All Questions
4,128
questions
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Understanding how Stern-Gerlach tests Bohr-Sommerfield Hypothesis
I am trying to get to the bottom of a few things in the Stern-Gerlach experiment. First, on wikipedia, it says
The Sommerfeld model predicted that the magnetic moment of an atom measured along an ...
2
votes
1
answer
345
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When did the error function get its modern definition?
I am currently writing an essay on the error function and after researching its historical origin, I found out who first defined it: J.W.L. Glaisher. But his definition is different from today's form. ...
- 23
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71
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classified dissertations in WWII
What were the most important classified doctoral dissertations in physics and/or mathematics written by grad students during WWII on any or all sides of the war (US, UK, Japan, SU, Germany, Italy, etc....
- 195
4
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79
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On Bryce Seligman DeWitt's Name Change
Weinberg, in his memoir on Bryce Seligman DeWitt (available at https://www.nasonline.org/publications/biographical-memoirs/memoir-pdfs/dewitt-bryce.pdf) states that
In 1950 two major but totally ...
- 275
5
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1
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386
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The Originator of Cobweb Diagrams
A cobweb diagram is a visualization tool that allows one to qualitatively study the iterates of a self-map of the real line based on the graph of the function; here is an example:
(Here the map is ...
- 275
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49
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Where did the index of a subgroup notation $[G:H]$ begin to be used?
In texts of algebra, the cardinality of cosets is written in $[G:H]$ or $|G:H|$. Where did this notation originate?
The history about $G/H$ can be found here. $[G:H]$ is called index of a subgroup. ...
- 303
3
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114
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References on the role of diagrams in scientific advancement
A number of diagrammatic formulations have played an important role in the advancement of science. Some embody representations of physical phenomena, while others model mathematical or logical ideas ...
- 241
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Did Einstein attribute a physical meaning to the affine connection in his unification models?
As seen in Einstein's 1920 address from the University of Leiden, for example, he did consider it meaningful to distinguish between the presence and absence of the aether, and certainly he seemed to ...
- 135
4
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116
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Terminology associated with mathematical induction
In "Number: The Language of Science" (1930), Tobias Dantzig refers to what we call the base case of mathematical induction as "the induction step" (and refers to what we call the ...
- 261
-1
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1
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111
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Why the scaling rule $\delta(a x)=\frac1{|a|}\delta(x)$ was historically adopted? [closed]
It seems to me that it would be more natural to consider Dirac Delta as a piecewise-defined function, as described here, with the scaling rule $\delta (ax)=\delta(x)$. This way we keep all the ...
- 614
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1
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68
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Where can I find the early proofs for the simplicity of $\text{PSL}(n,q)$?
I am doing a research project on the history of group theory, and want to know about the early developments on the subject. There are plenty of proofs about why the projective special linear group ...
- 41
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108
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History of group actions as their own structures
I'm interested in when (and how) the modern idea of a group action developed and how group actions became their own algebraic structures.
As far as I can tell in the 19th century group actions were ...
1
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1
answer
66
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Biographical info on Alan Earnshaw (Chemistry of the Elements)
I'm looking for any bio/info/obit on Alan Earnshaw, who was a co-author of Norman Greenwood (who has a wiki page and an online obit).
FYI, I tried several different Google searches, but the best I ...
- 13
6
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199
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When did people first know that the sky was illuminated by the Sun?
During the day, the sky is bright blue and, along with the yellow light from the Sun, it illuminates the surface of the Earth.
What is the earliest recorded knowledge that the sky wasn't self-...
- 316
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190
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Was not chess notation an earlier sort of Cartesian Coordinates?
I realize modern algebraic notation is fairly new but for as long as there have been recorded chess games, every square I think was referred to using two coordinates, in old descriptive notation a ...
- 1,041
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86
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The history and origin of the Argument Principle ( or Cauchy's argument principle)
I am looking for a book that discusses The history and origin of the Argument Principle ( or Cauchy's argument principle) Thanks!
1
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132
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Katz's symbol 兄 for Gauss-Manin connections
In his famous 1970 paper [1], Nicholas Katz used the character 兄 for the Gauss-Manin connection. I have always been curious about the history behind this symbol.
Question: What motivated Katz to use ...
- 11
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2
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177
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When was the first time/s that sheaves entered algebra and algebraic geometry?
I'm interested in knowing about the first published texts in which sheaf-theoretic methods were used in algebra and/or in algebraic geometry.
The oldest instance I am aware of is J.-P. Serre, ...
2
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120
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Does Galilean/Newtonian mechanics reject both consequences of Aristotle's dynamical pseudo-law : $ V = F/m$, or only consequence (1)?
Note : my question is not as to whether consequence (2) is correctly derived from Arstotle's "law" ( I think it is the case) but as to whether this consequence is still true in Newtonian ...
- 121
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48
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When was the hydrogen's absolute mass found first in history?
When was hydrogen's absolute mass i.e, in Kg, was found for the first time.
What method was used and what information from earlier researches were used for it?
Also was there any method at that time ...
- 121
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1
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107
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How did Thomson claim that charge on hydrogen ion was equal to charge on electron without knowing charge on electron?
From "The Electron" by J. J. Thomson, published in The Scientific Monthly Vol. 20, No. 2 (Feb., 1925), pp. 113-115
https://www.jstor.org/stable/7115
[Continued discussion] previously ...
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1
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161
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How and when did the dedicated study of locally compact groups begin?
How and when did the dedicated study of locally compact groups begin?
Specific instances from literature, recorded stories, etc., may help supplement the answers. There seems to be no reason why I ...
4
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99
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When was the calculus first part of college curriculum in USA?
Or I guess the Colonies, if it happened before 1776?
I know that mathematics tended to be both applied and emphasized things like taking fifth roots. Also, I think long ago high school and college may ...
- 1,041
20
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2
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5k
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What type of abrasive grit was used to grind lenses for telescopes?
Today the standard for fine grit is Alumina and Cerium Oxide. However, in the 1600s, the elements Al and Ce were not known.
What type of fine grit did they use to grind and polish the lenses for ...
- 861
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1
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133
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From where did Heisenberg (1925) obtain the classical frequency equation?
In Quantum-Theoretical Re-Interpretation (1925), Heisenberg gives the following:
In order to characterize this radiation [of an electron] we first need the frequencies which appear as functions of ...
- 1,009
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0
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90
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Was there a French nuclear weapons project during WWII?
France research pioneered the discovery of radioactivity and nuclear research. However looking at the names of non-US Americans in the Manhattan project there are very few French names (maybe just ...
- 1,799
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91
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Finding the Letter from Freeman Dyson to Gerald Gabrielse in 2006
In 2006, the renowned physicist Freeman Dyson wrote a letter to his colleague Gerald Gabrielse regarding an advance in precision about measuring the magnetic moment of an electron. An excerpt of his ...
- 141
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329
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Is there a theorem proof whose accuracy is doubted because it is short?
Is there a theorem proof whose accuracy is doubted because it is short?
He told me while chatting with a friend of mine. It's about a mathematician who proves a difficult theorem very briefly and ...
- 163
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58
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What was the chronologically first derivation PV=nRT?
Wikipedia describes the Ideal Gas Law as coming from a combination of Boyle's Law, Charles' Law, Avogadro's Law, and Gay-Lussac's Law. It gives several derivations, both empirical and theoretical, ...
- 160
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214
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Has Penrose ever acknowledged criticism of the Penrose-Lucas argument?
So, Roger Penrose is a bright guy, I mean, he won the Nobel Prize, but the Penrose-Lucas argument that the human mind is a hypercomputer based on Godel's Second Incompleteness Theorem is laughably bad....
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77
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Resource recommendation for experiments that led to major concepts in physics
Any resource recommendations for history of physics giving special attention to experiments that led to certain concepts and theorems in physics? For example what led to the motivation of definition ...
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0
answers
61
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Reference Request: History of Chern-Simons Theory
Chern-Simons theory is a topological gauge field theory and play a prominent role in many brnaches of phyiscs and mathematics. On the physical side, it appears for example in three-dimensional ...
- 101
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124
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How futuristic was the use of a laser in 1964's "Goldfinger"?
In the 1964 adaptation of the James Bond novel "Goldfinger", in a famous scene, Bond is bound to a table and threatened to be cut in half by a powerful laser that Goldfinger later uses to ...
- 121
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1
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151
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"Just before he died, (Gregor) Mendel requested that an extensive autopsy be done." Why? Was he simply "very enthusiastic for all kinds of research"?
NPR's December 30, 2022 article Why scientists dug up the father of genetics, Gregor Mendel, and analyzed his DNA includes speculation by those involved about whether Mendel would want his body to be ...
- 2,006
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228
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Publication of mathematical papers in journals of enemy country
I restrict my question to mathematics since this is probably the most internationalized of all sciences. During WWII, did any British mathematicians (or mathematicians from allied countries) publish ...
- 45.4k
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146
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When Kervran suggested biological transmutation of elements did anyone argue this
My understanding is that Kervran fed chickens a diet lacking in calcium and yet eggs were produced with calcium in their shells.
Two related questions:
Could not the calcium have been from the bones ...
- 1,041
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1
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71
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Were oxocarbons other than carbon monoxide/dioxide always classified as organic compounds?
The simplest and most common oxocarbons are carbon monoxide (CO) and carbon dioxide (CO2). The general consensus is that they are inorganic (see: Is carbon dioxide organic or inorganic?). The other ...
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2
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164
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What was known about Chebyshev polynomials in 1900?
Around 1900, was it widely known that the Chebyshev polynomial $T_n(X)$ satisfies the identity
$$ T_n(X) \circ \frac{X+X^{-1}}{2} = \frac{X^n+X^{-n}}2?$$
And also, would one expect top-notch ...
- 121
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96
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Did the ancient Greeks know that "most" cube roots are irrational?
It is common knowledge that the Pythagoreans discovered irrational numbers (or incommensurability), for example if the hypotenuse of an isosceless right triangle is compared with one of the legs or ...
- 401
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174
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Leonhard Euler's Mathematical Proof of God
There is a famous legend inspired by Euler's arguments with secular philosophers over religion, which is set during Euler's second stint at the St. Petersburg Academy. The French philosopher Denis ...
- 121
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1
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142
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Which physical quantities were used or introduced by Newton?
I have never read his original works, but I would say that he must have used length, volume, time, velocity, acceleration, momentum or force, and maybe (kinetic) energy. Which quantities appeared in ...
- 182
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58
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What was Aristotle's experience with vacuums?
What was Aristotle's idea of a vacuum when he said that nature abhors one? How would any ancient have experienced/observed or created a vacuum beside, I guess, when one breathes or perhaps when water ...
- 1,041
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49
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Is there a resource which explains the history of how the Leidenfrost effect was explained?
The context is that I am trying to teach some middle school students that in science, a question could be posed/ an observation made but being able to answer or explain it, might take a couple of ...
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0
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98
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Is there a transcript or audio recording of the lecture on Riemann Hypothesis by John Nash at Columbia University in 1959 anywhere?
The film A Beautiful Mind depicts this scene, and it is mentioned on wikipedia as well as many articles/books. John Nash famously gave a lecture to 250 mathemeticians at Columbia University in 1959 ...
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2
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245
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Omar Khayyam is well known as a mystical poet (Quatrains). He is also known as a mathematician. Are these the same?
Omar Khayyam is well known as a mystical poet (his famous Quatrains).
He is also somehow known as a mathematician (Equations of degree 3 ?).
Are these the same person? A colleague in Arithmetical and ...
- 101
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2
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227
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What's the history of "left as exercise" or notions similar to that?
It is now common to come across the term "left as exercise" in mathematics textbooks, and from there a comical usage of such terms was developed, typically by applying them to absurdly ...
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1
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104
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Did Riemann invent the Riemann curvature tensor?
I'm pretty sure they weren't using tensors in the modern sense at that point, but to what extent did Riemann lay out the structure or significance underlying his eponymous tensor? In his habilitation ...
- 135
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177
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Poincaré's definition of mathematics (?)
Poincaré is said to have given this definition of mathematics:
It is the art of giving the same name to different objects. I can not believe this quote is from Poincaré.
Did Poincaré really say this? ...
- 101
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49
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Biographical details on Otto Zoll
Zoll's surfaces are a special kind of surfaces generalizing the spheres, in that all of their geodesics are closed and of the same length.
I've tried to gather some biographical details on Otto Zoll ...
- 1,647
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67
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Why are the views of quantum mechanics called the Copenhagen School?
Why was the name of a group of opinions about the meaning of quantum mechanics called the Copenhagen Interpretation, relative to the Danish city of Copenhagen and not the name of a scientist named ...
- 101