m00n

With that title and reception I can imagine people bookmarking this for „later“ and feeling good about it. But who reads that stuff really?

To each their own, but 700+ pages for material that is done in my experience in the first 2-3 weeks of undergraduate math is more disheartening than empowering for a student, in my opinion.

If you can open a math book anywhere in the last 20% of pages and just start reading, you are looking at pop science and not lecture notes.

It is also true that this a 500fold increase in prevalence when compared to the general population.

The 5-year survival rate of lung cancer noticed due to e.g a sore throat is below 10%.

A course in Arithmetic by Serre is for me THE book to get into Number Theory

If you are interested in this kind of role, it is usually called Executive Assistant in the corporate world. Had the fortune to support my CEO and attend e.g. all board meetings (because I did the minutes). This is at a >10$ bn revenue established company. Very rewarding, but experience depends very much on the style of your boss.

A map between algebraic curves is defined by polynomials. That the map is defined over K means you can find a coordinate system such that the equations of the curves and the equations of the morphisms have coefficients in K and not some larger ring, eg the complex numbers or a large extension field of F_p(field of p elements)

Good question, no there is no difference for elliptic curves, which you can think of as 1-dimensional geometric objects (curves) which posses group structure. A good map in this category should respect the geometry (be a so called rational map, ie defined by polynomials in a suitable coordinate system) and the group structure. Interestingly all these maps are either constant (map everything to 0) or surjective.

For higher dimensional geometric groups (abelian surfaces etc) one usually wants to make a distinction and calls the surjective homomorphisms with finite preimage isogenies.

The statistics worked for me too, just the streak was reset.

And they broke everybody’s streak in the process while reusing today‘s word…

Way to destroy a good brand.

Actually, a Banach-Tarski-like result is impossible in 2D space, since there is a Banach measure (= volume definition to all subsets of the plane) that extends the usual volume definition (e.g. for circles).

The crucial idea that makes Banach-Tarski work in 3D is the insight that the set of rotations around an axis through the origin in 3-space has a free subgroup F on 2 generators (finite strings of A's, B's and their inverses). From this fact the proof is quite easy, but this comment is too small for it.

Sorry, but the breathless way, that maths is often discussed on HN, makes me feel uneasy.

It feels strange to see adults that opine on every subject, from nuclear fusion energy, to virology and financial markets, like they know it all, to suddenly "I was never good at math", like a clichee party conversation.

I mean, I get it: It first feels strange and magical, since even the explanations of some of the vocabulary take more time than we are willing to devote to a single thought. But instead of digging in and looking up what "Borel measurable" might mean, the HN crowd rather watches the x-th numberphile video/emotionalized Quanta blurb.

/rant

More to your points:

Your kid has a greater chance of being a multi-millionaire NBA player than being smart enough to understand this stuff

There are >5000 math phds each year, so no, getting into the NBA is harder.

Even 18th century math would be a challenge for many math grad students. Just crazy

Not sure, what this is supposed to mean. Certainly as a math grad you should be able to _understand_ 18th century math. Now, to _come up_ with the stuff is something else entirely. But I'm not sure how many engineers would claim they had discovered the telegraph, were they be born instead of Gauss.

Some things that actuaries also do besides "memorizing formulas":

* Asset-Liability management, i.e. hedging of future claims on the financial markets [https://en.wikipedia.org/wiki/Asset_and_liability_management]

* Consulting multinationals and nations, how to structure their $bn pension schemes for future generations

* Valuation of embedded options and guarantees by stochastic modelling of the company [https://www.investopedia.com/terms/e/embeddedvalue.asp]

You can get a more balanced impression of topics, e.g. from the UK actuary society [https://www.actuaries.org.uk/studying/curriculum]

They also have past exams in full length incl. solutions.

The actuarial profession is quite broad, in my experience.

For the teams I worked with, memorization of formulas was to their daily work as whiteboard coding would be to the daily work of a sw-eng.

Regarding life insurance product offerings: disability insurance is often advised by consumer protection groups for young professionals, who crucially depend on future income.

Regarding savings products, nothing wrong IMO, with tax subsidizing a "consume later" mentality, if the products are cost-effective.

Ok, so this article is not about going meat free. Just about factory farming. If you "crave meat" maybe you could consider non-factory farmed meat, for all the reasons mentioned.

Regarding your 3 points: 'Availability' is a problem with non-meat? I would think in most neighbourhoods that have a butcher, you should find a supermarket.

'Satiability', really? You don't feel full after baked potatos with sour cream? Mac and Cheese? A pizza quattro formaghi? Noodle soup? Indian curry? All of the above and an apple pie? You need that patty, right?

As a life-long meateater, I can very well understand your last point on taste. Hard to argue with taste. Since I don't want to miss it either, I will have meat from time to time as a special treat. Usually when eating out fancy. So about 1-2 times a month. Makes me looking forward to those dinners even more and I don't have to go the hardest 10% of the meat-free way.

Why would the robot cost the same? If it costs the same, then there is no incentive to introduce robots in the first place. I think the wide-spread automation is a testament to the much lower price of robots compared to human labour, no?

Maybe it really is a cultural difference. I think there is a continuum of valuations at work here:

If a contractor gets his materials cheaper or does have cheaper labor available, I don't see any obligation or market process to pass these savings onto clients, when the work is of the same quality.

On the other hand, when you delegate work to an expert, and he doesn't tell you about the 99% savings you could employ with existing technologies, I feel this is bad conduct, regardless of output. It just amounts to a 9900% markup on his value. I don't think this kind of markup is ethical, but probably the market will catch up to this expert and revalue him.

You say you would feel "sad". To be honest, I would feel cheated. And to set up this smokescreen with pseudo-gardening people (or prerecorded data entry screencaptures to stay with the article) is outright fraught, IMHO.

Yes, to make the analogy better, say the gardener invented the robot while on your "gardening time".

Edit: Writing a script might be expensive, but is the market price of this script really a lifetime of data-entry salary? Seems unlikely, or we would not see as much automation.

A question for the people that have a positive attitude towards keeping time savings for yourself instead of passing them on to your employer.

Would you be also okay with the following situation: You have someone remodell your garden. He comes up with an estimate of 1 week worth of full-time work for two people. Based on your experience this seems reasonable and you agree on a fixed price of 10000$.

Two scenarios of what happens next: 1) He shows up the next day with a gardening robot you never knew existed and he never told you he would use. The work is done in 30 minutes. He goes home to spend time with his kids. (Or maybe contract more "2 week projects"?)

2) Two gardening people show up every morning to greet you when you drive to work. They leave when you come back and make steady progress every day. On the last day you come home early and witness that actually the daily work is done by a gardening robot in 5 minutes and the two people actually drive home during the day to spend time with their kids.

Would you contract this guy again?

You're right, I was thinking about univariate polynomials. The "preprint" is only concerned with functions of one complex argument, so this should suffice.

No, it is not "well written". I'm no expert in analytic number theory, but here are some sanity checks:

His definition of the critical strip (2.4) is wrong.

He works with some family of polynomial functions who agree on the sets K[a] that have open interior (2.1). Of course, two polynomials that agree on infinitely many points are identical. So there really is not much to his "Todd-function". It is just a polynomial.

From his claims 2.3 and 2.4 then follows T(n)=n, for all natural n and hence T(s)=s, as T is a polynomial.

What does "T is compatible with any analytic formula" in (2.4) even mean? Does it mean "for f(X) a everywhere converging power series, then T(f(s))=f(T(s)), for s in C"? This can only hold for T(s)=s, again. So maybe it means something else? He applies it to f(X)=Im(X-1/2), which is not a power series, so what does he mean?

The Hirzebruch reference is a 250pp book. The paragraph on Todd-Polynomials (which are a family of multivariate polynomials, btw. There is no "Todd-polynomial" T in Hirzebruch!) does not contain a formula as claimed in (2.6).

Considering the last two breakthrough claims, that Atiyah made (no complex S^6 sphere and a new proof of Feit-Thompson) vanished in thin air, I remain more than sceptical that this "preprint" can be salvaged.

What is the philosophical difference between an 'argument' that human minds following the laws of logic agree on "is correct" and a machine built by these minds flashing a "correct light"?

IMO the only advantage to be gained by introducing physical computers in the picture is lightning-fast book keeping.

Why would you trust an Intel CPU, a Samsung SSD and a linux fs driver running some verifying framework more than the human brains designing, writing and executing said framework?

To take one of your examples that I happen to be familiar with: Wiles' proof of FLT. I can assure you that in the >20 years that this proof has been out, thousands of professors, postdocs and grad students have read and reread every line of the two Annals papers.

They have been the foundation of hundreds of Phd projects and the scientific merit and public fame to be gained by finding a gap in the argument is clear.

Actually I think breakthrough papers are least problematic when it comes to unverified claims in math.

I was thinking along these lines, too. But the problem with job satisfaction is: Do you rely on self-reported job satisfaction or objective quantitities like absenteeism or turnover?

Both are hard to make comparable between different fields: In some (think med, law etc) the cost of education will prohibit changing careers, regardless of if you make millions as patent lawyer or heart surgeon (assuming that the latter adds more "value to society"). So I think it is hard to come up with a consistent objective measure of satisfaction. On the other hand, if you poll people, you might find, that fine arts majors were very happy with their college life, but actually work in a different field to pay rent (I happen to know some music majors).

The problem with the societal benefit definition is: It very much depends on your own system of beliefs. Is an education in business and employing 5 people, more or less valuable than a job as a veterinary? Since most of the undergrad majors also have a variety of possible jobs they could lead into, this is even harder to quantify.

So maybe just do away with rankings :-)

"Completely worthless" is not what comes to mind, when it provides your living.

If it doesn't fulfil you, and you have a math degree, why not change careers?

What interpretation of "valuable" do you propose instead? A discussion of remuneration was exactly what I expected when reading the headline.

May I ask who will lose his professional credentials, when your AI does not follow established practises and insurance coverage goes belly-up?

Interesting to see, how the usually data driven crowd on this site largely dismisses a data point and the usual talking points are reversed:

40h work-weeks that pay great -> Must be boring.

Economics study is done by economists -> Probably skewed.

How dare these people * equating carreer value with expected profits * using a weighted average to come up with a number * expect candidates to pass hard stats tests before constructing insurance products

Programming in JS web frameworks is clearly superior to any work done using Excel and be it supplying the nation with health coverage. /s

Seconded. It was a great game, albeit with not so much replay value.

There is a great interview with Blow on the technicalities of the warping effects in Braid: https://youtu.be/8dinUbg2h70

In addition to Limbo and Inside, may I also recommend:

Portal 1&2 Antichamber VVVVVV increpare.com

In particular Stephen Lavelle (@increpare) makes games with much darker and more interesting social implications. Although, Braid accurately predicted the "nice guys" trope.

I wonder why the authors took the time to generate an image of their pattern but refrained from giving the actual DEFINITION. This does not foster constructive discussion of any possible ideas present. As can be seen in dozens of well-meaning comments here, people waste time reversing and guestimating parameters etc.

Looking at the layman letters that my institute gets on a regular basis, I can say, that this is unfortunately a recurring theme with amateur mathematicians: They fail to state their basic definitions and assumptions and seem all to eager to dive right into applications, be it computer graphics, cryptography or finance.

More to the point: This picture seems from a cursory inspection to plot T(k,n) with n=row, k=column from the top left. But why is this interesting?