# All Questions

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### Who first derived $a =v^2/r$

This is a basic formula in mechanics, which determines the acceleration of a particle performing uniform circular motion. By who first derived it? In Newton's Principa, what one can find is that ...
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404 views

### When was the inverse relationship between tangents and quadrature/area first identified?

Problems concerning tangents and quadrature have a long history predating the Newton/Leibniz formulation of calculus; indeed, they are amongst the oldest problems in mathematics. It seems reasonable ...
• 6,909
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### What are Philolaos' “even-odd” numbers?

Number, indeed, has two proper kinds (ιδια ειδη), odd and even, and a third mixed together from both, the even-odd(αρτιοπέριττον). Of each of the two kinds there are many shapes, of which each ...
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882 views

### Riemann's Contribution to Integration

What did Riemann do for the theory of integration? I am asking because I hear his name a lot in relation to integration and it is often implied that he made large contributions, but I do not know ...
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### Why is one meter as long as it is?

The metre is defined as the length of the path travelled by light in a vacuum in 1/299 792 458 of a second Why is this so? Who decided that 1/299,792,458 of a ...
• 151
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### Was it suspected that the speed of electricity was equal to the speed of light?

Was it believed early on that signals sent via wire moved at exactly the speed of light or simply very fast? Who was the first to estimate the speed? EDIT: Given that they move at less than the ...
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374 views

### Was there any atomic model(s) that came between Bohr's and the actual beginning of Quantum Mechanics in early 20s?

Well, the question arose in the physics chat when slereah mentioned about it. So, was there any prominent model that came to light after Bohr and before the actual beginning of Quantum Mechanics in ...
466 views

### Reference request: What were the problems of accepting zero, negative numbers, and complex numbers? And how were they solved?

I asked this question on MSE and comments suggested I should ask it here I am currently reading Baby Rudin as my second analysis book (after Introduction to Real Analysis by Robert G. Bartle and ...
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1 vote
5k views

### How the law of inertia got discovered?

In the Feynman lectures, it is mentioned that [Vol 1; Gravitation]: Galileo discovered a very remarkable fact about motion, which was essential for understanding these laws. That is the principle ...
9k views

### How did German become the language of science?

Recently, I read an interesting article about how English replaced German as the language in which scientists communicate. But how did German become the leading language in the first place? In the ...
4k views

### What led to the fall of Göttingen?

Göttingen was the place in which many important mathematicians such as Riemann worked. It was also one of the main locations for the development of quantum theory in the twenties (e.g. Heisenberg, ...
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### Why did algebraic geometry need Alexander Grothendieck?

Grothendieck is arguably the most brilliant mathematician of the 20th century, with his influence felt the most in algebraic geometry, which he transformed. Some time ago the story used to be told was ...
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### What was Euler's motivation for introducing $i$ for $\sqrt{-1}$?

[Mauro Allegranza has answered the question of who introduced the notation $i$ (Euler, followed later by Gauss), so I have changed the title. I have also edited the question in other ways to make it ...
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### What motivated Cantor to invent set theory?

I can't imagine mathematics without sets, but the question "what was mathematics like before there were sets" is not answerable, I think. Instead, a good answer to the title question should cover a ...
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### Roman engineers

It is a common opinion that Romans did not contribute anything to exact sciences, but did contribute much to engineering. (How can it be otherwise, anyone who has been on the territory of the former ...
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### What attracted Einstein to the anomalous precession of Mercury?

The story is usually told starting with Einstein's 1915 paper Explanation of the Perihelion Motion of Mercury from General Relativity Theory, or at least its drafts from 1913-14. It was the first ...
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### How did scientists plot complicated graphs in the 19th century?

I am wondering how did Maxwell in the 19th century draw such figures as the one shown? What tools or procedures did he need? Is it all compass and ruler drawing?
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### Who discovered the covering homomorphism between SU(2) and SO(3)?

Who discovered this? It is quite nontrivial and very important in quantum mechanics.
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### What did Einstein contribute to Special Relativity that hadn't already been done by Lorentz in 1904 and Poincaré in 1905?

What did Einstein contribute to what is now called Special Relativity theory that hadn't already been done by Lorentz in his 1904 "Electromagnetic Phenomena in a System Moving with any Velocity ...
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### Ancient Chinese numbering system

It has been said that the invention of zero was a great leap forward, not only in abstract understanding, but in the ability to introduce place value notation and do computations; computing using ...
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### Hypothesis testing: Fisher vs. Popper vs. Bayes

I try to make my question short. I am familiar with Popper’s philosophy as well as with statistical hypothesis testing after Fisher and Neyman-Pearson. I am not so familiar with the Bayesian approach ...
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6k views

### What was the relationship between Einstein and Minkowski?

I read many Einstein's Biographies, but Minkowski was never mentioned, though his discovery of the union of space and time created the basis for GR. Minkowski was Einstein's teacher of mathematics ...
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16k views

### Why were 20th Century German scientists so impressive?

German (and Austrian) scientists of the late 19th - early 20th centuries seem to have been the backbone of most of modern physics - namely quantum theory/mechanics. The following are a few predominant ...
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### Is there any historical "evidence" maintaining that Euclid was a single person?

Bourbaki, for example, was the name of a set of mathematicians, rather than a single person, under which several books were published. Out of curiosity, I wonder if there is any historical evidence ...
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### Why did angular momentum get the letter L

Note - this question was inspired by this questions on physics.SE. Many (most) physical quantities are denoted with a single letter - latin or greek. For many, the letter chosen makes sense: $t$ for ...
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557 views

### What data did Kepler work out his laws from?

It's well known that Kepler worked out his laws by fitting curves to Tycho Brahe's data on the trajectories of planets through the sky. What was this data? How does one record the trajectory of a ...
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### How did Ptolemy know that days were unequal lengths?

Apparently Ptolemy was aware of the fact that the duration of time from noon to noon varied by many seconds throughout the course of a year. In modern times this fluctuation in length of day leads to ...
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### When and on what basis was it decided that an hour have 60 minutes and a minute have 60 seconds?

There were always some or he other means of measuring(estimating) the time. But I always wonder that when and how the present time system (1 Hr. = 60 Min., 1 Min. = 60 Sec.) evolved ?
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### Did Guinness Book of Records screw up on the "longest-standing maths problem (ever)"?

Did they screw this up? It says that Fermat's Last Theorem was the longest open problem - with only 365 years. See Guinness Book of Records. However, there are Greek problems that were longer open: ...
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### Did Archimedes use epicycles in his planetarium?

Archimedes constructed a planetarium where as described by Cicero "he had thought out a way to represent accurately by a single device for turning the globe those various and divergent movements with ...
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### Was Kolmogorov enraged after learning about the Karatsuba multiplication algorithm?

Some years ago, I read that Kolmogorov was so enraged that Karatsuba disproved one of his conjectures that he terminated his seminar shortly thereafter. This Wikipedia page claims that Kolmogorov was ...
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### What was the motivation for Minkowski spacetime before special relativity?

If I understand correctly, the concept of a Minkowski space/metric was already known before Einstein's paper on special relativity. Was there any physical motivation for studying this type of metric ...
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### How did mathematicians notate the empty set before $\varnothing$?

Recently, I learned that $\emptyset$ or $\varnothing$ is a relatively new notation for the empty set and was created in 1939. I know $\{\}$ is also used along with $\{\cdot\}$ to denote empty sets. ...
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### How did the publication feat of Einstein's four 1905 Annus Mirabilis papers get through peer review?

Einstein's early career is well-known for the lack of success he had applying for assistant lecturer positions with universities; he could not get a position, and he ended up working in a Bern patent ...
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### Who was the first to calculate $\pi$?

I am very interested in the history of $\pi$. I am first trying to find out who calculated it. Many sources have different answers, from the ancient Egyptians, to Archimedes, to the Babylonians. I ...
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### History of various definitions of topology

I have been reading Point Set Topology for a while, and turns out that there are various possible ways to define a topology. Most popular one is using open set axioms. Another one is using closure ...
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972 views

### Hidden agenda of the Galileo trial?

Redondi argued that Galileo's trial on heliocentrism was merely a show trial concealing the real objection against Galileo among the catholic establishment, which was his atomism thought to be at ...
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### Why did mathematicians not see that $f_n(x)=x^n$ is a counterexample to Cauchy's "theorem" about limits of continuous functions?

In 1821 Cauchy claimed that the limit of a sequence of continuous functions is continuous. In 1826 Abel gave a complicated trigonometric counterexample. When we teach analysis courses, we usually give ...
2k views

### Is Kline right that Cauchy believed that continuous functions must be differentiable?

Morris Kline, in Mathematical Thought from Ancient to Modern Time, writes in chapter 40 (The Installation of Rigor in Analysis), "Though Bolzano and Cauchy had rigorized (somewhat) the notions of ...
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### Did du Bois-Reymond invent the diagonal argument before Cantor?

The Wiki article on Cantor's diagonal argument mentions that the first use of a diagonal argument was in the work of Paul du Bois-Reymond in 1875. This would be one year after Cantor's first proof of ...
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### Did Kronecker say that set theory is not mathematics?

I have frequently come across Kronecker's statement about set theory: I don't know what predominates in Cantor's theory - philosophy or theology, but I am sure that there is no mathematics there. It ...
1k views

In Christoffel's 1869 paper in which he introduced the Christoffel symbols on the 3rd and 4th pages, they are written as $\left[\substack{ij \\ k}\right]$ and $\{\substack{ij \\ k}\}$. The notation $... • 5,689 14 votes 4 answers 3k views ### What was Einstein's motivation for relativity theory? I'm a high school student who never studied any relativity before, but I'm just wondering what was the question that Einstein asked himself before going into this field. I knew he has done lots of ... 14 votes 5 answers 708 views ### Which school of philosophy motivated thinking about spaces of higher dimension? I'm trying to make a link between important mathematical breakthroughs in history and the important philosophical schools at the time. I realize that this topic is awfully broad and could be the ... • 1,142 13 votes 2 answers 2k views ### Etymology of "power" (math.) Having done some searches on the internet, seems like the term "power" is a mistranslation. The Wikipedia article links to an article in the MacTutor History of Mathematics archive where it is written ... 13 votes 3 answers 5k views ### Why are quaternions more popular than tessarines despite being non-commutative? Is this simply because of marketing, hype, etc? The bicomplex numbers (especially tessarines) look just great being commutative and all. Images source:https://citeseerx.ist.psu.edu/viewdoc/download?... • 662 13 votes 2 answers 560 views ### What examples led to the modern definition of a topological space? Today the language of topological spaces via open sets is fundamental in many different areas of mathematics, and it is a bit mysterious that the same formalism successfully captures such a wide ... • 1,041 13 votes 5 answers 589 views ### How did prisoners of war discover scientific breakthroughs while interned? Reading the excellent thread What are some scientific breakthroughs that have been done during jail time?, it stands to reason to ask what are some scientific breakthroughs made by interned prisoners ... 12 votes 1 answer 14k views ### Euler's first proof of$e^{ix}=\cos(x)+i\sin(x)\$

What was Euler's first proof of his famous formula? In Euler's book on complex functions he used the following proof. But was this his first proof? Euler starts with writing down De Moivre's Formula (...
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