The article links to a series of letters between Fermat, Pascal, and Carcavi which are wonderfully intelligent and readable, while also deeply kind and personal.
> 1. I have been delighted to have had the thoughts conformed to those of M. Pascal, for I admire infinitely his genius and I believe him very capable of coming to the end of all that which he will undertake. The friendship that he offers me is so dear to me and so considerable that I must have no difficulty in making some use of it in the publishing of my Treatises.
> Our blows always continue and I am as glad as you in the admiration that our thoughts are arranged so exactly that it seems that they have taken one same route and make one same path
It makes me wonder if future generations will look back on correspondences between guys like Ken Thompson and Dennis Ritchie.
This does happen some on other websites. I've often seen people in math discuss things that Bill Thurston (a fields medalist) has posted on mathoverflow
Math is particularly nice in that whole papers can be discussed/compressed into a single conversation, unlike, a scientific experiment which requires many figures and controls to confirm or deny one's hypothesis. It's why teatime culture is so great in academic math departments worldwide. I'd listen in at my undergrad institution and usually a single conversation between two professors at teatime could be written up into a paper if they really wanted to. During undergrad I was mentored by one of Bill's students, and he'd often comment that Bill's glib throwaways would usually be very profound if you thought through it carefully.
> I have not time to send you the demonstration of a difficulty which greatly astonished M. de Mere, for he has a very good mind, but he is not a geometer (this is, as you know, a great defect) and he does not even understand that a mathematical line is divisible to infinity and believes very well to understand that it is composed of points in finite number, and never have I been able to pull him from it. If you could do that, one would render him perfect.
Another example is how Godel wrote a letter to Von Neumann towards the end of his life. This letter contained, among other things, the (now very funny) question of whether a certain NP complete problem may be solvable in quadratic time.
Practically though, modern correspondence is often through a disjoint set of technologies, that (importantly) someone cleaning up the estate of a deceased person does not necessarily have access to. So it seems unlikely we'll get this kind of insight going forward (with notable exceptions, for example the Epstein emails).
Just wanted to flag that the works of Ian Hacking, especially The Emergence of Probability (1975) and The Taming of Chance (1990) are excellent on this. Dense and challenging at times but also well written and the product of a very original mind.
The latter book has a Wikipedia page with some more info - was surprised to see Hacking not mentioned here since the featured article is partly based on his work: https://en.wikipedia.org/wiki/The_Taming_of_Chance
I'm busy reading a book [0] by Keith Devlin about the correspondence between Pascal and Fermat. It's called the unfinished game and has been really good so far. It goes through the letters and provides some context around them.
[0] https://www.goodreads.com/en/book/show/4443547-the-unfinishe...
Luca Pacioli invented (or really, put down on paper) double-entry accounting
it is funny how probability has always been way behind other maths. i got to use the Birthday problem at work, once, which made the math undergrad totally worth it
fortunately my Polymarket and Kalshi wagers are protected by AES et al
Right, and Cauchy is the person we have to thank for Bayes’ Theorem, and of course Euler, De Moivre, Poisson and Gauss for the Gaussian integral[1]. You can’t really get figures more central to mathematics than that.
[1] Athough Gauss apparently credited it to Laplace.
As one lecturer put it: modern probability theory derived from two foundations - measure theory and gambling. The latter explains why it has long lacked mainstream mathematical recognition :)
But that's all in the past. Probability is absolutely established in math academia today, Fields medals and all. And despite its applied nature it's pervasive even in pure math.
The article links to a series of letters between Fermat, Pascal, and Carcavi which are wonderfully intelligent and readable, while also deeply kind and personal.
> 1. I have been delighted to have had the thoughts conformed to those of M. Pascal, for I admire infinitely his genius and I believe him very capable of coming to the end of all that which he will undertake. The friendship that he offers me is so dear to me and so considerable that I must have no difficulty in making some use of it in the publishing of my Treatises.
> Our blows always continue and I am as glad as you in the admiration that our thoughts are arranged so exactly that it seems that they have taken one same route and make one same path
It makes me wonder if future generations will look back on correspondences between guys like Ken Thompson and Dennis Ritchie.
https://probabilityandfinance.com/pulskamp/Pascal/Sources/pa...
Perhaps future generations will reference certain threads here on HN.
This does happen some on other websites. I've often seen people in math discuss things that Bill Thurston (a fields medalist) has posted on mathoverflow
https://mathoverflow.net/users/9062/bill-thurston
note that he has been deceased for nearly 15 years now.
Math is particularly nice in that whole papers can be discussed/compressed into a single conversation, unlike, a scientific experiment which requires many figures and controls to confirm or deny one's hypothesis. It's why teatime culture is so great in academic math departments worldwide. I'd listen in at my undergrad institution and usually a single conversation between two professors at teatime could be written up into a paper if they really wanted to. During undergrad I was mentored by one of Bill's students, and he'd often comment that Bill's glib throwaways would usually be very profound if you thought through it carefully.
We're already referencing the Dropbox antagonist whenever we can.
> I have not time to send you the demonstration of a difficulty which greatly astonished M. de Mere, for he has a very good mind, but he is not a geometer (this is, as you know, a great defect) and he does not even understand that a mathematical line is divisible to infinity and believes very well to understand that it is composed of points in finite number, and never have I been able to pull him from it. If you could do that, one would render him perfect.
In math, Grothendieck's correspondences are quite famous. Here's a book that is entirely 300 pages of letters between him and J.P. Serre
https://webusers.imj-prg.fr/~leila.schneps/grothendieckcircl...
There are many others for Grothendieck though.
Another example is how Godel wrote a letter to Von Neumann towards the end of his life. This letter contained, among other things, the (now very funny) question of whether a certain NP complete problem may be solvable in quadratic time.
https://www.cs.cmu.edu/~odonnell/15455-s17/hartmanis-on-gode...
Practically though, modern correspondence is often through a disjoint set of technologies, that (importantly) someone cleaning up the estate of a deceased person does not necessarily have access to. So it seems unlikely we'll get this kind of insight going forward (with notable exceptions, for example the Epstein emails).
> It makes me wonder if future generations will look back on correspondences between guys like Ken Thompson and Dennis Ritchie.
We kinda had that, on Usenet, before spammers flooded it to death.
[dead]
> a French gambler and intellectual socialite enlisted the help
Imagine Blaise Pascal and Pierre de Fermat teaming together to solve your problem.
Just wanted to flag that the works of Ian Hacking, especially The Emergence of Probability (1975) and The Taming of Chance (1990) are excellent on this. Dense and challenging at times but also well written and the product of a very original mind.
The latter book has a Wikipedia page with some more info - was surprised to see Hacking not mentioned here since the featured article is partly based on his work: https://en.wikipedia.org/wiki/The_Taming_of_Chance
I'm busy reading a book [0] by Keith Devlin about the correspondence between Pascal and Fermat. It's called the unfinished game and has been really good so far. It goes through the letters and provides some context around them. [0] https://www.goodreads.com/en/book/show/4443547-the-unfinishe...
Luca Pacioli invented (or really, put down on paper) double-entry accounting
it is funny how probability has always been way behind other maths. i got to use the Birthday problem at work, once, which made the math undergrad totally worth it
fortunately my Polymarket and Kalshi wagers are protected by AES et al
In what way was it always behind? This work of Fermat and Pascal is ballpark contemporary to the development of calculus.
Right, and Cauchy is the person we have to thank for Bayes’ Theorem, and of course Euler, De Moivre, Poisson and Gauss for the Gaussian integral[1]. You can’t really get figures more central to mathematics than that.
[1] Athough Gauss apparently credited it to Laplace.
Most of the names you mention belong to the next (18th) century.
Gauss worked out some sort of probability distribution too.
As one lecturer put it: modern probability theory derived from two foundations - measure theory and gambling. The latter explains why it has long lacked mainstream mathematical recognition :)
But that's all in the past. Probability is absolutely established in math academia today, Fields medals and all. And despite its applied nature it's pervasive even in pure math.
Gambling is also (allegedly) responsible for giving us the sandwich[0] and the modern sushi roll.
[0]https://en.wikipedia.org/wiki/John_Montagu,_4th_Earl_of_Sand...
There's a coffee-table book in there somewhere.
Against the Gods: The Remarkable Story of Risk by Bernstein is an enjoyable read on this.
… and a Student’s quest for quality beer led to the t-test.
https://en.wikipedia.org/wiki/William_Sealy_Gosset
A nice video explainer about this dispute: https://www.youtube.com/watch?v=_YRfSe-f1FE