> His answer was that I may just not have the "mathematical maturity" for the material. I was so discouraged that I dropped out of the program.

There's a problem with making a statement like that and not following it up with what you need to do gain the needed "maturity". Even adding "maybe you should take this course over here and come back to this one in a semester..." could make a world of difference.

I think usually it boils down to teachers in advanced schools were the kind of pupils who got most things easily and have no clue how to explain things more than <list of set comprehension>. Got me to think that these universities are more magnets from strong ex-pupils to similar minded new pupils that will fit in without much pedagogical efforts.

The average IQ of math majors is absurdly high, more than two sigma above the mean[1]. In an organization like that the smartest person is likely going to be a breathtaking five sigma above the general population mean[2]. I get the impression that people in math departments like it that way, so weeding out persons of more ordinary intelligence is more of a feature than a bug. I doubt many would admit to that, but it fits the observables.

[1] https://chhaylinlim.wordpress.com/2014/09/24/average-iq-per-...

[2] Assuming gaussian distribution with no skew, which is probably a bad assumption, but I'm spitballing here. Suffice to say math departments at elite colleges have many extremely bright people.

I wouldn't say feature, but they're probably not naturally inclined toward spending more time raising the average level instead of enjoying the few genius newcomers.

There's a small sadness in this but I can't word it out perfectly.

ps: I mean I would understand very much that these people just want "new buddies to play hyperstimulating math games with no drag whatsoever" but from school I expect just a few pointers. The rest is on me (us).

edit:

IQ has no skew by definition. That said, I think there are a number of IQ boosting mutations and innate mathematical aptitude is likely correlated to possession of one or more of these rare(ish) mutations.

survival bias skews IQ in certain fields. taken to the extreme, you're essentially saying that the IQ of field's medalists are not skewed.

I misread the point they were trying to make, I took the 5 std to be a sign they were pulling from general population IQ. On second reading it’s clear that is not their intended point.

In any case the resulting intermediate distribution from selection criteria bias would be a Chi distribution (I think - it has been a while.) 5 standard deviations on a normal distribution is 175 IQ or top 1/700K which is insane.

A few additional biases, Physics majors have higher average IQs, and not everyone smart enough to do the math has the desire or the opportunity.

The point I was making is that IQ score has been normalized, when imagining the intermediate distribution of IQ it would make more sense to look at composite probabilities of factors that led to the IQ score and consider the probability that those same factors lead to a sufficient innate ability in math.

Does intermediate distribution here correspond to a Sampling distribution? If so I think you got it right.

Is it? I would indeed hypothesize that within the population of Fields medalists, IQ distribution is roughly normally distributed.

Are you arguing that it is actually skewed towards some cutoff point of "just smart enough to get the medal"?

Let's say every mathematician draws an IQ from the IQ distribution and a luck score from the luck distribution. Then, the highest sum of numbers wins a Fields medal.

That would be distributed according to the distribution of the maximum of N Gaussian-distributed random variables, and according to this[0] stack overflow answer, it's skewed downwards, below its mean. (Its mean, of course, is much higher than the mean IQ+Luck).

[0] https://math.stackexchange.com/questions/2105921/pdf-for-min...

> Let's say every mathematician draws an IQ from the IQ distribution and a luck score from the luck distribution.

That's a huge assumption. I could easily propose a half dozen other models each with a different conclusion. You would need to look at the data.

He just proves there exists models that gives a skewed distribution by providing an example. So having a skewed model is a possibility.

The more selection criteria depends on cut-off (which it is in the university setting), the more likely selection from normal distribution is going to be skewed. Then Fields medalists are selected from long tail of already skewed population, all bets are off.

>IQ has no skew by definition.

There isn't a skew per se but possible inflation that gp intended to account for. See Flynn Effect.

This is a really deep point. A math professor at The University of Chicago wisely pointed to me as this being a super important thing to keep in mind when teaching (I've gone into secondary education). Often the material you are and how well the student is receiving has a much smaller impact on the student than what the emotional experience of it communicates to them about their own capabilities, including their chance at continue to struggle through the material in the hopes of fully grasping it. Especially in the latter years in school, it seems you find a lot of teachers who almost revel in making their courses "impossible" for kids, which can sometimes be very motivational for extremely high-achievers but absolutely devastating to a well-intentioned student who is having a challenge with the material.

Another UChicago student here (former math major). I think the UChicago math department took education seriously in a unique way that I wish they got more credit for; the Inquiry-Based Learning classes, the summer classes for Chicago public school teachers, and the Research Experience for Undergraduates were all pretty special, I think.

Also, the math classes all had a shared policy of "you can work with anyone you like on a problem set, as long as everyone's name is listed on there when you hand it in." I loved that, and I did all my problem sets in groups while I was there, and I think I learned more because we were always explaining things to each other and arguing about solutions. I heard a rumor at one point that this policy was the direct product of Peter May's bad experience at Princeton, which required students to work alone when he was there.

TFA does seem like a pretty stinging indictment of Princeton's math department.

You think Mathematicians in general have people skills? Most Mathematicians i met were good people but they definitely kinda lived in their own world, they were super helpful, but only if you explicitly asked for their help.

Mathematicians in general maybe not, but teachers definitely should have people skills. At least those teaching introductory courses.

At places like Princeton, most people become professors because they are good at research.

The issue today, IMHO, is that every university is looking for professors who are "good at research" (meaning, they can win grants), and teaching is not even a secondary or tertiary thought (if a thought at all). The last four professors we hired in our STEM department could barely speak English (I am in the states), let alone get points across or create examples. You know what they can do well? Write grants that get awarded.

Research and teaching are both important, and a smart university tries to use its professors' talents most effectively.

I studied at the VU, where Andy Tanenbaum, writer of a ton of famous CS books teaches. Of course I followed his classes. His books are excellent, but his classes are basically him reciting his books from memory. The jokes are literally identical.

At some point, more and more of his classes would be taught by Maarten van Steen instead; he's an excellent teacher who really knows how to engage the students and make them think about problems, instead of merely telling them the answer.

There was another professor who, as far as I know, didn't do any research at all; he just taught a ton of classes.

A professor who is great at one thing is not necessarily good at something else.

Research professors who have 0 interest in teaching and farm out the actual teaching/grading to grad students has been going on for decades.

Perhaps, we should have a conversation about whether professors are indeed even teachers.

>a grad class called "Hard problems in combinatorial optimization".

I don't think that that is an introductory course.

People skills? The informal prereqs/expected background for a class should be listed in the syllabus. Lack of "mathematical maturity" is a non-answer, they should make it clear what sort of math knowledge that refers to.

I disagree. 'Mathematical maturity', to me, means: There is no specific advanced prerequisite knowledge, but you need to be able to follow something technical.

As an example: you'd reasonably expect a student with mathematical maturity to know what a set, the Cartesian product of two sets, and a function are. That's high school level math.

From there you can define a ring and a module over a ring, in like 5 mins.

So at that point the Prof, strictly speaking, told you everything you need to know to start studying modules.

Of course, many students will be like whaaaaaa?! When a ring is defined. But here's the point: Mathematical maturity does not mean that you already know what a ring is, but when the Prof defines a ring, you are following along.

Anyway, my point is that there is nothing specific that you need to know.

Mathematical maturity should be well defined if you are using it as a prerequisite. Mathematicians, of all people, should be good at coming up with such precise definitions.

It's not a precise definition (and I'm not sure how actionable it is) but it is a term of art. https://en.wikipedia.org/wiki/Mathematical_maturity

Some people are better with math than others. Undergrad math majors thought the major was pretty easy. Many of us in engineering majors--who weren't that bad at math (it was a good school)--could no more have graduated with a degree in math (or physics) than have flapped our arms and flown.

That is why they rarely list is as a prerequisite; and instead list specific classes that likely fostered it.

Any good definition of mathematical maturity would likely be so technical that you need mathematical maturity to understand it.

Isnt' that basic set theory as a prereq

It's abstract thinking and ability to work with new math constructs on the spot.

Maybe the class did have pre-req? I mean i think it is obvious that a class called "Hard problems in combinatorial optimization" is aimed more at future Mathematicians/Computer Scientists than people who want to take it for the fun of it.

Mathematical maturity is a soft skill. You can't point to a particular technical skill that provides it.

Most colleges have classes designed to foster mathatical maturity, but that is done by how the class is taught, not what is taught in it.

STEM in general I think struggles in this regard and can be mistaken for gatekeeping. Or it actually is gatekeeping, idk.

I felt this in Spain. In my little local university it seemed like they were gatekeepers. Some professors were hostile and treated you like if you were dumb.

It didn't help that I went to uni at 24 IIRC while I was working my ass off, so I wasn't that happy to put up with the BS.

It seems less like gatekeeping and more like "I'm struggling for my life to climb this mountain on my own, and I'm not strong enough to drag up your dead weight up behind me. I'll train you if you seem to have the aptitude and drive to eventually become a useful partner in my struggle, but I'm not going to waste my life energy on people who will never be anything more than dead weight."

Calling it gatekeeping seems like a fish complaining that the birds are gatekeeping the sky. The sky is open for anyone, but only if you have wings to fly.

The difference is the fish is not paying the birds in exchange for education.

And nobody checked if you could grow wings

> they were super helpful, but only if you explicitly asked for their help

It also usually helps if it's an interesting problem...

Maybe they should teach self esteem and resiliency in the face of criticism and failure, because you will definitely be criticized and you'll definitely fail. You will face setbacks and discouragement at many points in your life. More often than not, your biggest critic will be yourself. That much is certain.

This wasn't even really intentional discouragement, but it was perceived as such. Hopefully, you learned the higher lesson.

You can have plenty of self esteem and resiliency and also decide based on evidence that an activity may not be the best use of your time. If you respect a teacher's evaluation of your performance in a subject and the teacher's evaluation is that you don't have the maturity to learn from them, it may make much more sense to try other things than insist on forcing them to teach you anyways. People don't have to intend to say cruel things in order to be cruel-- for example, you don't have to intend to hurt someone who recently miscarried by talking about your successful pregnancy and its definitely not considered the fault of the person who is grieving. Similarly a professor doesn't have to intend to be discouraging in order to be discouraging.

I think we can reasonably argue that the statement is overdetermined. Charitably, perhaps the professor did mean mathematical maturity in the sense of "try learning some background first, and give yourself the time to let your skills and intuition develop." Uncharitably, perhaps the professor did not, and meant mathematical maturity in the sense of, "you have an inherent deficiency that makes this an inappropriate undertaking for you."

I think where the fruit of this discussion may be is deciding to what degree an authority figure like a professor has a responsibility or an obligation to their students and advisees to make themselves clear which way they intend their statements to be interpreted. Personally, this begets a discussion of the nuances between the obligations and responsibilities of communication between (1) strangers, (2) peers/colleagues, and (3) authority figures and their charges.

I think this happens a lot. For some reason people have a really strong tendency with math to attribute it to innate talent. Of course talent matters, but people get hung up on it and discount other factors. The word "maturity" is supposed to help indicate that it's a matter of having and digesting the right experiences, but it honestly isn't great, because maturity can be driven by experience, but it can also be dictated by biology. If someone is isolated from human contact between the ages of ten and twenty, they will emerge fully mature in some ways and immature in others. We need a less ambiguous way of saying that somebody hasn't yet had the exposure and practice that will prepare them to tackle certain material.

I wonder if the whole "weeding out" theory extends to college education in general, and like you ask, how constructive to society that is.

I, very briefly and quite honestly, attended a lower tier state school that was an absolute joke. Shortly after I started, there was an outreach program for local high school kids where if they showed a high school ID, they got admission for the upcoming year. The head of my dept dismissed it and quipped, "It's ok. Anyone that wasn't meant to be here will just drop out after a year anyway and we have their money."

I, thankfully, ended up at a much bigger P5, well-known university. One of the controversies was the engineering departments were trying to get as many students as possible to the point of exceeding infrastructure and admitting lower quality students into the program. Upperclassmen I talk to said, "that's why everyone hates <1st semester math for engineers> and <2nd semester math for engineers>. They immediately weed out those that don't qualify."

"Weeding out" is what college admissions should be doing, not the departments. When the departments weed someone out, they've wasted at least a year of their life and a year in tuition, and demoralized them.

This is what really the "college for everyone" mentality has led to. If the kid shouldn't be there, or should have started in junior college first, we need to be more upfront about that earlier.

I disagree with that. Even if someone fails all their classes in their first year the experience will teach them much more about life than any job would. The real problem is that US universities cost a lot of money so the cost of failure is insane.

>"Weeding out" is what college admissions should be doing, not the departments. When the departments weed someone out, they've wasted at least a year of their life and a year in tuition, and demoralized them.

Admissions can't weed people out, they can only copy the weeding that highschool has done. If you rephrases the question that way, as in, "should highschool teachers be responsible for college admissions," then the idea of letting people join a major they haven't proven themselves capable of doesn't sound so bad after all.

> [...] may just not have the "mathematical maturity" for the material.

LOTS of non-math-major science/engineering students face that problem as soon as they start grad school.

It's a consequence, IMHO, of math curriculums failing to focus on the fundamentals rigorously enough. There's too much focus on what we used to call "plug-n-chug" mathematics where students learn just enough to apply formulae to get their problems solved. It might seem like "just enough" but it ends up pushing out higher mathematics and keeps students from being able to apply more advanced mathematical concepts that they would have gained from a much deeper dive into Real Analysis, abstract algebra, differential geometry, etc, and the grind of the theorem-proof cycles. Many of us felt this right away upon taking graduate level courses.

I wish that I had been counseled to take additional math courses before (or even at the beginning) of grad school. It would have reduced my suffering A LOT and I would have gotten more out of the degree.

I thought I had it - lots of real analysis and abstract algebra proofs - but then in grad school I hit a 400 level numerical methods class that I simply lacked the mathematical sophistication for. Just completely at sea - an experience which I lacked the academic maturity to deal with.

I obviously don't know your specific situation, but often this is the result of idiotic cost cutting measures by universities.

As a lecturer, I've had several job interviews where half of the questions were some variety of "are you ok to put up with having way too many students and not enough time?". I had the luxury of not having to take these jobs, but obviously someone ended up taking them.

I thought about this a lot. In college I often failed and teacher would look at me dumbfounded (followed by the traditional "it's trivial"). Very discouraging indeed. Years later I revisit some things, and without struggling too much, I get insights and ideas and overall easier time actually solving things. So in the end it does look like some "maturity" was lacking. Now it's bothersome that schools can only operate on people with magic maturity and other people are left on the side (the school as semi-comb theory) and I wish we could have some pedagogical light on what is that missing maturity and how to grow it explicitely.

First day of college algebra. Teacher shouted out “75% of you will drop out. Please leave now”

4 hours a night 6 days of week and I got a C. Less the 25% made it to end. Don’t think many of remaining passed.

Got a lot out of it though.

That sounds like either an absolutely terrible teacher, or a terrible program. Why were so many people enrolled in a class that less than 25% would pass? I'm not American so I don't really understand the course names but I guess a class just called "Algebra" shouldn't be too hard? Stuff like basic groups/rings/fields or is it a more advanced class?

The title "College algebra" in the US indicates material that is well pre-groups/rings/etc.; it is about the basic skills of computations involving manipulation of variables, often involving such topics as solving linear and quadratic equations, and perhaps inequalities.

At least at my university, the reason that such classes have a high failure rate is that the university is incentivized to have high enrollment numbers by admitting students who do not have the background to succeed at college mathematics at the level of calculus or above, and so need some pre-calculus courses; but someone who does not have a solid grounding in pre-calculus mathematics will often struggle to learn it when it is taught at a rapid pace at the college level—especially by professors most of whose teaching experience is with college-level math.

My high school AP calc course started out somehow getting behind in the first week. After that, the teacher kept assigning homework for material we wouldn't even cover until the day it was already due to be turned in. It was pretty brutal for someone like me who was accustomed to coasting through all of my other courses.

I took a bit more math in college. It wasn't easier; the professor simply kept pace with the material. If you needed help, you had to go to a TA or the professor out of class hours (an option that wasn't really available for a high school setting).

I can easily imagine that many students who were exposed to college level math for the first time in one of those courses would flounder and drop out (though I didn't witness much of it myself).

But what incentivises the students to take a class that so many won't pass? I don't really understand the American university system but surely the sensible choice would be to take a course you're most likely to pass?

I guess its possible to learn stuff from a course you fail, but you should be able to find a course that you're likely to pass and learn something from?

It's mandatory for the degree, that's the motivation. It's typically required for all students who didn't score high enough on entrance exams or take enough math courses in high school. They also likely don't talk to their advisor and say, "I want to take something else, like prob/stat or calculus, to substitute for this requirement." STEM majors will find it easier to substitute another course than non-STEM majors (because they likely have the background to skip it from HS course work). Engineering universities and the like usually send their first year students straight to calculus, though.

It's a "weed out" class. When a huge number of people want to be STEM, but there is no way they're going to last, it's better to have a tough class that sets that expectation early, so they have time to pursue a more achievable major. In my case, huge State university, Freshman year Physics was the weed-out class. It was not advanced or (to me) particularly difficult, but there was a LOT of content, we moved very fast, and the workload was punishing. If I recall correctly, our first class was over 1000 people in a huge auditorium forum. By the time we took final exams, we were down to around 100 people.

So the 75%+ who don't pass this course don't graduate or what? They have to change degree?

I've never heard of so many failing a college algebra course, at my second university it was around 25% failing and mostly because they'd relaxed the entry requirements in order to increase enrollment.

However, for non-STEM and non-Business majors college algebra is rarely a prerequisite for any other courses so you can still continue your major without it, you do need to pass a math course before graduating though. They also have other math courses that can be used that aren't college algebra and may be easier.

At my university, CS was called math-CS, it required intenses calculus courses with a similar failure rate.

Of those who failed : ¼ retook the course, ¼ pivoted to the bussines-CS program (given by the CS department) , ¼ pivoted to bussines-IT (given by the business and management school) and as far as I know, the rest disappeared from the university.

> Stuff like basic groups/rings/fields or is it a more advanced class?

No, it's usually basics like functions, graphs, and trigonometry. It's basically a remedial class for what students didn't learn in highschool.

Maybe I'm massively out of touch but I'm pretty sure a good teacher could teach that stuff to almost anyone.

Like this stuff isn't particularly complicated, I'm not a very good teacher but I did teach some undergrad seminars during my PhD and I think even my worst students were capable of understanding functions, graphs and trig.

That's not the issue. College algebra courses are super compressed, they're basically trying to teach the whole of junior high + high school math in a single semester. That's barely teaching, and the natural outcome of such a cursorily taught course is to act as a 'weedout' course.

Yup. My observation (having not had to take College Algebra myself, but knowing people who did) is that it's a class to make sure people who fell off the math train back at operations on fractions or factoring or whatever, don't get any farther.

I was a tutor in business school on behalf of the MBA program. Basically, there was a small group of students who were... not prepared with respect to math. We're talking really simple algebra, maybe the simplest of differentiation (e.g. maxima of a simple quadratic function).

One of them told me one day "I don't understand graphs." I tried but it's impossible at that point to make up for an apparent total lack of at least high school level arithmetic/math.

I mean, what do you want them to do? Invest resources in splitting up material into multiple courses when they should have learned it before even coming to college? It's not their fault public schools suck.

State universities kind of do have this responsibility. My school is doing more or less this, restructuring some of the math sequences that have a high failure rate, like precalc/calc 1.

Also state universities are where most of the public school teachers and administrators trained, so they probably deserve a little of the blame for the state of public schools.

IMO the only stuff a student "should have learned" is stuff that they can't get onto the course without knowing. Allowing someone onto the course, for which "x" is a prerequisite, who doesn't know "x" is entirely the university's responsibility.

All public schools do not suck but especially urban schools can have a lot of problems and many of the students don't have a great home environment either,

You are in touch with your kind of people, the kind who graduate from university.

If you were doing a PhD you were at the kind of university that has a PhD programme. Probably it was one of the 200 or so US universities out of a thousand that are selective, rejecting more students than they accept. I doubt there was a single student in your seminar who wasn’t in the top 30% by academic aptitude of their age group.

> According to the U.S. Department of Education, 54% of adults in the United States have prose literacy below the 6th-grade level.

https://en.m.wikipedia.org/wiki/Literacy_in_the_United_State...

I would assume that class that is described as:

"4 hours a night 6 days of week and I got a C. Less the 25% made it to end. Don’t think many of remaining passed.

Got a lot out of it though."

Actually is abstract algebra and not highschool level. Nobody teaches remedial classes in such a way that only 25% make it to the end.

Hah that sounds exactly like my uni.

The old joke about sufficient "mathematical maturity" is "write a lowercase zeta".

> What I didn't realize at the time was the particular meaning of that term. His advice was well intended and accurate.

I had a similar experience - and while it was a blow to my confidence I’m happy that he didn’t tiptoe around it with feel-goodisms. What I was doing as a student, and what had ben successful so far, was not working and doing more of it or doing it harder wasn’t going to help.

Honestly leaving that program was the right thing to do, I probably shouldn’t have been in it, though I’m confident a few years later I would have been successful, but I lacked the maturity and mathematical sophistication to get it then.

Maybe they are interested only in future Ph.Ds and Professors. Anybody else is a burden to be sent somewhere else as soon as possible. Maybe they think they're doing a favor to those students because they won't be wasting their time on subjects that are too difficult for them to grasp in the short time of a university class.

> His answer was that I may just not have the "mathematical maturity" for the material.

What a clueless, absolute piece of shit..

Clearly he lacks the emotional maturity to deal with students (or just people in general) and unequivocally should be fired as a teacher and restricted to doing research.

Can you explain the particular meaning of that term for the rest of us?

The Wikipedia article on it is pretty good: https://en.wikipedia.org/wiki/Mathematical_maturity

> So much pain could have been avoided if we just extended the conversation by a few minutes, or he invited me for a discussion over coffee.

Or if you had the maturity to accept criticism like an adult.

I’m not sure that college students - or, to call them by their age group, teenagers - are really appropriately assumed to be “adults” at all times. Obviously we don’t think that when it comes to alcohol and partying - universities step in and make heavy-handed decisions we’d never apply to full adults all the time (example, shutting down a house & evicting residents for having a party where an assault happened). So why not apply that same “not yet fully mature adults” logic when it comes to something with massive social benefits, which society has in interest in promoting: more mathematically literate university graduates?

This is precisely what first year students are not.

How did you interpret “immature” as “not smart enough”? A baby is not mature, which doesn’t mean he won’t grow up. “Immaturity” means that there’s room for improvement and that that improvement is attainable.

What I mean to say is that this issue stems from your misunderstanding of the meaning of the word “mature” and nothing else.

Assuming OP was an undergrad, it’s totally fair to assume that the prof in question was trying to euphemistically say that they weren’t good enough for the class, especially since “mathematical maturity” is something of a term of art in the field. I don’t think it’s worth putting down teenagers for not understanding the nuances of every single bit of terminology in a field they’re dipping their toes into, the expectation should be that professors be more empathetic to that.

"mathematical maturity" would be a combination of "not smart enough" and "haven't studied enough". Highly talented people can reach high levels of maturity very quickly, people who are just a bit above average can reach a reasonable maturity through hard study, and below average talent means it is very unlikely that the person will be able to comprehend university level theoretical math.

A teacher who doesn't know you will not know if you're not smart enough or just didnt study hard enough, and probably doesn't care much, especially for an undergrad. For a phd student, they may care if they think they've identified a "diamond in the rough" that can be turned into a gem with some work, but that is quite a bit beyond basic linear algebra.

> “mathematical maturity” is something of a term of art in the field

Fascinating, it sounds like "MM" is tacit knowledge, which begs the question why it isn't explicitly taught.

In mathematics, mathematical maturity is an informal term often used to refer to the quality of having a general understanding and mastery of the way mathematicians operate and communicate. It pertains to a mixture of mathematical experience and insight that cannot be directly taught. Instead, it comes from repeated exposure to mathematical concepts. It is a gauge of mathematics students' erudition in mathematical structures and methods, and can overlap with other related concepts such as mathematical intuition and mathematical competence. The topic is occasionally also addressed in literature in its own right.

https://en.wikipedia.org/wiki/Mathematical_maturity

If you understand the basic English meaning of "maturity", the intended meaning of "mathematical maturity" should be perfectly clear.

It was a part-time masters program, 2nd semester IIRC.

It's been a long time, but IIRC I recognized that my understanding of the term was vague but that all interpretations boiled down to, if I wasn't ready now I never would be.

I'm not claiming that my response was entirely rational or measured. I'm not blaming the professor, and I'm not justifying my own reaction. I was just saying what my reaction was, in case it shows a pattern of student experiences that's worth addressing.

If you have reasonable people skills, you may well have correctly inferred what the lecturer was communicating: overly questioning the words can be damaging. As I have matured, I have learnt better to trust my intuitive reading of what someone says, especially when I detect that the meaning of their words is divergent from what I believe they think beneath the surface.

Stubbornness, tenacity and self-belief are useful skills for success - perhaps you gave up too quickly? Unfortunately, soft skills are very rarely taught well. We all rely upon our subconscious learning and a good amount of luck to gain necessary skills, and those skills are often learnt by osmosis while very young. I also think the meta-skill of being able to teach yourself soft skills is not common either and it - although we can make an effort to improve that meta-skill even though it is somewhat self-referential.

Oh hey a lack of empathy, do you teach at Princeton perhaps?