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.
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.
Or a good one, forcing governments to have robust infrastructure that this info isn't useful. Similar reasoning as with security and open source software.
Yeah, and it’s not like the enemy would take the information from here, they already have it and likely even more detailed. It is quite basic stuff to have when preparing to defend (or attack).
I'm a data scientist and a lot of my R code are dplyr-chains a la data |> select(features) |> filter(low_quality) |> mutate(feature=...).
It just saves time to comment on what those chains do instead of having go through them every time I want to change something.
or even
$ cat source | <find the flags and give me some documentation on how to use this>
Could you please elaborate on this? Do I get this right that you can set up your your command line so that you can pipe something to a command that sends this something together with a question to an LLM? Or did you just mean that metaphorically? Sorry if this is a stupid question.
Having gone through the explainations of the Transformer Explainer [1], I now have a good intuition for GPT-2. Is there a resource that gives intuition on what changes since then improve things like more conceptually approaching a problem, being better at coding, suggesting next steps if wanted etc? I have a feeling this is a result of more than just increasing transformer blocks, heads, and embedding dimension.
Most improvements like this don't come from the architecture itself, scale aside. It comes down to training, which is a hair away from being black magic.
The exceptions are improvements in context length and inference efficiency, as well as modality support. Those are architectural. But behavioral changes are almost always down to: scale, pretraining data, SFT, RLHF, RLVR.
I once bought an Office 2016 license and when I installed it this year on a new laptop, it turned itself into a trimmed down O365. After the first Office update, I got a non-closable ad next to my Excel spreadsheet to upgrade to a full O365. Even more, I was only able to save files to OneDrive and not locally. That was not what I originally paid for!
> I was only able to save files to OneDrive and not locally.
I find this very infuriating, and I've stopped using MS for more than 10 years now. They used to be a proper software company, with their flows, of course, but quite professional in the great scheme of things. But what you're describing goes against everything that I've valued as a computer programmer when I entered this field of work ~20 years ago.
The problem for me is not getting my DNA sequenced but not having to trust a third party with my genetic information. As wirtten in the article, they only achieved a 13% coverage (even less if because you have to assume that not all base calls are correct), which is not useful for any sort of genetic analysis. So the title is really misleading.
Terence Tao uses a trick, I think he calls "structured procrastination": When there is a thing he doesn't want to do, he recalls another thing he doesn't want to do more. This way he's procrastinating on the other thing by doing the not favoured one.
I think that sounds like productive procrastion, it won an Ig-Nobel award. As you say, it's basically finding something you don't want to do even more than the thing you need to do, so you instead procrastinate productively by doing the needful.
