# Tag Info

70

You are most likely referring to the 1903 presentation by American mathematician Frank Cole. The original false conjecture was that the 67-th Mersenne number $M_{67}:=2^{67}-1$ is prime, and it goes back to the preface to Mersenne's own Cogitata Physica-Mathematica (1644). However, Cole was already confirming rather than disproving, that $M_{67}$ is ...

40

An immediate motivation of Cantor to work on what became set theory was his earlier work on trigonometric series. To solve a problem in that domain he considered the set (a closed set) of zeros of such a function, then the derived set of this set, the derived set of this set and so on. This is all still classical, but then had to go a step beyond that to ...

28

We must locate this passage into a double context : the general historical context the specific context of the "rivalry" between Hooke and Newton. See Robert Purrington, The First Professional Scientist : Robert Hooke and the Royal Society of London (2009), Ch.8 : And All Was Light : Hooke and Newton on Light and Color, page 135-on. For the general ...

25

Newton's notation, Leibniz's notation and Lagrange's notation are all in use today to some extent they are respectively: $$\dot{f} = \frac{df}{dt}=f'(t)$$ $$\ddot{f} = \frac{d^2f}{dt^2}=f''(t)$$ You can find more notation examples on Wikipedia. The standard integral($\displaystyle\int_0^\infty f dt$) notation was developed by Leibniz as well. Newton did ...

25

This is a common claim which has been repeated enough times that one can find many sources claiming it to be true. However, this doesn't seem to be corroborated by accounts of the time or serious biographies. Indeed, Helen M. Walker, in her 1934 biography of De Moivre in Scripta Mathematica Volume II, Number 4, August 1934, (reproduced here freely on Google ...

25

The man is Paul Erdős. As pointed out by the OP in the comments, his "nomadic" lifestyle is briefly mentioned in the Brown Numbers - Numberphile video, 3.05-3.30. It is also concisely described in Currey's book Daily Rituals read in this YouTube video that refers to Hoffman's popular biography The Man Who Loved Only Numbers, which is featured in ...

24

Karatsuba's own report can be found in his 1995 paper Сложность вычислений (Complexity of computations). The phrasing he uses is "сильно взволновалo", which Google does translate as "very excited" or "greatly agitated". But we can see the usual dynamic of an anecdote in the making on the Reddit thread, where Kolmogorov is "...

23

How To Solve It was originally published in English in 1945 by Princeton University Press in English, after being rejected by three other U.S. publishers. However, the original text at least started out in German as a draft. Pólya began writing the draft prior to 1940, while he was living in Zürich, and presumably initially intended for the text to be ...

23

A good account is Weinstein, Max Born, Albert Einstein and Hermann Minkowski's Space-Time Formalism of Special Relativity. They did no have much of a relationship, what it was is well-summarized by Sommerfeld: "Strangely enough no personal contacts resulted between his teacher of mathematics, Hermann Minkowski, and Einstein. When, later on, Minkowski ...

19

The first serious use of complex numbers is in finding the roots of quadratic, cubic, and quartic polynomials. Cardano, in his Ars Magna (1545), first showed that quadratic equations could have (formally) complex roots, although he didn't call them that; he said they were "as subtle as [they are] useless". In Bombelli's algebra text (1572), he developed the ...

19

I too was told this story, by my father as we drove through Nobel, Ontario. While the main purpose of dynamite may never have been warfare, it most certainly was used for that purpose during his lifetime, and he didn't expect or like that very much. As well, he invented a number of other chemicals which were explicitly for use in war, but he didn't feel they ...

19

Marie Curie is probably the most famous example of a person who died of the effects of radiation (handling a lot of radium mostly - for the discovery of which she won the Nobel prize in Chemistry). In general, people were indeed very ignorant of the effects of radiation. A couple of examples: Shoe shops used to have an X-ray machine to look at the "fit" of ...

19

Unlike Einstein, Planck did not quantize electromagnetic waves themselves, only the exchanged energies, and even them only statistically. So the other two questions have no satisfactory answer because he was not dealing with specifics of emission/absorption at the level of individual quanta. The quanta were meant as mathematical fictions for the purposes of ...

18

Actually Cantor was working on a specific problem from the theory of trigonometric series, the so-called uniqueness problem (I cannot be more specific until MathJax is introduced to this site). This problem led him to consideration of arbitrary sets on the real line. I mean more complicated sets than finite sets or finite union of intervals. At that time ...

18

The paper 'Some facts about Kurt Gödel' by Wang (1981) (regrettably paywalled) contains a section that suggests Hilbert was not present when Gödel originally announced his sketch of the First Incompleteness Theorem at Königsberg, on the 7th of September, 1930. Notable mathematicians that were present include Carnap, Heyting and most importantly von Neumann,...

18

Scientists and mathematicians rarely self-report on psychological circumstances of their creative process, at best presenting a rationalization of their path to discovery. Kekule's dream and Kepler's vivid struggles described in Astronomia Nova are exceptions (and there are doubts that Kepler's descriptions are factual, see How did Kepler "guess" ...

18

According to this, it's a modern fabrication: Although Einstein’s initial application for a doctorate at the University of Bern (he had previously been awarded a PhD by the University of Zürich in 1905) was indeed rejected as insufficient in 1907, and it was not until the following year that he completed a new dissertation that resulted in his being ...

17

Newton used anagrams which are not the usual ciphers. It is not designed for a secret communication, but only for proving at a later time that you knew something. So nobody is supposed to be able to decode the message until you tell what the message was. To do this, he used a simple procedure: he wrote a sentence (in Latin) and then just counted letters in ...

17

Mauro Allegranza's comment pretty much says it all but to elaborate a bit one could mention that Leibniz came to mathematics rather late in his intellectual career and was essentially a self-educated scholar. His older colleague Huygens encouraged him to pursue mathematics, and his encouragement (on many occasions) was instrumental in Leibniz's development. ...

17

Bertrand Russell wrote many books and essays on philosophy and social justice, and was awarded a Nobel Prize in Literature. And the Persian mathematician Omar Khayyám wrote poetry: quatrains that have been translated into English as the Rubáiyát of Omar Khayyám.

17

Fermat wasn't so much a "lawyer" as a magistrat which means that he sat on successively higher levels of the Parlement of Toulouse, France. This period (17th century) was before the emergence of the doctrine of the separation of powers in Western thought, so that the Parlement was not a "Parliament" in the modern English sense of the word, but rather the ...

17

I take that your primary goal is to know what Feynman thought of Hawking's work. While it is possible that they have met I would consider it unlikely given that Feynman mentioned several times how his attendance of the Chapel Hill conference (on general relativity) made such a bad impression on him that he never attended another conference on that theme, so ...

16

One of the most recent famous examples is Yitang Zhang, who proved in 2013 that, if $p_i$ denote primes, then $$\liminf_{n\to\infty} (p_{n+1}-p_n)<7\times 10^7$$ i.e. there are infinitely many primes that are less than $7\times 10^7$ apart. In particular, there are infinitely primes that separated by less than some finite number. This was an amazing ...

16

Hausdorff wrote many literary and philosophical works, including poems and a play, under the pseudonym Paul Mongré.

15

I could not find any direct sources to confirm and support this claim. W.W. Rouse Ball (1850 – 1825), writes in A Short Account of the History of Mathematics first published in 1908, pages 383-384: The manner of his death has a certain interest for psychologists. Shortly before it he declared that it was necessary for him to sleep some ten minutes ...

15

This story bears characteristic signs of a tall tale, although in this case one can identify the origin. It appears to be an amalgamation of two anecdotes, neither of which is itself very credible. Both are traceable to Warren McCulloch, Pitts's co-author on "A Logical Calculus of Ideas Immanent in Nervous Activity" (1943), which proposed the first ...

14

Of course, the naive description as many heard it (which includes Newton having an apple fall on his head) is not true. There also does not exist any known source where Newton discusses anything about apples, and how they relate to his thoughts on gravitation. However, there are multiple secondary sources, providing accounts of a related 'apple incident', ...

14

Einstein made a number of contributions of momentous importance to quantum theory in the 'early days'. In 1905, his famous annus mirabilis, he published a paper on the photo-electric effect that laid the basis for the modern understanding of photons (i.e. quantized wavepackets). This was twenty years before the foundations of quantum mechanics were ...

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