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Comment by derektank | Hacker News Reader

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

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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).

You're correct that the culture of mathematics has changed a lot, and has become much more collaborative. The rise of the modern doctoral training system in Germany later in the 19th century is also relevant. So really Gauss's example points primarily to how much mathematics has changed. But at the same time, I think you could reasonably take Gauss to task even applying the standards of his own era - compare him with Euler, for example, who was much more open with publication and generous with his time and insights, frequently responding to letters from random people asking him mathematical questions, rather like Tao responding to random comments on his blog (which he does). I admire Euler more, and he was born 70 years before Gauss.

Of course, irascible brilliance and eccentricity has an honorable place in mathematics too - I don't want to exclude anyone. (Think Grigori Perelman and any number of other examples!)

There's also this notion of holding themselves to their own standards.

They, Newton included, would often feel that their work was not good enough, that it was not completed and perfected yet and therefore would be ammunition for conflict and ridicule.

Gauss did not publicize his work on complex numbers because he thought he would attacked for it. To us that may seem weird, but there is no dearth of examples of people who were attacked for their mostly correct ideas.

Deadly or life changing attacks notwithstanding, I can certainly sympathize. There's not in figuring things out, but the process of communicating that can be full of tediousness and drama that one maybe tempted to do without.

Weird typo in what I wrote. It's past the edit window. This is what I had meant to type:

There's joy in figuring things out, but the process of communicating what has been so figured can be tedious and full of drama -- the kind of drama that one maybe tempted to do without.

not sharing something you had no time to properly check is entirely understandable

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.

Not to mention instrumental in getting the Manhattan Project going, along with many other research projects during WWII. He basically knew everyone. I didn't know he was Shannon’s advisor though!

> 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?

It’s unusual to tell others not to do something because you’re projecting they’re secretly doing it to compete with you, or that they’ll be depressed when they don’t do what you did.

Doubly so when the rationale is “I’m so fucking awesome”

Triply so when it’s something you’re passionate about, presumably inherently.

Quadruply so when it’s your child. Its tough as a kid hearing your parents come up with elongated excuses why you can’t dream and work towards a future.

When you let people find their own way, you might even learn something from it (ex. 70 yo Gauss learns he didn’t need to tie his mental state to his work because his son doesn’t suddenly become depressed from not matching dads output)

Re: second half, sounds about right, confused at relevancy though (is the idea the child would only do it to pursue nepotistic spoils and an additional reason is the spoils aren’t even good?)

I posit Gauss knew he was a GOAT and had ego. But I also posit he loved his children.

So, a nepotistic delivery was beneficial for his family, and advising his son to seek excellence outside the shadow cast by Gauss himself wasn't stamping on dreams (in my view) it was seeking the happiest outcome.

Without overdoing it, the suicide rate for rich kids with famous parents isn't nothing. There are positive examples, Stella McCartney comes to mind. She isn't wings.

What does "She isn't wings" mean?

Paul McCartney started a band called Wings and she was also in it. I think the idea is "she received nepotistic spoils, lived in the shadow of dad even in his backup projects that 0.01% of people who know the Beatles even recognize." (This elides a very successful career as a fashion designer, as well as the awkward question of what _would_ have guaranteed her more “success”, as well as a lack of understanding of how you feel after grand success you were chasing for it’s own sake (empty))

I meant, she isn't defined by wings and being daddy's kid. She struck out into a field neither Paul nor Linda had occupied. She isn't (defined by) wings.

For what it’s worth, his children were quite successful by all accounts. Two of the boys became successful businessmen after emigrating to the US and one of the boys became a director of the railway network in Hannover. Seems as though they weren’t harmed by their upbringing.

I mean just like most scientists at the time Gauss was rather wealthy, so it is unsurprising they were fine.

> But what he deemed being posited as true

Implicit in the "correctness" of this motive is the idea that unless you're #1 in your field, you are nothing (depression implies strong feelings of worthlessness).

I don't know if you think that's a great lesson to teach your kids as a parent, but I don't.

A valid point. I might add I followed my dad into the field and my son followed me into the field and both academically and in capability he exceeds my ability. I'm enormously proud of him, and I did not seek to prevent him following his heart into the field beyond noting there are other dreams to follow worth considering. I did seek to persuade him not to become a chef, it's a really hard, stressful life.

I totally did not exceed my dads abilities: as one of the 1950s computing pioneers who build some of the first machines in the UK, founded a department of computer science and did work in IFIP, and the BCS, this was always going to be hard.

Not wanting your child to be permanently compared to you for their entire career is entirely understandable

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, ...

Chutzpah.

no TV

Nor Internet

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.

That's 30 more fingers he could count with.

30? Did they only count on one hand back then?

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.

He wasn't as productive as he could have been. This seems like Chuck Norris and Jeff Dean territory after all.

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