# 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) ...
12k 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?...
1k 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 ...
548 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 ...
2k 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 ...
784 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 ...
506 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 ...
9k 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 ...
10k views

### Did Gauss find the formula for $1+2+3+\ldots+(n-2)+(n-1)+n$ in elementary school?

I heard Gauss's primary school teacher gave some busy-work to his class: to add all the numbers between 1 and 100 up. Gauss immediately wrote 5050. His teacher was shocked, so she told him to add up ...
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 ...
86k views

### Discovery of zero

I have read at many places that zero was discovered by Aryabhata but when i was discussing this with my mathematics teacher he told me that zero had already been discovered before Aryabhata and it was ...
852 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' ...
525 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 ...
4k views

### The history and motivation of eigenvectors

I want to understand more about the history of eigenvectors. Was the discovery of eigenvectors inspired from an application to achieve a result in a historical context, was there a phenomenon which ...
2k views

### How did Newton prove the generalised binomial theorem?

Do we have any idea of how Newton proved the generalised binomial theorem?
268 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 ...
94 views

### Existence of Pythagoras Resources

I am aware that approximately two years ago a question was posted on the existence of Pythagoras. After two years, I want to gain more incite on the thought of those on this site. I was drawn to the ...
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?
15k 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 ...
10k 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 ...
9k 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 ...
3k 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 ...
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 ...
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. ...
17k 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 ...
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 ...
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 ...
2k views

### Source for Hilbert's famous quote “Mathematics in Göttingen? There really is none anymore”

Reportedly this was uttered at a banquet in which Hilbert was seated next to the new Minister of Education, Bernhard Rust, in response to Rust inquiring as to the state of mathematics in Göttingen now ...
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 ...
18k 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 ...
529 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 ...
781 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 ...
802 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 ...
582 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 ...
334 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.
164 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? ...
167 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 ...
674 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, ...
401 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 ...
301 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 ...
1k 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?
898 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, ...