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1500 questions
23
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2 answers

Why is there no named unit for momentum but there is one for energy?

Momentum and energy play very similar roles in mechanics, each being changed by the application of force over a interval. For energy the interval is in space and for momentum it is in time. Both have associated conservation laws. Yet, energy units…
23
votes
2 answers

Hilbert's reaction to Gödel's incompleteness theorems

Is it known how Hilbert initially reacted to Gödel's incompleteness theorems upon their announcement at the Königsberg conference in 1930, or their publication in 1931?
Felix
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23
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2 answers

When did it become understood that irrational numbers have non-repeating decimal representations?

I know that the notion of irrational number (in one form or another) goes back to the Pythagoreans, and therefore far predates the decimal system, and certainly the representation of non-integer quantities with decimal fractions. I also know that…
mweiss
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23
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7 answers

In ancient times, how did people conclude that the shape of Earth is a sphere?

This is more of a philosophical question, but I want a mathematical explanation. During ancient times, it was well accepted that the surface of Earth was spherical. People first observed this when they saw that starting from a point going to any…
Anubhav Mukherjee
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23
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4 answers

What was the answer to this paradox before Cantor?

I do not remember the name/source of this paradox,but I remember I have discussed this with mathematicians and non mathematicians at least 5 times. It goes like this: "Every point of a line has length $0$ and every line segment consists of…
23
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1 answer

How did group theory enter quantum mechanics?

How did the physicists in the 1920s become aware of the importance of group theory in quantum mechanics? Was group theory already part of the physics curriculum at that time, perhaps in connection to crystallography?
Felix
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23
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9 answers

Are there any mathematical objects that got renamed over time?

I'm wondering if there are any mathematical objects that were given a name when first discovered (and wildly used at their time), but then got renamed to match their characteristics later? Counter examples: Imaginary number was coined by Descartes…
neizod
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22
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3 answers

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 in Zürich. How did Einstein comment on Minkowski's…
Realist753
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22
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12 answers

Has a stereotypical "mad scientist" ever made a significant discovery?

Most people are familiar with the famous "mad scientist" trope from science fiction - the scientist who is typically a loner, often self-funded from family wealth, frequently mentally ill, engaged in secretive research that may be unethical,…
Robert Columbia
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22
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3 answers

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 names: Max Planck Albert Einstein Max…
galois
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22
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1 answer

Why is the Pythagorean Theorem so ubiquitous?

We all know the Pythagorean Theorem is one of the most fundamental formulas in mathematics, but it is very interesting to me that this ratio shows up as often as it does. It seems to have been discovered multiple times (a few times even before the…
galois
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22
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4 answers

Why are étale morphisms called "étale"?

Alexander Grothendieck developed the theory of "locally trivial coverings spaces for rings/schemes" in SGAI as an analog to the theory of covering spaces in algebraic topology. He called such coverings étale morphisms; does anyone know why? Étale…
User0112358
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22
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1 answer

What sorts of calculations called for the invention of logarithm tables?

It's often stated that Napier invented logarithms in order to simplify the task of engineers and scientists who had to crunch numbers by hand. Now, logarithms obviously do simplify calculations (as I learned myself when I turned up at a chemistry…
Jack M
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22
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6 answers

Why were so many pre-18th century Mathematicians polymaths?

It is well known that famous names such as Gauss, Euler and Newton were polymaths as well as their main fields of study and contributed from optics to ship building. Why was this the case in the past? It is known, as far as I am aware, to exist…
Ali Caglayan
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22
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3 answers

How did Gauss become the "the prince of mathematicians"?

Gauss is probably the most famous mathematician today, his face even appears on one of European bills. But he did not have a charismatic personality, like Galois, nor was particularly interested in self-promotion, more of a recluse. Also Euler,…
Conifold
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