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History and philosophy of mathematics, biographies of mathematicians, mathematics education, recreational mathematics, communication of mathematics.

114 votes

Are there any serious investigations of whether "mathematicians do their best work when they...

These two studies arrive at what seems to be a more sensible conclusion: Age and Scientific Performance, Stephen Cole (1976). The long-standing belief that age is negatively associated with scien …
92 votes

The most outrageous (or ridiculous) conjectures in mathematics

$P=NP$ Let me tick the list: Most likely false, because, as Scott Aaronson said "If $P = NP$, then the world would be a profoundly different place than we usually assume it to be." Yes, it's The Ope …
84 votes
Accepted

How did "normal" come to mean "perpendicular"?

normalis already meant right-angled in classical Latin; for example, angulus normalis appears in the first century text De institutione oratoria (volume XI, paragraph 3.141) by Marcus Fabius Quintilia …
Carlo Beenakker's user avatar
79 votes
Accepted

Who is the "young student" André Weil is referring to in his letter from the prison?

This must have been Heinrich Kornblum (1890-1914). [note by E. Landau in German, my translation] $^1$ The author, born in Wohlau on August 23, 1890, had before the war independently made the discover …
Carlo Beenakker's user avatar
59 votes
Accepted

J. H. C Whitehead (and his pig)

The first record I found of this photograph is in Oxford Figures: Eight Centuries of the Mathematical Sciences. Professor Michael Atiyah shares some recollections of J.H.C. Whitehead and his pigs: …
Carlo Beenakker's user avatar
58 votes
Accepted

Did Hilbert laugh?

Constance Reid describes the recording on page 196 of her book Hilbert (1969). The recording was not made directly from the live address. Instead, Hilbert was asked to repeat the conclusion of his s …
Carlo Beenakker's user avatar
55 votes

Who started the "-oid" suffix fashion in math?

The suffix "-oid" means the same as "quasi", so "resembling", "like". A groupoid is a quasi-group, like a group. There are hundreds of words in that category, covering many scientific disciplines. In …
Carlo Beenakker's user avatar
53 votes
Accepted

Whence “homomorphism” and “homomorphic”?

I found this footnote on page 195 of Fricke and Klein's Vorlesungen über die Theorie der automorphen Functionen (1897): Translation: The term "homomorphic" seems more appropriate than the previously …
Carlo Beenakker's user avatar
50 votes

Hilbert's Hotel

The True (?) Story of Hilbert's Infinite Hotel, by Helge Kragh (2014) What is known as "Hilbert's hotel" is a story of an imaginary hotel with infinitely many rooms that illustrates the bizarre conse …
Carlo Beenakker's user avatar
47 votes
Accepted

Who discovered the surreals?

Norman Alling's Conway's field of surreal numbers (1985) gives full credit to Conway: Conway introduced the Field No of numbers, which Knuth has called the surreal numbers. No is a proper class …
Carlo Beenakker's user avatar
43 votes
Accepted

Why did Euler consider the zeta function?

This history is described in Euler and the Zeta Function by Raymond Ayoub (1974). In his early twenties, around 1730, Euler considered the celebrated problem to calculate the sum $$\zeta(2)=\sum_{n=1} …
Carlo Beenakker's user avatar
41 votes
Accepted

How did Lefschetz do mathematics without hands?

Photograph by Paul Halmos showing the artificial hands of Solomon Lefschetz [source] This quote [source] shows how Lefschetz overcame some limitations of his disability:
Carlo Beenakker's user avatar
39 votes

What was Hilbert's view of Gödel's Incompleteness Theorems?

The reaction of Hilbert to Gödel is described in detail by Solomon Feferman in Gödel on finitism, constructivity and Hilbert’s program (2011). Hilbert was unaffected by any of the reconsiderations of …
Carlo Beenakker's user avatar
37 votes
Accepted

Did ancient mathematicians know Euler's characteristic for convex polyhedra?

there is no doubt the answer to your question is "no"; for a wonderful and scholarly recent book on the whole story, see Euler's Gem: The Polyhedron Formula and the Birth of Topology by David Richeson …
Carlo Beenakker's user avatar
37 votes
Accepted

Institutional response to "Esquisse d'un programme"

I would think this is from an authoritative source, since apparently the author consulted with Bourguignon (chair of the hiring committee at CNRS). When Grothendieck reapplied to the CNRS in 1984, …
Carlo Beenakker's user avatar

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