Questions tagged [mathematicians]

For questions about those who do mathematics.

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How were irrational numbers accepted by mathematicians?

What was behind accepting the existence of irrational numbers historically? Especially numbers that are not constructible on the real number line, say for example $\sqrt[3]{2}$. Was it a (somewhat) ...
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22 votes
2 answers
2k views

Who first considered the $f$ in $f(x)$ as an object in itself, and who decided to call it a function?

The question is in the title, but allow me to provide some background. I’m aware that Leibniz introduced the word “function” into mathematics (around 1673) and that Johann Bernoulli or Euler ...
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12 votes
3 answers
690 views

What resources are available for lives of recent mathematicians besides E.T. Bell's Men of Mathematics?

I am about halfway through reading E.T. Bell's Men of Mathematics, and I absolutely love it. I'm a mathematician, and I enjoy learning about the lives behind the names that I know and use so often. (I ...
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13 votes
1 answer
13k views

Who invented short and long division?

I am curious who came up with algorithms that we use today to manually solve mathematical division problems, such as short or long division; how were they established or standardized that way and why?...
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6 votes
3 answers
610 views

When were the concepts of pure and applied Mathematics introduced?

I know that there are no standard definitions for pure and applied mathematics however I would like to know who first considered them as two separate entities, I have seen people mention it was around ...
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43 votes
44 answers
13k views

Which mathematicians died very young or in a tragic way?

When I first thought of this question, I wanted to ask: If you could give one mathematician his remaining life until an average age for the time he lived in, who would you choose? However, this ...
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35 votes
6 answers
9k views

Who introduced the Principle of Mathematical Induction for the first time?

Can you tell me the name of the mathematician, who introduced the Principle of Mathematical Induction for the first time? (with reliable source). Please don't say De Morgan because I have read the ...
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  • 955
11 votes
5 answers
3k views

Who gets credit for the real numbers?

If Simon Stevin already pioneered the unending decimal representation for every number (rational, surd, etc.) at the end of the 16th century, why do Cantor and Dedekind (who certainly gave a more ...
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  • 3,639
12 votes
1 answer
1k views

Did Cauchy forget or lose mathematical papers aside from Abel's and Galois's?

Augustin-Louis Cauchy was a prolific writer, his writings range widely in mathematics and mathematical physics. As a professor at École Polytechnique he came in contact and reviewed Abel's and Galois' ...
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5 votes
1 answer
952 views

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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21 votes
4 answers
1k views

Is there any historical "evidence" maintaining that Euclid is a single person?

Bourbaki, for example, is 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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7 votes
1 answer
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How did Newton prove the generalised binomial theorem?

Do we have any idea of how Newton proved the generalised binomial theorem?
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15 votes
1 answer
599 views

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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6 votes
1 answer
307 views

Fraenkel's appointment at Göttingen

Abraham Fraenkel grandpère writes on page 127 of his book recently translated into English: My professional career began in March 1919 with... an invitation to Göttingen to Privy Counselor Felix ...
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  • 3,639
6 votes
1 answer
217 views

Who coined the term random variable?

Who is the first person defined the concept of a random variable?
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  • 315
80 votes
16 answers
25k views

Examples of when the professional scientists or mathematicians were wrong, but the nonprofessionals were right

What are the most glaring examples — if any — of when the professional scientists or mathematicians were wrong, but the nonprofessionals were right?
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  • 809
87 votes
14 answers
16k views

What famous theorems or results were proven by female mathematicians?

We know that there were/are many famous female mathematicians who influenced the mathematics as we know it today, but their numbers are few compared to male mathematicians. While we have numerous ...
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72 votes
5 answers
12k views

Why was Évariste Galois killed?

It is well known that Évariste Galois died a young man. I have heard that he died in a duel. What was the duel about? More rather what is the back story behind his death and did he really write down ...
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  • 1,516
71 votes
3 answers
11k views

What evidence is there that Fermat had a proof for his Last Theorem?

Aside from the fact that Fermat was a genius, is it probable that he actually did have a proof? Some specifics that I think would point one way or another: Would the mathematics of his day allow him ...
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22 votes
22 answers
4k views

Literary works authored by mathematicians

At a first glance, Mathematics and Literature look like two completely unrelated subjects. I wonder whether there are examples of acclaimed mathematicians which wrote novels, poems, or other ...
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37 votes
3 answers
3k views

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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  • 752
9 votes
2 answers
2k views

What was Kolmogorov’s point of view in the philosophy of mathematics?

Today the standard interpretation of intuitionistic logic is the Brouwer-Heyting-Kolmogorov interpretation which was presented independently by Arend Heyting and Andrei Nikolajewitsch Kolmogorow. ...
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  • 421
19 votes
2 answers
18k views

How did Ramanujan learn to do mathematics?

Did Ramanujan have any formal training in mathematics? I read that he did not. Then how did he learn to do mathematics? Mathematics does not come from instinct. You have to learn the basic facts. How ...
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  • 903
20 votes
6 answers
2k views

Claims of mathematical breakthroughs while in an altered state of consciousness?

A similar question is found below: Scientific progress claimed to be caused by dreaming Has anyone ever made similar claims regarding other altered states of consciousness, besides dreaming? I know ...
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12 votes
4 answers
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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15 votes
7 answers
3k views

Mathematical results that became known long after their authors passed away

Liouville published Galois' work a decade after the death of this singular mathematician. Are there other cases of results being rescued by the mathematical community long after their authors were ...
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19 votes
4 answers
19k views

Did Abraham De Moivre really predict his own death?

At the last point of his life, he noted that he slept 15 minutes extra every night then he calculated that he would die on the day that the extra 15 minutes a night accumulated to 24 hours. That day ...
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  • 389
9 votes
1 answer
570 views

Who was first to differentiate between prime and irreducible elements?

I recently learned about irreducible and prime elements in a commutative ring. However, my professor was not quite sure who was the first to make this distinction, or give an example of an irreducible ...
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  • 113
9 votes
5 answers
1k views

What was the appeal of numerical analysis before computers?

I'm currently doing a numerical analysis course, and it seems many of the techniques were developed by mathematicians, such as Euler and Newton, who lived before the age of the computer. Why were ...
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8 votes
5 answers
1k views

Are there well-known mathematicians who shared Arnold's view about mathematics as natural science?

V. I. Arnold asserted that mathematics is a natural science: Mathematics is a part of physics. Physics is an experimental science, a part of natural science. Mathematics is the part of physics where ...
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7 votes
2 answers
4k views

What are some famous mathematicians that disappeared?

In physics there is this famous history facts about Ettore Majorana, brilliant student of Enrico Fermi that predicted the neutron and developed the idea of Majorana fermions, that suddenly disappeared....
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13 votes
5 answers
751 views

Are there any anonymous contributions to mathematics that had a great impact?

Are there any examples of mathematical ideas being communicated in an anonymous manner that had a substantial impact on mathematics at the time. It seems to me that it is very rare for an author to ...
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  • 1,516
13 votes
2 answers
516 views

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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12 votes
1 answer
465 views

Alexander Grothendieck's "stolen" correspondence in 1985?

On the website that now displays the part of Grothendieck's archives that had been held at the University of Montpellier, it is mentioned that: Dans une lettre adressée à Monsieur Lefranc datée du 13 ...
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7 votes
2 answers
854 views

Who discovered integer triangles with one angle trisecting another?

When & who was the first mathematician to discover the following simple triangle with a unique property that it has one angle is equal to one third of another angle in the same triangle? The ...
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3 votes
4 answers
678 views

Did Kronecker attribute immutable origin to the integers?

The familiar quote is often incorrectly attributed to Kronecker directly. Actually a colleague of his named Weber claimed after Kronecker's death that Kronecker said this. I have doubts about this ...
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  • 3,639
7 votes
2 answers
415 views

Where can I find the translated manuscript of Abel?

I am looking for the translated manuscript of Abel where he proved the unsolvability of the quintic. Can anyone give me a pointer? I tried Google, but nothing came up.
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5 votes
1 answer
291 views

Why was Kronecker dissatisfied with Cantor's submitted paper?

It is said here that In 1874 Cantor published an article in Crelle's Journal which marks the birth of set theory. A follow-up paper was submitted by Cantor to Crelle's Journal in 1878 but already set ...
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  • 205
4 votes
4 answers
168 views

Time for big results to become widely recognized in the scientific community

What are some examples of big results in mathematics and or physics that took a long time to be considered groundbreaking? What was the length of time from the original publication to the recognition? ...
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4 votes
1 answer
204 views

Lost memoir of Évariste Galois

According to the Wikipedia article on Évariste Galois He submitted his memoir on equation theory several times, but it was never published in his lifetime due to various events. Though his first ...
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  • 161
4 votes
2 answers
179 views

Did F. P. Ramsey complete a graduate degree?

There are numerous online sources giving biographical sketches of Ramsey's life; E.g., Wikipedia, Cambridge respository, St. Andrews MacTutor. We learn that Ramsey died just before his 27th birthday ...
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3 votes
2 answers
263 views

Origins of proof in Mathematics

Why was the idea of writing, formalising and creating new proofs brought about? For example, why even though we have found hundreds of proofs of the Pythagorean Theorem are we still trying to find ...
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  • 153
9 votes
4 answers
698 views

Help translate from German a quote by Hermann Weyl in Space Time Matter

I would like to find an accurate translation to the following quote from Space Time Matter: Man muß gegen diese Orgien des Formalismus, mit dem man heute sogar die Techniker zu belästigen beginnt, ...
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  • 375
8 votes
2 answers
426 views

Was Riemann's zeta function paper based on Euler's unproven observation?

According to this website, we see that Euler formally proved (observed?) his result connecting the harmonic series and a product over primes. Riemann wrote his historical paper in 1859 which considers ...
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  • 183
8 votes
2 answers
605 views

Did Euler ever write $f(x)$, with parentheses?

Euler is often credited with introducing the notation $f(x)$, and people cite the example $f(\frac{x}{a}+c)$, where he had to use parentheses around the function argument. On the other hand, when the ...
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5 votes
1 answer
321 views

Source of cartoon lampooning Felix Klein

There is an interesting cartoon in the book Lillian Hoddeson, Ernst Braun, Jurgen Teichmann, Spencer Weart (Eds.) Out of the Crystal Maze: Chapters from The History of Solid State Physics. Oxford ...
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  • 3,639
3 votes
2 answers
1k views

What is the international standing of Italian mathematics?

Being Italian, I have a biased view on my homeland's mathematical impact in the world, so I would like to get some impartial opinion on the topic. I would measure the mathematical relevance in terms, ...
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3 votes
1 answer
2k views

Who Invented The Number Line?

Recently, I came across this article and wondered if there really is a definitive answer to the question of who invented the number line?
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2 votes
1 answer
190 views

First time the unique factorization theorem was called FTA

First of all, a comment, before this gets marked as a duplicate: I have searched this website for the question I’m asking and I’m aware that this exact question has been asked before. However, Eric ...
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