Use this tag for questions concerning history of mathematics, historical primacies of results, and evolution of terminology, symbols, and notations.

learn more… | top users | synonyms (1)

9
votes
3answers
1k views

When the trig functions moved from the right triangle to the unit circle?

I have to write a paper about the unit circle and I'm trying to uncover some of its origins. Also, when the trig functions were expanded to angles greater than 90° and what was the rationale behind ...
17
votes
1answer
1k views

Mathematically, why was the Enigma machine so hard to crack?

Mathematically, why was the Enigma machine so hard to crack? In laymen terms, what was it exactly that made cracking the Enigma machine such a formidable task? Everything I have seen about the ...
5
votes
1answer
79 views

How fast was the Turing's machine for breaking the enigma code?

We know that, recently, personal computers make around $10^9$ calculations per second, and I'm just curious about how many calculations was able to compute the machine invented by Turing for breaking ...
3
votes
2answers
266 views

History of Calculus

Newton/Leibniz invented calculus on approximately 1680's. Cauchy/Weierstrass defined the $\epsilon - \delta$ definition of a limit in approximately 1820's. So how did they define derivatives? I ...
86
votes
15answers
9k views

Has lack of mathematical rigour killed anybody before? [closed]

One of my friends was asking me about tertiary level mathematics as opposed to high school mathematics, and naturally the topic of rigour came up. To provide him with a brief glimpse as to the ...
1
vote
1answer
49 views

informal semantics regarding CH and AC

why is the assertion $\aleph_1=2^{\aleph_0}$ referred to as a hypothesis, whereas $$\forall \alpha( S_\alpha \ne \varnothing) \Rightarrow \prod_\alpha S_\alpha \ne \varnothing$$ is called an axiom? ...
4
votes
3answers
2k views

On the Origin and Precise Definition of the Term 'Surd'

So, in the course of last week's class work, I ran across the Maple function surd() that takes the real part of an nth root. However, conversation with my professor ...
0
votes
1answer
60 views

Which one of the following logical propositions is to be preferred?

I'm trying to update the symbolism of Giuseppe Peano's "Arithmetices Principia", to make the translation freely available. Might I ask you, which of the following might be a correct mathematical ...
64
votes
12answers
10k views

Is zero odd or even?

Some books say even numbers start from two but if you consider the number line concept, I think zero should be even because it is in between -1 and +1 (i.e in between 2 odd numbers). What is the real ...
3
votes
2answers
74 views

Why do we think of group compositions as multiplication?

This has bothered me for some time: The composition in a group is usually denoted $xy$ or $x\cdot y$. Powers (note the word) are denoted by $x^n$, inverses by $x^{-1}$, and the neutral element by $1$. ...
0
votes
2answers
71 views

What comes after seconds?

Angles can be measured in different ways. For example, one can measure angles in degrees/minutes/seconds. So $1^\circ$ is divded into $60$ min. and $1$ min is divided into $60$ sec. That way a tenth ...
2
votes
0answers
51 views

How much math was “Broken” by Russell's Paradox?

As you know, the phrase "the set of all sets that don't contain themselves" caused a paradox that "broke" (made trivial) Naive set theory. How much mathematics had to be redone because of this? Most ...
1
vote
0answers
30 views

Why are logrithms of trigonometric functions useful

I have noticed that in many trigonometric tables the logarithm of the trigonometric values are given. Why this is given and not the actual values of the trigonometric functions? For example, instead ...
-3
votes
1answer
15 views

How to solve this parallelism problem? [closed]

How do you solve this problem step by step because I don't understand how to do it all...
108
votes
33answers
11k views

Can you provide me historical examples of pure mathematics becoming “useful”?

I'm trying to think/know about something but I don't know if my basis premise is plausible, here we go. Sometimes when I'm talking with people about pure mathematics, they usually dismiss it because ...
1
vote
2answers
33 views

What are these numbers in a logarithmic table?

Below is an image from a table of logarithms. As an example, one sees that $\log(661.3) = 2.82\color{red}{040}$. In this logarithmic table there are some numbers to the right. My question is: What is ...
13
votes
3answers
596 views

Journals of math history?

In a related question to this one, in what journals do math historians publish their article in? Brian M. Scott provided a link to Judy Grabiner's, who is a math historian, home page and it seems that ...
1
vote
1answer
23 views

Derivation of the discriminant of a cubic polynomial by algebraic manipulation.

The problem was asked before: Using Vieta's theorem for cubic equations to derive the cubic discriminant . I tried to solve it by purely algebraic manipulation but was faced with an explosion of ...
1
vote
5answers
61 views

What does the solution of a PDE represent?

So I took a course in PDE's this semester and now the semester is over and I'm still having issue with what exactly we solved for. I mean it in this sense, in your usual first or second calculus ...
1
vote
1answer
81 views

What is the difference (or relationship) between geometric length and arithmetic numbers?

In Abbott's Understanding Analysis there was a phrase like, "Ancient Greeks did not understand the difference (or relationship) between geometric length and arithmetic numbers." What is this ...
2
votes
1answer
17 views

Noether comment to Dedekind and Weber's work

I am trying to consult Emmy Noether's “Erläuterungen zur vorstehenden Abhandlung”, some sort of epilogue or comment to Richard Dedekind and Heinrich Weber's “Theorie der algebraischen Funktionen einer ...
3
votes
1answer
64 views

A question regarding Kummer [closed]

As you know, Ernst Kummer noticed that examples such as $$6 = 2\cdot 3 \text{ or } 6 = 3 \cdot 2 \text{ and, crucially } 6 = (1 + \sqrt{-5}) (1 -\sqrt{-5}) $$ proved the failure of unique ...
0
votes
3answers
54 views

History and early development of Mathematics

Please provide references (books, articles, websites) that describe the conceptual development of calculus, complex numbers, group theory and matrix. I am curious about how the Mathematicians ...
8
votes
1answer
452 views

What is the history of “only if” in mathematics?

A quick search on the use of "only if" returns questions asking about its use and meaning in mathematics, such as here, here and here, revealing confusion in its interpretation and use for some ...
3
votes
0answers
54 views

Why didn't Bernoulli and Euler use an integral comparison to estimate the solution to the Basel problem?

I was reading the history of the Basel problem in William Duhnam's book, Euler - The Master of Us All. The book tells how Jakob Bernouili did some clever manipulation to show that the sum of $1/n^2 ...
0
votes
1answer
30 views

On Dedekind's prime ideals

Prime ideals were an essential tool for Dedekind to save or restore unique factorization. Is it fair to say that the shift from Kummer's ideal numbers to Dedekind's ideals (with prime ideals, and so ...
5
votes
1answer
217 views

What does “hom” stand for in hom-sets and hom-functors?

With given category $\mathcal{C}$ and its objects $A$ and $B$, a hom-set $\hom_\mathcal{C}(A, B)$ is the collection of all morphisms from $A$ to $B$. There is also a related notion of hom-functor ...
2
votes
3answers
142 views

In Whitehead & Russell's PM, does every Series contain a $P_1$ (immedeately precedes)?

✳204.7 $\vdash: P \in Ser .\supset. P_1 \in 1 \rightarrow 1$ Which says if $P$ is a series, then $P_1$ is one-one. ✳201.63 $\vdash: P \in trans \cap Rl‘J .\supset. P_1 = P \overset{.}{-}P^2$ ...
10
votes
7answers
629 views

Interviews of famous modern mathematicians

I was wondering, are there any good collections of interviews of famous modern mathematicians? It can be text interviews, or audio or video recordings. I am not sure what exactly I mean by "modern". ...
1
vote
0answers
25 views

Notations for interior product

There are two symbols in the Unicode "Supplementary Mathematical Operators" range whose names intrigue me 2A3C: INTERIOR PRODUCT: ⨼ (like $\lnot$ upside down) 2A3D: RIGHTHAND INTERIOR PRODUCT: ⨽ ...
7
votes
1answer
78 views

(Co)homology theory and electrical circuit

I have read that one of the origins of the theory of (co)homology is the study of electrical circuits by Poincare. I'd like to know more about that. Could someone sugest any reference on this subject? ...
1
vote
2answers
66 views

Why is the letter “F” used for the curvature 2-form?

Given a differentiable manifold $X$, a vector bundle $E\to X$ and a connection $A$ on $E$. The curvature $2$-form of the connection is a $2$-form with values on the endomorphisms of $E$ defined as ...
2
votes
1answer
39 views

Original paper by Gauss on gaussian integers

Could anyone provide me with the title and date of Gauss's paper where he first introduces gaussian integers and proves their unique factorization? If you could also provide me with his exact proof ...
0
votes
0answers
22 views

Maltsev on Algebraic Systems

As far as I know, it was A.I Maltsev who fist coined the term "Algebraic systems" in a paper from 1953. Then Birkoff, MacLane and others extended its usage and appplications. My question is a simple ...
4
votes
1answer
113 views

Question about Wantzel's proof of the necessary condition for compass/straightedge constructibility

I'm trying to understand Wantzel's original proof of the necessary condition for constructibility with a straightedge and compass. It's expressed in terms of polynomials rather than field extensions. ...
4
votes
0answers
74 views

In the mean value theorem, we are guaranteed $c$ such that $f'(c) = (f(b)-f(a))/(b-a)$. Does $c$ have a name?

The Mean Value Theorem says approximately that for differentiable $f$, there is a $c \in (a,b)$ such that $$ f'(c) = \frac{f(b)-f(a)}{b - a}. $$ I presume that the number $f'(c)$ is the mean value. My ...
1
vote
0answers
51 views

When did Liouville come up with the first transcendental numbers?

There are some conflicting sources regarding this. It is a matter of fact that Liouville defined what it was for a number to be approximated to degree $n$ by rational numbers. He then effectively ...
0
votes
1answer
45 views

On Gaussian Primes

Some primes in the ring of integers (17, for example) cease to behave as such in the ring of gaussian integers, while others (7, for instance) keep being prime there as well. The former are of the ...
3
votes
1answer
44 views

who coined the prime ideals?

I know that Ernst Kummer first made used of "ideal complex numbers", and, hinging on that, Dedekind later introduced his "ideals" in Vorlesungen über Zahlentheorie. But, who coined the term "prime ...
-1
votes
0answers
66 views

diophantine-equations

Why there are no solutions in positive coprime integers for the following diophantine equation $$2x^3 + y^2 = z^k$$ where, (x,y,z) are (pairwise) positive coprime integers, and k is positive integer ...
0
votes
0answers
39 views

DeMoivre's approximation to the ratio of $\binom{n}{n/2}$ to $2^n$

I'm reading Stigler's History of Statistics and am trying to understand as many of the derivations as I can. Stigler begins his discussion of DeMoivre's contributions by stating the result that the ...
2
votes
2answers
69 views

Calculus without functions (or, how did Newton differentiate?)

I was recently reading about how functions did not really exist at the time of Newton and Leibniz; They thought in terms of geometry. That makes me curious. I can understand that derivation would be ...
0
votes
0answers
51 views

Historical calculations of $tan^{-1}x $ and $e^x$

SineBhaskara_I One reads that $tan^{-1}(x) $ series expansion existed in early (Indian) history. But like the Sine trigonometric function, did any similar approximation exist as well? The query ...
22
votes
6answers
2k views

Where did mathematicians learn how to do truth tables?

I'm trying to find out who invented truth-tables. Here is what I have so far. Leibniz 'invented' binary arithmetic, or at least is the first one recognized to have codified and explained a base 2 ...
11
votes
3answers
542 views

How was the first log table put together?

Henry Briggs compiled the first table of base-$10$ logarithms in 1617, with the help of John Napier. My question is: how did he calculate these logarithms? How were logarithms calculated back then? ...
10
votes
2answers
1k views

Who discovered the first explicit formula for the n-th prime?

I just found out on Wolfram that there is a formula for the n-th prime in terms of elementary functions. I wonder who found it and if he was rewarded for this. The formula (here) is: Also shown at ...
2
votes
4answers
52 views

motivating diagonalization of a matrix [duplicate]

I have to teach about diagonalization of a matrix to a first year undergrad student and I was wondering what would be a good way to motivate this concept. I would appreciate any suggestions. Thanks!
39
votes
8answers
1k views

Original works of great mathematicians

In almost every mathematical text there is a line as This was first proved by Gauss or This formula first appeared in a work of Riemann, but for me it's more like My friend told me once that... For ...
0
votes
0answers
18 views

Who is the inventor of slovin's formula?

And how can I use it in the population contain 10000 people with confidence interval 95%? Also, why there is only a few information about the inventor in the web?
0
votes
1answer
18 views

Table of Contents from André Weil's Edition of Kummer's papers

I would be very grateful if someone could provide me with the table of contents of Volume 1 (pertaining Number Theory) of Andre Weil's edition of Ernst Kummer's papers, published by Springer Verlag in ...