7 ms·

I think about this often. Having studied mathematics, it's a field where there is a huge range of talents, even at 18 (and younger). There are genuinely gifted

I think about this often. Having studied mathematics, it's a field where there is a huge range of talents, even at 18 (and younger). There are genuinely gifted people who stride ahead, but the sad reality is that even at top institutions most of the undergraduate cohort will be merely averagely clever people who have received great (often private) tuition. In a field where finding every genius really matters because of the difficulty of expanding the frontiers it's heartbreaking to realise most just never get the opportunity of good mathematical education in the first place.

wikfwikf 4y ago
I don't think this is the whole story. Of course, it is a tragedy when people who had undeniable raw talent are neglected or passed over and don't get to achieve as they might. It's also sad and disappointing when we observe structural injustices in our society. However, isn't it possible that giving great teaching resources to people who aren't already at the top level in terms of raw talent, allows them to succeed at a very high level? If so, it's not a zero sum game - the 'averagely clever people who have received great tuition' and who go on to succeed might be a sign of the education system working, not its failure. We might focus more on making sure a wider group of 'averagely clever people' get such good tuition, rather than on the finding and promotion of undiscovered geniuses. Two examples that I often think about in this context: firstly the Budapest school of mathematics in the early 20th century. A hugely disproportionate number of the world-class mathematicians from that era were directly taught by Fejer and/or part of his seminar and mentee group. (He stands out as a supervisor to a far greater extent than any mathematician stands out from the pack for his own achievements.) Is it possible that while one or two of this group might have been 'born geniuses', it also includes several who might otherwise have been second-rate, but who became world-class because of the influence both of Fejer and of their high-performing colleagues? Secondly, George Harrison of the Beatles. In the second half of the Beatles' recording career, he wrote some of their best-loved songs, several of which are regarded as absolute classics. Did the Beatles happen to contain three inherently gifted songwriters, by sheer coincidence? Or is it more likely that working for a decade alongside two extremely talented and successful songwriters nurtured and elevated Harrison far beyond what might otherwise have been expected?
- TheOtherHobbes 4y ago
  I think the Beatles included three inherently gifted songwriters by sheer coincidence. No doubt the apprenticeship helped, but Harrison was writing songs like Taxman and experimenting with Indian classical music on Love You Too in 1966.
  - jaapz 4y ago
    It's not either/or, it's both. They were gifted, but they also had the time, money and motivation to work on their skills and hone their craft. It's not by coincidence that in literally every community that talks about how to level up their skills, the first response is always "practice practice practice".
  - wikfwikf 4y ago
    By 1966 George Harrison had been in a group (with various names) with Lennon and McCartney for 8 years, their songwriting partnership had been actively writing songs for 5 or 6 years, they had written almost all the songs for 6 or 7 albums, several of which are regarded as among the best albums of all time.
- ebjaas_2022 4y ago
  > rather than on the finding and promotion of undiscovered geniuses. There's a catch in it as well, which is that you cannot really identify a genius up-front. A genius is, by definition, someone who thinks differently. A lot of people think differently. But the thing with the genius is that he thinks differently and correctly. The latter part won't be obvious until after the fact. When Alex Ferguson started out as a Manchester United manager he probably already was a genius, but it wasn't obvious until many years later. Same with Sergey Brin and Larry Page. They probably had a genius vision for the company right from the start. But it's only in retrospect that we recognize that it was, in fact, a genius vision. Finding a genius is, I think, almost by definition, impossible.
  - toyg 4y ago
    Alex Ferguson might have been a good football manager, but he wasn't a genius - and I say that as a Man United supporter. He didn't advance football in any significant way, and even towards the end of his career he was somewhat naive from a tactical perspective. He was just a good man-manager in what is a sea of managerial mediocrity - football management is largely restricted to ex-pro-footballers who can't do anything else. Rinus Michels was a genius, Arrigo Sacchi was a genius - they actually advanced the sport.
dublin 4y ago
Given that even our first-tier colleges and universities still have no real idea how to teach math in a way that ensures that students will internalize and understand it, this isn't surprising. I think one of the most curious things about the modern world is that centuries into working with higher math, we still do not have good ways to teach it. Most students with creative insights that could help advance the field tend to wind up one of two ways: (We need to create a viable, replicable third way - today it seems to require exceptional personalities for both student and teacher...) 1) They slog through the existing math education system, but it crushes their creativity and insight, leaving them mostly useless husks (this pit catches most mathemeticians, IMO), or, 2) They become disgusted by the incomprehensibility of higher mathematics and abandon the field entirely (this is a huge chasm of a pit, that prevents most all engineers and scientists from ever becoming more than moderately competent in mathematics and methods.)
rcarr 4y ago
This is the problem right here. The solution is that Maths teaching needs to be brought online Duolingo/Brilliant style (with in person teacher support obviously). We can completely standardise the curriculum and do A/B testing to find out what is the most efficient way to get the information into students’ heads. The data could be analysed further to see if there were certain mathematical learning styles (I suspect there are). One cohort of students might be better off on the visual/geometry heavy track, one might be better on the abstract track etc. It should be initiated at the national government level and mandated to use in schools but the actual building of the application should be contracted out to a company from Silicon Valley/Roundabout/$COUNTRY_TECH_HUB. Until this happens or something similar we’re just going to continue having this grossly unequal and unfair state of affairs where access to good mathematics education is complete geographical potluck for anyone whose parents can’t afford tuition. The amount of wasted potential is staggering.
psb 4y ago
I think you mean tutelage instead of tuition there (I could be wrong)

wikfwikf 4y ago

I don't think this is the whole story. Of course, it is a tragedy when people who had undeniable raw talent are neglected or passed over and don't get to achieve as they might. It's also sad and disappointing when we observe structural injustices in our society. However, isn't it possible that giving great teaching resources to people who aren't already at the top level in terms of raw talent, allows them to succeed at a very high level? If so, it's not a zero sum game - the 'averagely clever people who have received great tuition' and who go on to succeed might be a sign of the education system working, not its failure. We might focus more on making sure a wider group of 'averagely clever people' get such good tuition, rather than on the finding and promotion of undiscovered geniuses. Two examples that I often think about in this context: firstly the Budapest school of mathematics in the early 20th century. A hugely disproportionate number of the world-class mathematicians from that era were directly taught by Fejer and/or part of his seminar and mentee group. (He stands out as a supervisor to a far greater extent than any mathematician stands out from the pack for his own achievements.) Is it possible that while one or two of this group might have been 'born geniuses', it also includes several who might otherwise have been second-rate, but who became world-class because of the influence both of Fejer and of their high-performing colleagues? Secondly, George Harrison of the Beatles. In the second half of the Beatles' recording career, he wrote some of their best-loved songs, several of which are regarded as absolute classics. Did the Beatles happen to contain three inherently gifted songwriters, by sheer coincidence? Or is it more likely that working for a decade alongside two extremely talented and successful songwriters nurtured and elevated Harrison far beyond what might otherwise have been expected?

TheOtherHobbes 4y ago
I think the Beatles included three inherently gifted songwriters by sheer coincidence. No doubt the apprenticeship helped, but Harrison was writing songs like Taxman and experimenting with Indian classical music on Love You Too in 1966.
- jaapz 4y ago
  It's not either/or, it's both. They were gifted, but they also had the time, money and motivation to work on their skills and hone their craft. It's not by coincidence that in literally every community that talks about how to level up their skills, the first response is always "practice practice practice".
- wikfwikf 4y ago
  By 1966 George Harrison had been in a group (with various names) with Lennon and McCartney for 8 years, their songwriting partnership had been actively writing songs for 5 or 6 years, they had written almost all the songs for 6 or 7 albums, several of which are regarded as among the best albums of all time.
ebjaas_2022 4y ago
> rather than on the finding and promotion of undiscovered geniuses. There's a catch in it as well, which is that you cannot really identify a genius up-front. A genius is, by definition, someone who thinks differently. A lot of people think differently. But the thing with the genius is that he thinks differently and correctly. The latter part won't be obvious until after the fact. When Alex Ferguson started out as a Manchester United manager he probably already was a genius, but it wasn't obvious until many years later. Same with Sergey Brin and Larry Page. They probably had a genius vision for the company right from the start. But it's only in retrospect that we recognize that it was, in fact, a genius vision. Finding a genius is, I think, almost by definition, impossible.
- toyg 4y ago
  Alex Ferguson might have been a good football manager, but he wasn't a genius - and I say that as a Man United supporter. He didn't advance football in any significant way, and even towards the end of his career he was somewhat naive from a tactical perspective. He was just a good man-manager in what is a sea of managerial mediocrity - football management is largely restricted to ex-pro-footballers who can't do anything else. Rinus Michels was a genius, Arrigo Sacchi was a genius - they actually advanced the sport.

dublin 4y ago

Given that even our first-tier colleges and universities still have no real idea how to teach math in a way that ensures that students will internalize and understand it, this isn't surprising. I think one of the most curious things about the modern world is that centuries into working with higher math, we still do not have good ways to teach it. Most students with creative insights that could help advance the field tend to wind up one of two ways: (We need to create a viable, replicable third way - today it seems to require exceptional personalities for both student and teacher...) 1) They slog through the existing math education system, but it crushes their creativity and insight, leaving them mostly useless husks (this pit catches most mathemeticians, IMO), or, 2) They become disgusted by the incomprehensibility of higher mathematics and abandon the field entirely (this is a huge chasm of a pit, that prevents most all engineers and scientists from ever becoming more than moderately competent in mathematics and methods.)

rcarr 4y ago

This is the problem right here. The solution is that Maths teaching needs to be brought online Duolingo/Brilliant style (with in person teacher support obviously). We can completely standardise the curriculum and do A/B testing to find out what is the most efficient way to get the information into students’ heads. The data could be analysed further to see if there were certain mathematical learning styles (I suspect there are). One cohort of students might be better off on the visual/geometry heavy track, one might be better on the abstract track etc. It should be initiated at the national government level and mandated to use in schools but the actual building of the application should be contracted out to a company from Silicon Valley/Roundabout/$COUNTRY_TECH_HUB. Until this happens or something similar we’re just going to continue having this grossly unequal and unfair state of affairs where access to good mathematics education is complete geographical potluck for anyone whose parents can’t afford tuition. The amount of wasted potential is staggering.

psb 4y ago

I think you mean tutelage instead of tuition there (I could be wrong)