27 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 ...
Alexandre Eremenko's user avatar
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 ...
Conifold's user avatar
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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 ...
Conifold's user avatar
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15 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 ...
Mikhail Katz's user avatar
  • 5,496
15 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 ...
mdewey's user avatar
  • 596
13 votes
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Who was the first to say "Shut up and calculate!"?

Mermin has a thorough analysis1 and traces the phrase to himself in a 1989 Physics Today column2 & makes a case that the numerous attributions to Feynman may or may not be mistaken. Mermin, Could ...
vzn's user avatar
  • 246
12 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. According ...
nwr's user avatar
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12 votes
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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, ...
Nicola Ciccoli's user avatar
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 ...
Alexandre Eremenko's user avatar
12 votes
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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 ...
Conifold's user avatar
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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 ...
R.P.'s user avatar
  • 654
11 votes

Historical examples of "pseudoscience" becoming "science"

*copied from my answer to another question It seems ball lightning was disbelieved by scientists until around 1960. See Wikipedia . I knew a geologist who told us how his eye-witness account of ball ...
Gerald Edgar's user avatar
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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 ...
Geremia's user avatar
  • 5,289
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), ...
Conifold's user avatar
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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 ...
user6530's user avatar
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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 ...
AChem's user avatar
  • 4,049
9 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 ...
Marble's user avatar
  • 191
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. ...
Conifold's user avatar
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9 votes
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Why is pure mathematics important? More generally, why do some scientists deal with inaplicable notions?

Historical experience shows that pure mathematics is one of the most useful parts of science. Pure mathematicians discover things which find applications later. Without pure mathematics, most of the "...
Alexandre Eremenko's user avatar
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 ...
Bence Mélykúti's user avatar
9 votes

Historical examples of "pseudoscience" becoming "science"

Plate tectonics It was put forth by a meterologist, and offered no explanation how, given the solid crust and mantle, the continents could drift about like icebergs on the liquid core. The discovery ...
Mary's user avatar
  • 617
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 ...
Alexandre Eremenko's user avatar
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 ...
Gottfried William's user avatar
8 votes

Why was modern science and mathematics a European phenomenon?

It's hard to put a precise date without generating debate, but I'd put forward that Europe took the lead at some point between the early 14th to late 15th century. Several processes were in full ...
Denis de Bernardy's user avatar
8 votes
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Who influenced Gauss in his abstract approach to mathematics?

Gauss in Disquisitiones Arithmeticae (1799) does indeed express something close to what is now called mathematical formalism and structuralism. He writes: "What is calculated (in the sense of ...
Conifold's user avatar
  • 75.2k
8 votes

Mathematics PhD dissertations that opened a new field of research

There are many examples. Here are a few that come to mind: Simon Donaldson's thesis The Yang-Mills equations on Kahler manifolds contains the first major steps in his work on the differential ...
Dan Fox's user avatar
  • 384
8 votes

The Greeks did not discover "a single scientific law"

Euclid wrote an Optica (300 BC) — surely “Visual rays proceed in a straight line indefinitely” ranks with the best physical laws. So did Ptolemy (160 AD), and Hero wrote a Catoptrica (50 AD). ...
Francois Ziegler's user avatar
8 votes
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When and how did the notion/idea of physical constant emerge?

Going by Wikipedia's definition, a physical constant is a number "generally believed to be both universal in nature and have constant value in time". The significance of these constants ...
Conifold's user avatar
  • 75.2k
8 votes

Have there been instances in physics where different scientists have interpreted the same data differently?

The comments correctly say that this happens all the time. For a recent example, you can see my answer to: Can a highly-cited published paper have this type of error? I will explain here some details ...
Nike Dattani's user avatar
7 votes

Who is the philosopher Feynman cites as saying that existence of science requires the same conditions to produce the same results?

Nobody in particular, it is what is called collective image in literature. Feynman's attitude towards philosophy is expressed by another of his quotes, "philosophy of science is about as useful to ...
Conifold's user avatar
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