25
votes
How were irrational numbers accepted by mathematicians?
Let me clarify a couple of things. No student of Pythagoras discovered irrational numbers, although this is a common misconception, Pythagoreans and even Euclid did not associate numbers with ...
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25
votes
Accepted
Did ancient Greek mathematicians consider numbers independently of geometry?
The answer is yes. There was a split. First of all, for the Greek mathematics (and very long after them)
"numbers" were integers. "Rational numbers" were called fractions, and no ...
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23
votes
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Hypothesis testing: Fisher vs. Popper vs. Bayes
According to Mayo, Popper did not designate statistical tests implementing his logic of falsification, or as Hilborn and Mangel put it "Popper supplied the philosophy, and Fisher, Neyman and ...
- 71k
22
votes
Accepted
Is the Scientific Method uniquely Western?
In a word, yes, but only interpreting "western" broadly. The tradition of precise and systematic astronomical observations comes from ancient Babylonians, i.e. from Mesopotamia, and even ...
- 71k
16
votes
Accepted
What is the origin of polynomials and notation for them?
Although many problems that we now reduce to polynomial equations were solved since time immemorial early occurences are coached in verbal and/or geometric terms, and polynomials are not treated as ...
- 71k
16
votes
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What was Kolmogorov’s point of view in the philosophy of mathematics?
Kolmogorov was not exactly free to express his views considering the situation in the Soviet Union. Philosophical issues, even concerning mathematics, were ideologically sensitive, and everyone had to ...
- 71k
13
votes
Why did Aristotle make mistakes in his laws of motion?
Air or more generally medium resistance was not yet treated as a separate effect in Aristotle's time. Nor was there a clear idea of motion in a vacuum, in fact most ancient Greek philosophers, ...
- 71k
12
votes
In ancient times, how did people conclude that the shape of Earth is a sphere?
Eratosthenes of Cyrene did an experiment that confirmed that the Earth was roughly spherical, and estimated its circumference around 200 BC.
Note that the lunar eclipse observation mentioned by ...
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12
votes
Who was the first to say "Shut up and calculate!"?
Some centuries before Mermin, Leibniz in the 17th century was seeking a solution to some of the denominational quarrels that were plaguing his generation by envisioning a calculus ratiocinator that ...
- 3,759
12
votes
Accepted
Does Lakatos' argument in favour of 'informal mathematics' hold up in most cases?
I do not agree with the assumptions made in the title and in main text of this question, namely that Lakatos rejects the Euclidean methodology and exposition of mathematics.
In the way I read it, ...
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12
votes
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The Greeks did not discover "a single scientific law"
It is a strange idea that scientific laws can be only expressed with algebraic means. The Greek did discover several scientific laws. The oldest one is attributed to Pythagoras himself: it relates the ...
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12
votes
Accepted
Who said that math or statistics is not free from class interest?
The quote is from Lenin, in his instructions to Popov when discussing the project of organizing Soviet statistics in summer of 1918:"Statistics, as any other scientific discipline, poses problems ...
- 71k
11
votes
Accepted
Why and when did some areas separate themselves from philosophy and some not?
The area of knowledge separates itself from philosophy as soon as a reliable method of obtaining exact knowledge in this area is invented. Thus mathematics separated from philosophy at its very ...
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11
votes
Accepted
Who was the first to say "Shut up and calculate!"?
Mermin has a thorough analysis[1] and traces the phrase to himself in a 1989 Physics Today column [2] & makes a case that the numerous attributions to Feynman may or may not be mistaken.
[1] Could ...
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11
votes
What's the origin of the concept of the five senses?
It goes back at least to Aristotle's De Anima, Book II, ch. 7-11 (these five chapters being respectively devoted to sight, hearing, smell, taste, and touch). This is perhaps where it started, since ...
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10
votes
Conflict between physics and philosophy
The modern conflict is not so much between physics and philosophy, as between physics and "half" of philosophy, the continental philosophy. Scientists, and physicists in particular, see culturally ...
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10
votes
Why did Newton want lines to be generated by continued motion of points rather than by apposition of parts?
Problem: classical geometry is not happy with infinitesimals
Newton is systematically trying to avoid basing calculus on infinitesimal geometric quantities. We can see this from how he emphasizes ...
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10
votes
Accepted
How was difference in water pressure perceived in ancient cultures or the middle ages?
One has to distinguish static pressure from the dynamic pressure in a flow.
Static pressure was understood to some extent by Archimedes and later Hellenistic writers like Hero and Ctesibius. At least ...
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10
votes
Hidden agenda of the Galileo trial?
The Assayer & Redondi's "G3"
Michele Camerota's 2008 Complete Dictionary of Scientific Biography entry on Galileo describes this theory in a section entitled "Atomism and the ...
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10
votes
Historical examples of "pseudoscience" becoming "science"
For a long while it was widely believed that the main cause of peptic ulcer disease was stress or spicy food. When the theory arose that it was in fact usually an infection this was rejected by the ...
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10
votes
Did the Idea of Universal Gravitation predate Newton?
The idea, yes, Aryabhata speculated about something like that as early as c. 500 AD, Brahmagupta called it gurutvākarṣaṇ. So did Kepler, at about the same time as Ahmad Baba al Massufi (late 1500-s), ...
- 71k
10
votes
Gauss on philosophers
The quote is not accurate but Gauss actually wrote something similar to Schumacher in the letter of 1 November 1844 cited here, where he complains about concepts and definitions given in math books by ...
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10
votes
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What was the full name of I. Bernard Cohen?
I am quoting the full footnote published in Seven Decades of History of Science: I. Bernard Cohen (1914–2003). The full text is available in JSTOR Link.
Cohen’s sister, Harriet, was three years older ...
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9
votes
Nowadays I see a distinct "line" dividing people working in Mathematics and the Physical Sciences. Why?
You do not say what field of mathematics you are working in, and perhaps there are signs of separation there. Overall however, lively interaction between mathematics and physics is alive and well. ...
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9
votes
Mathematics PhD dissertations that opened a new field of research
John Forbes Nash Jr. got a Nobel Prize for his.
Nash earned a Ph.D. degree in 1950 with a 28-page dissertation on non-cooperative games.
The thesis, written under the supervision of doctoral advisor ...
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9
votes
What was Kolmogorov’s point of view in the philosophy of mathematics?
Kolmogovov expressed his views in this paper:
MR2278817 Kolmogorov, A. N. Modern debates on the nature of mathematics. (Russian). With a commentary by V. A. Uspenskiĭ. Reprinted from Nauchnoe Slovo ...
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8
votes
Accepted
History of the study of indeterminism in classical mechanics
Perhaps, the most insightful analysis (possibly to this day) of indeterminism in classical mechanics and its implications was given by Joseph Boussinesq, best known for his work on solitons, in a book ...
- 71k
8
votes
Who was the first to say "Shut up and calculate!"?
N. David Mermin (born March 30, 1935, in New Haven, Connecticut, USA) is Horace White Professor of Physics Emeritus at Cornell University
his quote was like this
If I were forced to sum up in one ...
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8
votes
Who was the first to say "Shut up and calculate!"?
As noted, Mermin was probably the first to utter the exact words “Shut up and calculate”. However, the equivalent rallying cry of “Get the numbers out” has its origins some decades earlier.
...
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8
votes
What did it historically mean in physics for something to "exist"?
To not be measured is not to have any behavior. No dynamic is induced on any other system in the universe by this object (Rosen 1978).
Objects without behavior do not exist. Their behavior is that ...
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