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up vote 21 down vote

added by quid Feb 16 '14 at 12:54

I used to think that the answer to your first question had to do with some computations which Gauss made between 1792 and 1793, but Prof. W. Narkiewicz mentions in his "Development of Prime Number Theory" that L. Euler had already stated--sometime around 1762--that the number of prime numbers not exceeding x is approximately equal to x/log x. It seems that Prof. Narkiewicz based his assertion on the following paper: L. Euler, De numeris primis valde magni. Novi Acta Acad. Sci. Petropol. 9, pp. 99-153 (1764). – J. H. S. Feb 25 '14 at 0:33

@J.H.S. Thanks for the info. But one should not answer these questions here. – quid Feb 25 '14 at 7:24

@J.H.S. Arnold calls Legendre "the first scientist to study this problem", but your reference clearly shows Euler got there first. – Andres Caicedo Feb 27 '14 at 3:45

@Andres: Larry Goldstein mentions in his "A history of the Prime Number Theorem" that the first published statement which came close to the PNT was due to Legendre in 1798 (that's the year in which appeared the first edition of his "Essai sur la théorie de Nombres")... I wonder if somewhere in the Nachlaß of Legendre there are indications of the precise year in which Legendre started his research on the PNT. – J. H. S. Feb 27 '14 at 6:08

You are not supposed to answer the questions here – Helios Mar 1 '14 at 14:20

up vote 17 down vote

added by Jack M Feb 16 '14 at 0:14

Angles? Distances? Which ones? How were they measured? – Jack M Feb 16 '14 at 0:14

Tycho Brahe's observation data. – metacompactness Feb 16 '14 at 10:47

The question is about what the data said, not who recorded it. – Jack M Feb 16 '14 at 10:48

@meta please do not answer questions here. – quid Feb 16 '14 at 12:45

Please don't upvote questions that already have 10 votes! The proposal needs 40 questions with 10 or more votes, and you only get 5 votes, so upvotes on questions such as this are essentially wasted! If you can't see any questions you want to upvote, please start a discussion above and tell others what kinds of questions you would upvote. – Jack M Feb 19 '14 at 11:12

show 2 more improvement suggestions

up vote 14 down vote

added by kaine Feb 18 '14 at 19:01

This is a good on topic pure non-technical question, with a definitive answer and some juicy controversy in the story. I remember chatting about this in the main math.SE chatroom. I am out of votes. :) – J. W. Perry Feb 19 '14 at 4:01

up vote 12 down vote

added by Brian Rushton Feb 19 '14 at 17:09

Proposed by Jack M. – Brian Rushton Feb 19 '14 at 17:13

up vote 11 down vote

added by Helios Feb 17 '14 at 9:00

up vote 10 down vote

added by Jack M Feb 16 '14 at 0:10

	I am somewhat at odds with this question, as it seems to be based on a false premise or is "too broad" (the need coming up in most any numerical work). – quid Feb 16 '14 at 14:43
	I find this to be an excellent question. It is the sort of question to which I would endeavor to respond after assembling my research. It demands definitive answers focused around the era of John Napier. – J. W. Perry Feb 17 '14 at 6:31

up vote 10 down vote

added by Jack M Feb 16 '14 at 0:12

Did people used to think all matter was continuous? – Jack M Feb 16 '14 at 0:12

up vote 10 down vote

added by Andres Caicedo Feb 16 '14 at 8:35

	A well posed source request. I like this. It is an example of the sort of question I might ask in the proposed site. I find source hunting in mathematics history to be a challenging task, and compound that with translation issues. – J. W. Perry Feb 17 '14 at 6:23
	@J.W.Perry What is the rationale for deleting answers? – Robert Cartaino Feb 17 '14 at 15:18

up vote 10 down vote

added by Helios Feb 16 '14 at 10:44

up vote 10 down vote

added by quid Feb 16 '14 at 13:01

	"Europe" might be a bit broad and vague; one could narrow this down with more details. – quid Feb 16 '14 at 13:02
	I would say it's the "how" that's a bit broad. – Jack M Feb 16 '14 at 13:36
	Perhaps, but for something like this a "when" is always implicitly a "how" since it is about a longer process and not an isolated event. – quid Feb 16 '14 at 13:43
	Another legitimate typical question that I would expect to see on this site. In this case I would have an answer, but the how is difficult as it took so long to catch on and involved so many influences over time. – J. W. Perry Feb 17 '14 at 6:48
	I removed the explcit mention of 'how'. – quid Feb 18 '14 at 19:48

show 1 more improvement suggestion

up vote 10 down vote

added by Jack M Feb 16 '14 at 13:37

up vote 10 down vote

added by Kvothe, edited by e-sushi Feb 17 '14 at 9:15

up vote 10 down vote

added by abatkai Feb 16 '14 at 22:15

If I'm not mistaken, Cauchy worked in the early 19th century and Peano in the late 19th century. – Michael Hardy Feb 21 '14 at 4:49

Well, I guess it must have been somewhere in between. – abatkai Feb 21 '14 at 9:08

See the beautiful book by Judith Grabiner, The Origins of Cauchy's Rigorous Calculus (1981), page 140 : "Actually, his [Cauchy's] proof implicitly assumed the function to be uniformly continuous, though he did not distinguish between continuity and uniform continuity, just as he had not distinguished between convergence and uniform convergence." – Mauro ALLEGRANZA Mar 4 '14 at 10:39

up vote 10 down vote

added by Ana Galois Feb 17 '14 at 4:26

Probably too broad, but here's an idea for something similar: Has any culture ever used something other than squares to measure area?, that is, we use "square meters" as a unit shape to quantify area, but has anyone ever used eg triangles? – Jack M Feb 18 '14 at 11:19

up vote 10 down vote

added by neizod Feb 17 '14 at 4:37

This is an example of why a history-dedicated community could be useful - for incredibly specific questions such as this. Although a lot of people might know about the invention of logarithms, it takes a real grasp of history to be able to find a reference for something like this. – Jack M Feb 17 '14 at 15:00

Grammatical rephrase suggestion: Who invented the Haversine formula (or at least the oldest paper in which it was cited)? – J. W. Perry Feb 19 '14 at 5:54

up vote 10 down vote

added by Kvothe Feb 17 '14 at 9:06

up vote 10 down vote

added by BMS Feb 17 '14 at 16:23

up vote 10 down vote

added by Joel Reyes Noche Feb 18 '14 at 1:19

up vote 10 down vote

added by frabala Feb 18 '14 at 11:15

Maybe a bit too recent to count as history - this is what, 1970s? I think this would get better answers at MathOverflow. – Jack M Feb 18 '14 at 11:16

Maybe, but it is also a question about history. A historian might provide other answers than a mathematician, e.g. putting the question in a wider context. – rem Feb 18 '14 at 14:58

up vote 10 down vote

added by adrienlucca.wordpress.com Feb 18 '14 at 14:15

A little vague, but I imagine the question body would clarify. – Jack M Feb 18 '14 at 22:22

up vote 10 down vote

added by Michael Weiss Feb 18 '14 at 16:16

up vote 10 down vote

added by kaine Feb 18 '14 at 19:05

up vote 10 down vote

added by Ben A. Feb 19 '14 at 1:29

up vote 10 down vote

added by Nikolaj-K Feb 19 '14 at 9:14

Did you mean ever? – Jack M Feb 24 '14 at 18:54

@Jack: I mean as a research reference, not as note of historical importance. Working under Russel, he participated in the prediacte logic revolution but then abandoned this line of study. I read the book for philosophy but ended up learning maht from it (not recommended as an intro, though). He definitely is opinionated in the subject at the time of writing the book, but I hardly ever head mathematicians mention him. That's why I came to ask myself the question. – Nikolaj-K Feb 24 '14 at 19:12

Tractatus has no significant mathematical content. His contribution to logic was limited to the "divulgation" of truth-tables. W's influence on the Phil of Math debate of the '30s is important, and also "later" W's philosophy has interesting discussions on Phil of Math (W adopted a "finitist point of view) : see at least Mathieu Marion and Paolo Frascolla books on Wittgenstein's Phil of Math. – Mauro ALLEGRANZA Mar 4 '14 at 10:33

up vote 10 down vote

added by Nikolaj-K Feb 19 '14 at 9:17

up vote 10 down vote

added by Brian Rushton Feb 19 '14 at 17:08

up vote 10 down vote

added by Brian Rushton Feb 19 '14 at 17:09

up vote 10 down vote

added by MathsBooks Feb 21 '14 at 14:29

up vote 10 down vote

added by Wrzlprmft Feb 24 '14 at 12:51

up vote 10 down vote

added by Per Manne Feb 24 '14 at 21:13

up vote 10 down vote

added by BMS Feb 26 '14 at 17:29

up vote 10 down vote

added by User51 Mar 1 '14 at 9:56

up vote 10 down vote

added by User51 Mar 1 '14 at 10:10

Wow, this is a great question. – Jack M Mar 2 '14 at 9:13

Thanks, I am not an English native speaker, thus... ;-) – User51 Mar 17 '14 at 11:23

up vote 9 down vote

added by Jack M Feb 16 '14 at 13:37

up vote 9 down vote

added by BMS Feb 18 '14 at 1:01

This seems incredibly broad. – quid Feb 18 '14 at 19:37

Agreed; Changed "in what ways did science..." to "What are examples of science.." – BMS Feb 18 '14 at 22:31

(To give a better sense of this question, an "example" I'm thinking of is Newton's planetary work & Calculus.) – BMS Feb 18 '14 at 22:33

@BMS I think having either a specific science or a specific field of maths would improve this question even further. – Jonathan Van Matre Mar 22 '14 at 20:31