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Old 2022-01-22, 23:45   #34
masser
 
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Quote:
Originally Posted by VBCurtis View Post
In his honor, we were leaving the list incomplete.
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Old 2022-01-23, 07:10   #35
a1call
 
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I believe Birumi discovered that a point on a the circumference of a circle will move on a straight line when that circle is rolled along a circle with double diameter to it. A significant discovery in translating rotation to a linear motion.

https://en.wikipedia.org/wiki/Al-Biruni

But certainly not the greatest mathematician. That title can only belong to Euler. I'm sure all the mathematicians on the list would agree if they were to be honest.
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Old 2022-01-23, 15:24   #36
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Quote:
Originally Posted by a1call View Post
I believe Birumi discovered that a point on a the circumference of a circle will move on a straight line when that circle is rolled along a circle with double diameter to it. A significant discovery in translating rotation to a linear motion.

https://en.wikipedia.org/wiki/Al-Biruni

But certainly not the greatest mathematician. That title can only belong to Euler. I'm sure all the mathematicians on the list would agree if they were to be honest.

Al-Biruni is an impact crater that lies on the far side of the Moon, just beyond the eastern limb. This portion of the surface is sometimes brought into sight due to librations of the Moon, but due to its location the crater is viewed from the side. Al-Biruni lies to the south of the crater Joliot, and to the northeast of Goddard. It is named after the great Persian scientist Al-Biruni.

Al-Biruni
https://images.app.goo.gl/VL2Q4KeB84Hj6CSZ6
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Old 2022-01-23, 16:08   #37
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What makes a mathematician a great one? Different people have different criteria.

Two things I would look for are
  1. Enlarging the scope of mathematics by creating new areas or disciplines
  2. Advancing existing areas or disciplines
The first criterion favors earlier mathematicians. The smaller the "base" of existing mathematics, the greater the relative contribution a given advancement would make. This is why Archimedes stands out in my mind. Nowadays, most of what he found is within the grasp of college freshmen taking engineering mathematics, physics, or statics and dynamics. In his day, though, his discoveries - particularly in geometry and prefiguring integral calculus - were revolutionary. This puts him on my "short list."

Euclid's development of a logical framework (postulates, hypotheses, theorems), as well as his applying it to geometry and number theory, earns him a place on my short list. However, his "Euclid's windmill" proof of the Pythagorean Theorem knocks him down a peg

Isaac Newton created a whole new area of mathematics - calculus - and invented modern mathematical physics. He goes on my "short list."

By both criteria, I would say Euler deserves to be at the top of the list. He is responsible for what may be the most amazing equation in mathematics,

e^{i\pi}\;+\;1\;=\;0

It contains the fundamental constants 1 and 0; the constants \pi and e (so named in honor of Euler), the plus sign, and the equals sign. It is of course, a special case of "Euler's formula,"

e^{i\theta}\;=\;\cos\(\theta\)\;+\;i\cdot\sin\(\theta\)

He also deserves high ranking on the list of "Famous last words." He was sitting on his couch smoking a pipe when he suffered a massive stroke. The pipe fell from his mouth. He said (in English translation) "I die." And then he was gone.

I would say that Gauss also makes the "short list." I have heard it said that he was the last "complete mathematician" - that is, he understood all the mathematics of his day, and that nobody since then has. (This is because after Gauss, there was simply more mathematics than a single person could possibly understand.)

It is a bit hard to assess Gauss's contributions, however. On one hand, he was so intent on polishing his work to perfection before publishing it, that some of his discoveries were rediscovered by others before he made them known. (His motto was "Pauca sed matura.") On the other hand, those reading his work sometimes felt deprived of understanding what led him to his results. Legend has it that he would say things like, "When a building is done, the scaffolding should be removed," but the complaint was more like he had thrown away the designs and blueprints.

George Bernhard Riemann revolutionized geometry. Riemannian geometry laid the theoretical foundation for General Relativity. Riemann also wrote a single 9-page paper on number theory, Über die Anzahl der Primzahlen unter einer gegebenen Grösse. IMO it meets the criteria I give above. In addition, Riemann left notes behind. They led to further advances, e.g. the Riemann-Siegel formula.

David Hilbert contributed not only many important mathematical results, but also a program to formalize proofs, and named a number of questions for further research. He goes on my "short list."

IMO Chen Jingrun rates an Honorable Mention.

I will also mention a mathematician who, although he did not originate any new mathematical concepts or prove any major results, nonetheless contributed substantially to mathematics. His name was August Leopold Crelle. Although his mathematical talent may not have been exceptional, he earned a doctorate in mathematics. He was also genuinely enthusiastic about mathematics, and was a good organizer. He also had an extraordinary facility for recognizing the importance of the work being done by talented young mathematicians, and encouraging them in their research. And, at the urging Niels Henrik Abel and Jakob Steiner, he founded a new mathematical journal, Journal für die reine und angewandte Mathematik, AKA "Crelle's journal."

Its first volume had several articles by Abel, including his proof that quintic polynomials were not generally solvable by radicals, as well as articles by Steiner. The list of other mathematicians whose early work was published in Crelle's journal includes Johann Peter Gustav Lejeune Dirichlet, Ferdinand Gotthold Max Eisenstein, Carl Gustav Jacob Jacobi, Ernst Eduard Kummer, August Ferdinand Möbius, and Karl Theodor Wilhelm Weierstrass.
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Old 2022-01-24, 03:00   #38
chalsall
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Quote:
Originally Posted by Dr Sardonicus View Post
What makes a mathematician a great one? Different people have different criteria.
Thank you for taking the time to put that body of language together, and posting it here.

This is an example of why I absolutely love the MF. After a day of tolerating noise, one can come here and read some really serious and considered stuff.

Thanks again for that. I'm reading it now for the second time, and am enjoying the high bandwidth signal...
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Old 2022-01-24, 11:38   #39
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Quote:
Originally Posted by Dr Sardonicus View Post

By both criteria, I would say Euler deserves to be at the top of the list. He is responsible for what may be the most amazing equation in mathematics,

e^{i\pi}\;+\;1\;=\;0

It contains the fundamental constants 1 and 0; the constants \pi and e (so named in honor of Euler), the plus sign, and the equals sign. It is of course, a special case of "Euler's formula,"

e^{i\theta}\;=\;\cos\(\theta\)\;+\;i\cdot\sin\(\theta\)
De Moivre?

A few more names worthy of consideration, Omar Khayyam, Stirling (see Ian Tweddle's book), Maclaurin..

[Off thread:
Suppose that all of the names listed in this thread (thus far) were put into teams for a mathematical Olympiad where some of these "teams" may consist of one person. Rather than solve questions, who would be the one(s) to dream up or create the best questions to stump everyone. (I don't think AI has come far enough bootstrapped by quantum processes to "imagine" well enough ..yet.) Look at what stumped Euler and what presently stumps everyone..Langlands, P vs NP, prime number distribution..]

Last fiddled with by jwaltos on 2022-01-24 at 12:06
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Old 2022-01-24, 20:57   #40
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Dedekind and Kronecker have not been mentioned yet, I believe. Not the greatest but good ones.

Last fiddled with by Till on 2022-01-24 at 21:00
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Old 2022-01-25, 13:14   #41
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Quote:
Originally Posted by Dr Sardonicus View Post
What makes a mathematician a great one? Different people have different criteria.
Again, something of a digression but it goes to the quote above regarding interpretive perspective and judgement criteria where effective utilization of language has a part to play. If the "most renowned" replaced "greatest" there would be a different connotation to the question. Second, the responses provided profile the "responder" somewhat;John Dewey and Sapir-Worf come to mind. Questions that are all encompassing (within stated boundary conditions) addressing absolutes (as a limit process) usually requires some additional qualitative associations as do certain mathematical statements or they are considered as ill-posed not that rudy's question was. Generalizing the question to the "greatest" (Muhammad Ali) "anything" such as actors, politicians, philosophers, scientists, civilizations..where survivability through words [culture..] and/or deeds [technology applied via culture..recursive] provides a context wherein the initial question can be considered both locally, globally..and non-locally ->(going quantum here).

Last fiddled with by jwaltos on 2022-01-25 at 13:16
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Old 2022-01-25, 15:41   #42
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No one from here https://www.mersenneforum.org/forumdisplay.php?f=136 ?
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Old 2022-01-25, 17:25   #43
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The most renowned would be without a doubt Sir Isaac Newton if it were a sort of popular contest where the general population with at least a high school education were polled.

But I am not looking for the most popular in the general consensus. I am thinking of the one who has influenced the course on mathematics in general.

I would say of those there is probably a short list of 5, 7, 12, 18. not a lot more. I believe if you take an extended approach many of those are French.
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Old 2022-01-25, 17:25   #44
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You think Google would be programmed to use the "Greatest" qualifier to indicate singularity. But still I agree with it's 1st choice:

Quote:
People also ask
Who is greatest mathematician of all time?
The best 10 mathematicians are:
Leonhard Euler. ...
Srinivasa Ramanujan. ...
Carl Friedrich Gauss. ...
Isaac Newton. ...
Euclid. ...
Archimedes. ...
Aryabhatta. ...
Gottfried W.
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