a brief tour of six core ideas—numbers, algebra, geometry, probability, analysis, and dynamics—that capture the beauty and power of mathematical thinking for everyone.
In Six Math Essentials, the renowned mathematician and Fields Medalist Terence Tao introduces readers to six central concepts that have guided mathematicians from antiquity to the frontiers of what we know today and now help us make sense of our complex world. This slim, elegant volume explores
numbers as the gateway to quantitative thinking;
algebra as the gateway to abstraction;
geometry as a way to calculate beyond what we can see;
probability as a tool to navigate uncertainty with rigorous thinking;
analysis as a means to tame the very large or the very small; and
dynamics as the mathematics of change.
Six Math Essentials—Tao’s first popular math book
Terence Tao's comment :- This book is for a general audience, without necessarily having a college-level math education. It is aimed more at adults than at children, but some children with an interest in mathematics may be able to get something out of it.
It is just 160 pages so must be information dense with no fluff. I am sold !
I used to have a LinkedIn account, a long time ago. To register I created an email address that was unique to LinkedIn, and pretty much unguessable ... certainly not amenable to a dictionary attack.
I ended up deciding that I was getting no value from the account, and I heard unpleasant things about the company, so I deleted the account.
Within hours I started to get spam to that unique email address.
It would be interesting to run a semi-controlled experiment to test whether this was a fluke, or if they leaked, sold, or otherwise lost control of my data. But absolutely I will not trust them with anything I want to keep private.
I do not trust LinkedIn to keep my data secure ... I believe they sold it.
This is a good example of why it's insane that nobody at Mozilla cares that they hire CEOs that have only a LinkedIn page. If you want to visit the website of the Mozilla CEO, you have to create an account and log in. No big deal if it's a CEO of a plastics manufacturing company, but when the mission is fighting against the behavior of companies like LinkedIn, it makes me wonder why Mozilla exists.
The CEO role at Mozilla is unstable. Even if Mozilla didn't require a LinkedIn page, chances are their CEOs would have an up to date account. Also, Mozilla's ARR is mostly their Google partnership.
If you visit the Mozilla website right now, you will see "Break free from big tech — our products put you in control of a safer, more private internet experience."
I don't think Mozilla requires a LinkedIn page. bachmeier is complaining that Mozilla's CEO doesn't have a personal webpage, and only has a LinkedIn page. By not having a personal webpage, and having a LinkedIn page, it appears that Mozilla's CEO doesn't really care about the open web.
The surest sign of incompetence is somebody claiming they are forced into a requirement for perfection when the requirement is simply a basic adherence to virtue
Remember when LinkedIn was condemned because they copied Gmail’s login page saying “Log in with Google”, then you entered your password, then they retrieved all your contacts, even the bank, the mailing lists, your ex, and spammed the hell out of them, saying things in your name in the style of “You haven’t joined in 5 days, I want you to subscribe” ?
The original version of the LinkedIn mobile app uploaded your personal contacts stored on your smart phone and SIM to their server (to also "invite" them), without requesting user permission.
After that, I never installed it again (but too late), and I bought a second (non-smart) phone.
When I created an account on LinkedIn, a long time ago, I used the web. When it asked if I wanted to invite other people from my list of contacts, I clicked yes. I thought it would let me manually enter some contacts, or at worst, give me a list to choose from, with some kind of permissions prompt. Somehow, it accessed my entire Gmail contact list, and invited them all. My goodness, that was terrifying (I didn't even know it was possible) and embarrassing. Companies are not to be trusted, ever. Especially now, as they've proven for decades they have zero moral compass, and no qualms about abusing people for profit.
But I have such low faith in the platform that I would readily believe that once they think you're not going to continue adding value, they find unpleasant ways to extract the last bit of value that they reserve only for "ex"-users.
Yes I notice that too. I hide my last name now because at my company it's just firstname.lastname so easy to guess.
It helps a lot but I still get a lot of sales goons. A lot of them follow up constantly too "hey what about that meeting invite I sent you why did you not attend"? My deleted email box is full of them (I instantly block them the minute I get an invite to anything from someone I don't know, and I wish Outlook had the ability to ban the entire origin domain too but it doesn't)
Put an emoji after your name in LinkedIn. Something that obviously isn’t part of your name. All the bots that scrape LinkedIn and guess your email address will include the emoji when addressing you in an email; no humans will. You can then use this in a spam filter.
I’m a bit on the fence with this one. Sure, spam is bad, but they also enable you to reach out to somebody outside of the LinkedIn’s walled garden (personally, without automation).
If it enables a tiny startup trying to solve the exact problem I have to reach out to me – I’d say it’s a net positive (but not by a huge margin), and having to blacklist @mongodb.com with their certifications bullshit is a price I’m ready to pay. If more spammers get their hands on this kind of dataset though it’ll probably be a disaster.
I think your example goes out of the scope of an expensive platform like Apollo that exists to maintain a shadow profile based off of your online presence, though.
Maybe the thought occurs that one is only accessible on LinkedIn on purpose and just because a recruiter from 8 years ago has your number, it's not up for grabs?
It's "intelligence platform" in the sense that you can gain a ton of information on individuals, organizations, and relationships that drive it all. If you can track how people move and interact between organizations, you can determine who someone is doing business with and even make an educated guess if that's a sale or interview.
It’s definitely not a fluke. I was getting between 20 and 30 spam emails per day. Simply out of curiosity I deleted my linkedin account and the spam abated. After a week the spam reduced to a trickle and now after a few months I only get a few spam emails per week. Shortly after discovering that LinkedIn was the problem I deleted Indeed as well. Indeed has a fairly robust data deletion program.
LinkedIn definitely sells/shares/leaks email address. I'm not sure which but I also have the same problem. I created my account with a unique email I've only used for LI. I occasionally get B2B and recruiter spam sent to that email.
It could be, but I think it's also as likely it was the scrapers treating that as a trigger event of some type. eg you got a job and might have regrets.
I also saw... not sure what to call them, but honeypot friend requests? I used to get regular requests from profiles I didn't recognize with a generic pretty woman (I'd assume stock photography). Since I ignored them, they would re-request on intervals that were exactly 90 or 180 days. I occasionally glanced at them and there seemed to be no rhyme nor reason to their friends. I'd assume this was also some type of scraping, probably for friends-only profile data.
I don't remember where I got this from, but I've heard long ago about a company which TOS stated vehemently that they would never sell the contacts of their customers... Only to sell them once the accounts are closed because, well, technically those were no longer customers.
A LinkedIn account's sole purpose is publishing, dissemination, and advertising information about you and your company. Anything that you badly want to keep private certainly does not belong there, much like it does not belong to a large roadside billboard.
Otherwise, LinkedIn can be quite useful in searching for a job, researching a company, or getting to know potential coworkers or hires.
Email spam is, to my mind, an inevitability. You should expect waves of spam, no matter what address you use; your email provider should offer reasonable filtering of the spam. Using a unique un-guessable email address, like any security through obscurity, can only get you so far.
You sound like someone that wants to normalize bad behavior. Good luck with that. I would never use a social networking site to find people or jobs. I'm not going to put support behind a entity that doesn't respect privacy and the fact that they are people who don't care, like you, are the problem and why we are in the situation we are in as a country at this point.
I won't call it a social networking site. I'd call it a business-card-exchange site, plus a corporate-flyers-handout site, and of course a self-promotion site.
Selling emails is of course bad, but expecting your email that you give to any big corporation to stay private for a long time is, alas, naïve. I've read the fine print; in most EULAs it includes a ton of clauses about sharing your contacts with a bunch of third parties, etc. LinkedIn, in particular, explicitly says that it may share your contacts with advertising partners.
In other words, if you need to enter this space, wear a hazmat suit, expect no niceties.
This is precisely why I give each website an alias such as website@example.com. If I start receiving spam to that address, I revoke the alias and name and shame the website online whenever I get the chance. Not that I would use LinkedIn anyway.
I usually try to make it obvious what company I have the account to, it makes it easier to track down in cases where the service isn't one that sends mail often. Samsung will not let me use Samsung in my email address. Many companies don't want your email address to include their name.
After I give up and use a real address, some companies will reject my personal first@last.family address because it's still Y2K and .family is not a valid tld.
> Nobody needs these narcisstic, BS spewing pseudo-networking places.
I mean I got my last job through LinkedIn. I'm currently interviewing at a few places, half of which came from LinkedIn. So I personally clearly do need LinkedIn, unless you want to hire me.
Trying to pay a bill. On the website ... it took 24 minutes to navigate to the right place. Then they needed 2FA, so they emailed it to her.
Now she's supposed to open her email while keeping the web page open. It took 5 minutes to do that, find the email, copy down the code, close the email ...
This is a fascinating experiment! I've just been reading the first few paragraphs of the paper ... easily readable, intended to be accessible by anyone.
In Gauss's time mathematicians would solve problems, publish the solutions in an encrypted form, and then challenge their contemporaries to solve the problems.
Here the authors of a paper on the arXiv say:
"To assess the ability of current AI systems to correctly answer research-level mathematics questions, we share a set of ten math questions which have arisen naturally in the research process of the authors. The questions had not been shared publicly until now; the answers are known to the authors of the questions but will remain encrypted for a short time."
Tao says:
"... the challenge is to see whether 10 research-level problems (that arose in the course of the authors research) are amenable to modern AI tools within a fixed time period (until Feb 13).
"The problems appear to be out of reach of current "one-shot" AI prompts, but were solved by human domain experts, and would presumably a fair fraction would also be solvable by other domain experts equipped with AI tools. They are technical enough that a non-domain-expert would struggle to verify any AI-generated output on these problems, so it seems quite challenging to me to have such a non-expert solve any of these problems, but one could always be surprised."
The title I've chosen here is carefully selected to highlight one of the main points. It comes (lightly edited for length) from this paragraph:
Far more insidious, however, was something else we discovered:
More than two-thirds of these articles failed verification.
That means the article contained a plausible-sounding sentence, cited to a real, relevant-sounding source. But when you read the source it’s cited to, the information on Wikipedia does not exist in that specific source. When a claim fails verification, it’s impossible to tell whether the information is true or not. For most of the articles Pangram flagged as written by GenAI, nearly every cited sentence in the article failed verification.
FWIW, this is a fairly common problem on Wikipedia in political articles, predating AI. I encourage you to give it a try and verify some citations. A lot of them turn out to be more or less bogus.
I'm not saying that AI isn't making it worse, but bad-faith editing is commonplace when it comes to hot-button topics.
Any articles where newspapers are the main source are basically just propaganda. An encyclopaedia should not be in the business of laundering yellow journalism into what is supposed to be a tertiary resource. If they banned this practice, that would immediately deal with this issue.
A blanket dimsissal is a simple way to avoid dealing with complexity, here both in understanding the problem and forming solutions. Obviously not all newspapers are propaganda and at the same time not all can be trusted; not everything in the same newspaper or any other news source is of the same accuracy; nothing is completely trustworthy or completely untrustworthy.
I think accepting that gets us to the starting line. Then we need to apply a lot of critical thought to sometimes difficult judgments.
IMHO quality newspapers do an excellent job - generally better than any other category of source on current affairs, but far from perfect. I remember a recent article for which they intervied over 100 people, got ahold of secret documents, read thousands of pages, consulted experts .... That's not a blog post or Twitter take, or even a HN comment :), but we still need to examine it critically to find the value and the flaws.
People here are claiming that this is true of humans as well. Apart from the fact that bad content can be generated much faster with LLMs, what's your feeling about that criticism? It's there any measure of how many submissions before LLMs make unsubstantiated claims?
Thank you for publishing this work. Very useful reminder to verify sources ourselves!
I have indeed seen that with humans as well, including in conference papers and medical journals. The reference citations in papers is seen by many authors as another section they need to fill to get their articles accepted, not as a natural byproduct of writing an article.
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No, apparently eu-west-1 went castors up earlier. I wouldn't be surprised if there was something related to this error.
The site came back around eu-west-1 which, while correlation isn't causation, it does look meaningfully in causation's direction and wiggle an eyebrow suggestively.
It will be interesting to see if Tao's writings are as clear, though possibly he is targetting a different audience.
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