Comment by derektank
1 day ago
My favorite story about the Fourier Transform is that Carl Friedrich Gauss stumbled upon the algorithm for the Fast Fourier Algorthim over a century before Cooley and Tukey’s publication in 1965 (which itself revolutionized digital signal processing).[1] He was apparently studying the motion of the asteroids Pallas and Juno and wrote the algorithm down in his notes but it never made it into public knowledge.
[1] https://www.cis.rit.edu/class/simg716/Gauss_History_FFT.pdf
There is a saying about Gauss: when another mathematician came to show him a new result, Gauss would remark that he had already worked on it, open a drawer in his desk, and pull out a pile of papers on the same topic.
One of the things I admire about many top mathematicians today like Terence Tao is that they are clearly excellent mentors to a long list of smart graduate students and are able to advance mathematics through their students as well as on their own. You can imagine a half-formed thought Terence Tao has while driving to work becoming a whole dissertation or series of papers if he throws it to the right person to work on.
In contrast, Gauss disliked teaching and also tended to hoard those good ideas until he could go through all the details and publish them in the way he wanted. Which is a little silly, as after a while he was already widely considered the best mathematician in the world and had no need to prove anything to anyone - why not share those half-finished good ideas like Fast Fourier Transforms and let others work on them! One of the best mathematicians who ever lived, but definitely not my favorite role model for how to work.
Well, in that time it was more or less how mathematics worked. It was a way of showing off, and often it would be a case of "Hey I've solved this problem, bet no-one else can". It was only later it became a lot more collaborative (and a bit more focused on publishing proofs).
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Someone blew my mind by convincing me to read Bush’s “As we may think” which was published in 1945. Then I started digging into him and discovered he was also the second president of the ACM, was instrumental in shaping the formation of the National Science foundation (mainly by critiquing their initial plans as unworkable) and also Claude Shannon’s doctoral advisor. Because of course he was.
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not sharing something you had no time to properly check is entirely understandable
> There is a saying about Gauss: when another mathematician came to show him a new result, Gauss would remark that he had already worked on it, open a drawer in his desk, and pull out a pile of papers on the same topic.
As if phd students need more imposter syndrom to deal with. Ona serious side, I wonder what conditions allow such minds to grow. I guess a big part is genetics, but I am curious if the "epi" is relevant and how much.
Imposter syndrome? If I was a PhD-level student (back then) and had an idea - and it turned out that Gauss had also thought of the idea, then written it out, and he kept the notes right in his desk - yeah. I'd take that as proof that I was one of the world's top mathematicians.
Gauss's notes and margins is riddled with proofs he didn't bother to publish - he was wild.
Not sure if true, but allegedy he insisted his son not go into maths, as he would simply end up in his father's shadow as he deemed it utterly Impossible to surpass his brilliance in maths :'D
> as he would simply end up in his father's shadow as he deemed it utterly Impossible to surpass his brilliance in maths
Definitely true but also bad parenting. Gauss was somewhat of a freak of nature when it came to math. Him and Euler are two of the most unreasonably productive mathematicians of all time.
But what he deemed being posited as true, was this really bad parenting? It could be to head off competition or it could be brutal realism to head off future depression.
Nepotism existed since time immemorial but for a mathematical genius, what was the nepotistic deliverable for the child? A sinecure placement at university?
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When I interned at Chevron someone said they (or some other oil company) were using Fourier transforms in the 1950's for seismic analysis but kept it a secret for obvious reasons. I think you couldn't (can't?) patent math equations.
Gauss is gonna Gauss.
How was Gauss so productive with 6 children?
Probably sexual division of labor.
Behind every successful man, ...
That's 30 more fingers he could count with.
30? Did they only count on one hand back then?
I'd hazard by not dealing with them until they'd been schooled enough to operate as computers and GI (general intelligence) assistants.
There's a spread of farmers, railroad and telegraph directors, high level practical infomation management skills in the children.
no TV
Nor Internet
He wasn't as productive as he could have been. This seems like Chuck Norris and Jeff Dean territory after all.
I only have 5 kids, and I am also not nearly as productive as Gauss but to a certain degree, it feels to me like responsibility kind of tries to force me to be more effective.
Chutzpah.