
mid-tier: Euclid, Ramanujan, Noether,
Low tier: Kaczynski (yes, unironically. I have some familiarity on the topic)
Shit tier: Wronski
