“Mathematician Laurence Sigler had made it his mission to translate [Fibonacci’s Liber Abaci], rushing to complete the task right before he died of lymphocytic leukemia in 1997. But his editor moved on, and the manuscript languished on floppy disks for years. For a while Sigler’s widow Judith Sigler Fell, fearing the project would be killed, took the extraordinary step of impersonating her husband in communiqués.
By the time Fell found a new publisher, Springer Verlag (now part of the same publisher as Nature), floppy disks had been superseded and she had to hire a hacker to extract the files. Fell then discovered that Springer only accepted submissions in TEX format, the technical standard for physics and mathematics texts. She learned it and spent six months retyping the text. Fibonacci’s Liber Abaci was finally published in 2002 — the 800th anniversary of the book’s first appearance.”
> Fibonacci did not, however, discover the sequence – it was recorded in Sanskrit at least as far back as 200 BC.
Possibly even earlier. This is not developed further because the article is about Leonardo.
Pingala's is perhaps the first recorded conception of the sequence. It showed up in his study of metre and rhythm of poetry. The problem he was trying to solve was to enumerate how many ways can an integral period of time be broken up into pieces of unit and double unit length.
If you are a drummer I think this will make a lot of sense.
Pingala is also known for his use of binary numbers, 'Pascal's' triangle, recursive generation of strings from context free grammars. Full formalization of Sanskrit grammar as a context free grammar goes to Panini (possibly his brother).
I'm always surprised by the abstraction level of Sanskrit ideas. Very rapidly they talk about infinite ways of assembling rules. Was there even a strong motivation (economic or logistical value) behind this?
> Such problems may seem trivial to someone trained in modern elementary-school algebra
I've often wondered about how school curricula evolve over time. Presumably people were doing _something_ in 13th century math classes? What were they doing? How soon did we end up incorporating modern number representation into elementary school?
Something like calculus was cutting edge when Newton and Leibnitz were around, now it's what people learn in high school.
Are there things that we currently consider to be new and exciting that in a few years will be taught to every student? What will drop out?
Perhaps related, I've read that Al-Khwarizmi's book on algebra [0] contained no equations or even any numerals. It was apparently a wall of text.
My take is that you pretty much had to be a philosopher to make your way through a text like that. Al-Khwarizmi wrote down a general solution to the quadratic equation, which had eluded humanity since the ancient Greeks. Today, the solution and its proof are taught to schoolchildren.
One thing that's happened is that notation has been improved. For instance we now have equations and we use numerals to write numbers.
Similar deal with Newton and Leibnitz. The notation that we use for teaching calculus resembles theirs but has been improved. Perhaps moreso for Newton's mechanics. Philosophers debated about Newton, now we teach his ideas to schoolchildren.
Likewise Clerk Maxwell. What I've read is that his theory was also unreadable by most of us, but his successor, Heaviside, came up with the notation that we teach to slightly older schoolchildren.
This seems to be a recurring story. Maybe someday there will be a notation that makes string theory seem obvious... to schoolchildren. ;-)
[0] The origin of both words "algorithm" and "algebra"
> I've read that Al-Khwarizmi's book on algebra [0] contained no equations or even any numerals
Yes the use of symbols came much later. Algebra used to be couched in terms of do this to that quantity while maintaining that relation between that and that quantity then to the quantity obtained in that step ....
> Something like calculus was cutting edge when Newton and Leibnitz were around, now it's what people learn in high school.
To your point, I had lots of such in (American public) high school in Chicago suburbia, but now decades later it seems a small fraction of Americans ever took calculus. I find that sad, since I thought it kinda beautiful work.
Quoting:
“Mathematician Laurence Sigler had made it his mission to translate [Fibonacci’s Liber Abaci], rushing to complete the task right before he died of lymphocytic leukemia in 1997. But his editor moved on, and the manuscript languished on floppy disks for years. For a while Sigler’s widow Judith Sigler Fell, fearing the project would be killed, took the extraordinary step of impersonating her husband in communiqués.
By the time Fell found a new publisher, Springer Verlag (now part of the same publisher as Nature), floppy disks had been superseded and she had to hire a hacker to extract the files. Fell then discovered that Springer only accepted submissions in TEX format, the technical standard for physics and mathematics texts. She learned it and spent six months retyping the text. Fibonacci’s Liber Abaci was finally published in 2002 — the 800th anniversary of the book’s first appearance.”
I admire the devotion of her to her husband and to the work of his
> Fibonacci did not, however, discover the sequence – it was recorded in Sanskrit at least as far back as 200 BC.
Possibly even earlier. This is not developed further because the article is about Leonardo.
Pingala's is perhaps the first recorded conception of the sequence. It showed up in his study of metre and rhythm of poetry. The problem he was trying to solve was to enumerate how many ways can an integral period of time be broken up into pieces of unit and double unit length.
https://en.wikipedia.org/wiki/Fibonacci_sequence#History
If you are a drummer I think this will make a lot of sense.
Pingala is also known for his use of binary numbers, 'Pascal's' triangle, recursive generation of strings from context free grammars. Full formalization of Sanskrit grammar as a context free grammar goes to Panini (possibly his brother).
https://en.wikipedia.org/wiki/Pingala
I'm always surprised by the abstraction level of Sanskrit ideas. Very rapidly they talk about infinite ways of assembling rules. Was there even a strong motivation (economic or logistical value) behind this?
I don't know enough to know why, but they were very interested in the extremes of size, both large and small, as well as the notion of infinite.
Fascination with the large seems to be a pan-cultural thing
https://en.wikipedia.org/wiki/History_of_large_numbers
The article does not talk about Mayan numbers, I would hazard a guess that they were interested in large numbers too.
There is also the Buddhist myth of Buddha enumerating a list of very large numbers.
https://en.wikipedia.org/wiki/Asa%E1%B9%83khyeya
https://jain108academy.com/buddha-recites-to-infinity-a-love...
Large numbers also show up in that problem posed by Archimedes.
https://en.wikipedia.org/wiki/Archimedes%27s_cattle_problem
https://sites.google.com/site/largenumbers/home/2-3/p12_2-3-...
> Such problems may seem trivial to someone trained in modern elementary-school algebra
I've often wondered about how school curricula evolve over time. Presumably people were doing _something_ in 13th century math classes? What were they doing? How soon did we end up incorporating modern number representation into elementary school?
Something like calculus was cutting edge when Newton and Leibnitz were around, now it's what people learn in high school.
Are there things that we currently consider to be new and exciting that in a few years will be taught to every student? What will drop out?
Perhaps related, I've read that Al-Khwarizmi's book on algebra [0] contained no equations or even any numerals. It was apparently a wall of text.
My take is that you pretty much had to be a philosopher to make your way through a text like that. Al-Khwarizmi wrote down a general solution to the quadratic equation, which had eluded humanity since the ancient Greeks. Today, the solution and its proof are taught to schoolchildren.
One thing that's happened is that notation has been improved. For instance we now have equations and we use numerals to write numbers.
Similar deal with Newton and Leibnitz. The notation that we use for teaching calculus resembles theirs but has been improved. Perhaps moreso for Newton's mechanics. Philosophers debated about Newton, now we teach his ideas to schoolchildren.
Likewise Clerk Maxwell. What I've read is that his theory was also unreadable by most of us, but his successor, Heaviside, came up with the notation that we teach to slightly older schoolchildren.
This seems to be a recurring story. Maybe someday there will be a notation that makes string theory seem obvious... to schoolchildren. ;-)
[0] The origin of both words "algorithm" and "algebra"
> I've read that Al-Khwarizmi's book on algebra [0] contained no equations or even any numerals
Yes the use of symbols came much later. Algebra used to be couched in terms of do this to that quantity while maintaining that relation between that and that quantity then to the quantity obtained in that step ....
> Something like calculus was cutting edge when Newton and Leibnitz were around, now it's what people learn in high school.
To your point, I had lots of such in (American public) high school in Chicago suburbia, but now decades later it seems a small fraction of Americans ever took calculus. I find that sad, since I thought it kinda beautiful work.
> Presumably people were doing _something_ in 13th century math classes? What were they doing?
Glad you asked. This is what one such endearing 13th century kid was doing in class
https://resobscura.substack.com/p/onfims-world-medieval-chil...