Looking around, can find curious things current AI can't do but likely can find important things it can do. Uh, there's "a lot of money", can't be sure AI won't make big progress, and even on a national scale no one wants to fall behind. Looking around, it's scary about the growth -- Page and Brin in a garage, Bezos in a garage, Zuckerberg in school and "Hot or Not", Huang and graphics cards, .... One or two guys, ... and in a few years change the world and $trillions in company value??? Smoking funny stuff?
Yes, AI can be better than a library card catalog subject index and/or a dictionary/encyclopedia. But a step or two forward and, remembering 100s of soldiers going "over the top" in WWI, asking why some AI robots won't be able to do the same?
Within 10 years, what work can we be sure AI won't be able to do?
So people will keep trying with ASML, TSMC, AMD, Intel, etc. -- for a yacht bigger than the one Bezos got or for national security, etc.
While waiting for AI to do everything, starting now it can do SOME things and is improving.
Hmm, a SciFi movie about Junior fooling around with electronics in the basement, first doing his little sister Mary's 4th grade homework, then in the 10th grade a published Web site book on the rise and fall of the Eastern Empire, Valedictorian, new frontiers in mRNA vaccines, ...?
And what do people want? How 'bout food, clothing, shelter, transportation, health, accomplishment, belonging, security, love, home, family? So, with a capable robot (funded by a16z?), it builds two more like itself, each of those ..., and presto-bingo everyone gets what they want?
"Robby, does P = NP?"
"Is Schrödinger's equation correct?"
"How and when can we travel faster than the speed of light?"
Spent a lot of time in education, K through Ph.D and as a college professor. Net, it seemed that the keys to good or better quality K-12 public school education was simply the parents, their quality that also showed in careers, income, standard of living, socialization, etc. A lot of that quality gets inherited, and Darwin wins again.
But here is a surprise: In college my wife made both PBK and Summa Cum Laude, won both NSF and Woodrow Wilson graduate fellowships, and got her Ph.D.
Her high school? Her family lived in Indiana, in a house her father built from some plans in Good Housekeeping magazine, on a 33 acre farm, surrounded by farms raising mostly corn, soy beans, wheat, and chickens. The local town consisted of a church, a school, and a tavern. The school building was a good accomplishment by the community, big enough for the number of students, taught grades 1-12, but had fewer than 12 classrooms and fewer than 12 teachers! Net, the facilities were poor, but the parents made sure the schooling was good.
The school I went to was relatively large, the pride of the city with a quite good Principal for 1-6 and another for 7-12, no bad teachers, and some good ones. They taught Latin, Spanish, and French and had a good math program. The year before me three guys went to Princeton and two of them ran against each other for President of the Freshman Class. In my year, myself and two others did the best on the Math SATs, all went to college, one MIT.
In both of the schools, 100% of the students were well behaved, i.e., no disruption in classes; this was just expected and without any particular efforts.
I really liked math and physics and wanted much more than the classes offered. So, the classes were beneath me and mostly taught myself from the books. So the school put up with that independent approach and sent me to a Math Tournament and some summer enrichment programs, which was good education: The good parents wanted good education.
Later there were some race riots with that school a target. So, the city changed to teaching cosmotology, etc. and picked another school to be a good one.
Net, with good parents, a school can be plenty good with modest facilities.
I heard from somewhere that Herstein was an Emil Artin student at Princeton.
Herstein went to the extra trouble to make his linear algebra also work for finite fields.
In the back he has group representation theory is a small nutshell.
Also in the back he does linear programming, but his treatment is obscure and for no good reason. Since then nearly every treatment, beginner or advanced is not obscure at all.
Math genealogy project says Herstein was a student of Max Zorn (the guy the lemma is named after), but Zorn was a student of Artin! Zorn doctorized under Artin in Hamburg in 1930, before Artin moved to Princeton.
(1) Didn't see anything on the math of probability or stochastic processes, e.g., nothing from Dynkin, Neveu, Breiman, etc.
(2) That it's important to study carefully that computing is about "switches" is something like knowing the details of the amazing work in the chemistry of rubber tires is crucial for truck driving or we should all early in our education achieve good mastery of each of the proteins in our DNA.
(3) After working through all those books, cancelling nearly everything else in life for some years, just what is the result, the payoff, the reason? Academic research or something in the mainstream economy, technology, etc.?
Ah, just today used TeX on a paper in anomaly detection that exploits the Hahn decomposition!
In the paper of the OP, was there a place where it claimed it had a subset of a set when it was really an element of the set. Don't be careful about the difference between
elements and sets and can get back to the Russell paradox.
Also, for some positive integer n, e.g., n = 3, we can have an n-tuple, e.g.,
(A,B,C)
but, guys, so far we've said nothing about the components of the n-tuple being numbers, e.g., for error correcting codes, elements of a finite field, multiplying an n-tuple by a number, adding n-tuples, taking inner products, so, so far, with just some n-tuples we a bit short of a vector space or vectors.
Early on, with a good technical background, I guessed that, of course, the key to success in technology was some good technology but soon discovered that VCs just want to make money, a lot of money, quickly, and otherwise will hear from the investors in their fund.
Just heard of Palmer Luckey. Hmm! Money? No big staff, not much equipment, essentially just one person?? $1B+, quickly? Example: Taylor Swift. Did she ever hear of Linux???
In the US there have been a few, i.e., apparently less than 20, universities with an applied math program up to date in and teaching optimization.
Sooooo, anyone at all seriously interested, long, for decades, would, could, should visit some of those math programs, meet some of the profs, get recommendations for their former students, call them, chat, and offer a job better than their current lawn mowing, fast food restaurant kitchen cleaning, or car washing. Instead of just the US, might also consider Waterloo in Canada. Actually the Chair of my Ph.D. orals committee specialized in optimization in logistics. After sending 1000+ beautifully written resume copies and hearing back nothing, can begin to conclude that optimization is not a hot field and for highly dedicated optimizers who want to sleep on a cot in a single room, forgo bathing, most days eat bread, other days peanut butter, have no children, wife, or family contact, don't own a car, and must get any needed medical care from some of the last resort special clinics. Ah, real optimization!
Easier: At the best, cheap in-state college, major in math, science, or tech. Do well, and then for an Ivy, etc. college, go there as a grad student which can be even better for meeting people than being a ugrad student at an Ivy. Going as a grad student might be for free.
Maybe teach some ugrad courses -- a way to meet people, especially girls 1-3 years younger. Generally do a lot of the obvious things to meet people -- much of the reason for an Ivy is to meet people. If you want an academic career, then a top research university can be a HUGE help, i.e., may have several world class research professors any one of whom could get you a good start on an excellent research direction.
As a ugrad, to help getting into the college you want as a grad student, be sure to work hard and do well. E.g., any free time you might have, get and study the books of courses you plan to take. Then in such courses you will have a head start that can make you look MUCH smarter. For some of the profs that taught courses you did well in, get them to help you with suggestions of courses, texts, papers. You will want one or more such profs to recommend you for the grad program you want. To do well, maybe write an honors paper.
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