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This seems to be a story of a kind that shows up regularly at HN. People who are smart in several ways but because they cannot do what some other (1 out of 100

This seems to be a story of a kind that shows up regularly at HN. People who are smart in several ways but because they cannot do what some other (1 out of 10000) people-with-or-without-children can, they don't feel smart and are a bit frustrated by it. Those others make a 'tutorial for creating a raytracer from scratch in a weekend', invent a format for a binary that runs as-is on several processor architectures, or are maintaining parts of the linux kernel. I easily recognize such stories, perhaps because that story might apply to myself as well. This unfulfillment treat applies to this post as well as the writer of the article (the writer indicated that before his 150 day submersion he felt a bit dumb at mathematics). The thing I want to bring across is now... we should not strive for such capability. There are many things to learn and ways to grow as a person, why beat ourselves up for not being very good at this or that particular thing?

nsxwolf 2y ago
Well, we let kids believe they’re just not good at math, and tell them that’s ok I’m sure you’re good at other things, and they believe it, and wish we’d stop doing that.
- nuancebydefault 2y ago
  While they are not studying maths, they can grow and improve themselves in other ways, not?
- dwaltrip 2y ago
  There’s a world of difference between that and beating yourself up for not being in the top 0.01% of performance.
  - MichaelZuo 2y ago
    To coast through a serious program (physics, engineering physics, pure math, etc…) at a major university while barely doing any work and also simultaneously getting high marks takes a lot more than 0.01% performance. More like 0.001%, at the very least, with some extra luck needed too.
- pxc 2y ago
  Worse still, we lead kids to believe that 'doing math' is performing computations. And so even many kids that can calculate passably grow up thinking that 'math' is boring and they hate it.
  - nuancebydefault 2y ago
    Pretty early after kids learn about numbers and computations, they learn about sets, units, lengths, surfaces, weights etc. Where i live, mathematical formulas are already thought to 7-8 year olds. Also real world questions are asked for which they need to find a solution, and where they need to explain how they found it. > grow up thinking that 'math' is boring How can it be thought in a less boring way, i do not immediately see it.
    - pxc 2y ago
      > real world questions are asked for which they need to find a solution, and where they need to explain how they found it. This could be fun if the questions are predictable enough, but typically in my own early education 'word problems' just ended up being computation problems with the single extra step of translating the question into one of a very small handful of known formulas. > mathematical formulas are already taught to 7-8 year olds That's great, but applying memorized formulas is still just computation. > How can it be thought in a less boring way, i do not immediately see it. Mathematics is the work mathematicians do. That work is fundamentally creative: it's about exploring, defining, and constructing abstract structures and conducted through writing. Mathematics as it's taught before college is typically presented almost exclusively as a mere instrument in service of engineering or the empirical sciences. This is like teaching physics purely as a parade of unexplained facts about past results and never giving students a chance to conduct experiments! There should be way less emphasis on the notion of a single track of linear progress from arithmetic to calculus. Formulas should be derived by students rather than just presented to them for memorization. Formal logic should be introduced about as early as arithmetic; first-order logic certainly isn't any more complicated than addition and multiplication. Teachers should prove the principles they expect students to rely on. Mathematical topics which do not require great facility with engineering computations (e.g., calculus, linear algebra, trigonometry), like propositional logic, discrete math, and basic geometry, should be used as opportunities to get students reading and writing proofs for themselves in multiple mathematical contexts as early as possible. The more students have a sense of the foundations of what they're learning, the more meaningful it can be to them. The more deeply they understand their formulae, the less memorization is required. And the sooner they engage with proofs, the sooner they have a chance to engage with mathematical as a creative and collaborative process.
- IOT_Apprentice 2y ago
  We have not acknowledged an approach that teaches the majority math properly. Find approaches that do and also have some problems that resonate to children in an age appropriate way set for their environment.
KronisLV 2y ago
> There are many things to learn and ways to grow as a person, why beat ourselves up for not being very good at this or that particular thing? I'd say that this takes a lot of work to unlearn, be it social media or whatever else seems to teach us to compare ourselves against others. Even though there are people way more brilliant than me out there (maybe they're naturally gifted, maybe they have a better work ethic, or different circumstances), it is definitely possible to be happy for their success, rather than lean into being jealous or what have you. Of course, they will often achieve more than I will and will lead better lives as a result of that, but that's also something to accept and take in stride, rather than for example believing that I'm some temporarily embarrassed soon-to-be millionaire who's one good idea away from a lavish lifestyle. Not that it should discourage me from being curious about new ideas, even if writing my own particle simulation quite quickly ran into the n-body problem and also the issues with floating point numbers when the particles get close and the forces between them great.
- MichaelZuo 2y ago
  What made you believe you were in the 99.999th percentile when going into university? (As opposed to something more realistic like the 99th percentile) Unless you were literally outsmarting your teachers every day at age 16, it seems difficult to successfully fool yourself in this way.
  - biotinker 2y ago
    There are a lot of things that one can be in the absolute top of, and overall academic achievement need not be one of them. Speaking personally, when these articles come out, there are always a lot of comments about "I didn't really try super hard in high school, but college was a huge wakeup call for me and I had to learn to learn." That wasn't me at all. I somewhat lazily skated through high school, and got a mix of 4s and 5s on AP exams. I did the exact same thing in college, with no change to my work/learning ethic, and lazily skated my way to finishing my 4-year molecular bio degree in 3 years, with a GPA of like 3.5 or so. Then I went to grad school, did more of the same for two years, and won an award for having the 2nd best masters thesis produced by the university that year. Then I got a great job in my field doing cancer research, did that for 5 years, then jumped careers entirely and now work in robotics. But you know what? I feel like I'm constantly surrounded by people smarter than me. I'm not some brilliant person, I'm just some dude that when presented with some problem, things just seem to make sense for a path forwards, and maybe my special thing is that I just always go explore that path and learn that either I was right or why I was wrong and that just pays dividends. When I see people around me who work hard at things, who study and memorize and read papers, they impress the heck out of me, because I really struggle to do the same thing. And when I do, I really struggle to absorb any information; if something doesn't make sense to me, it's like it just passes out of my head. I have to do/build/try it to make it make sense a lot of the time, or at least have things framed in a way that just intuitively makes sense for me. Anyway, my point is that maybe I was the top 99.99% of something, because, clearly I was/am pretty good at some things that apparently most "gifted" people struggle with. But I never got a 4.0, I never aced all my classes, and I never really cared to as long as I felt I was getting what I needed to out of the classes. I did the work I needed to do to gain the information and skills I felt I was there for, and as long as the number assigned to me by the professor for doing so was at least an 80, I was happy.
vasco 2y ago
The difference is that math is the only field of study of things that are 100% true about the universe. It's the most pure knowledge that humanity has, so it's normal people recognize it. You can read 100 philosophy books and maybe you will learn a few things that are correct among all the rambling, but everything you learn from the basics of math proof by proof all the way "up", you can be assured everything is true. There's something special about this field of knowledge that nothing else has.
- badpun 2y ago
  Math is not about the universe, it would be true even if the universe didn’t exist at all.
  - riwsky 2y ago
    It is, however, about turtles.
  - vasco 2y ago
    There must be a word for everything, so just replace with whatever you want instead, if universe triggers you.
    - badpun 2y ago
      ?
- tsurba 2y ago
  In a sense even this is not true, as in any sufficiently complex (which turns out to be quite simple) formal system you can create proofs that are true and untrue at the same time creating a contradiction. In other words, mathematics works by setting up useful axioms and following up on the logical consequences, but they usually can be used to create contradictory proofs even if useful in many problems. I recommend learning about Gödel’s incompleteness theorem behind it all. For a pop science book that explains it nicely I recommend ”I am a strange loop”. The wiki intro is also quite good https://en.m.wikipedia.org/wiki/G%C3%B6del%27s_incompleteness_theorems https://en.m.wikipedia.org/wiki/G%C3%B6del%27s_incompletenes...

nsxwolf 2y ago

Well, we let kids believe they’re just not good at math, and tell them that’s ok I’m sure you’re good at other things, and they believe it, and wish we’d stop doing that.

nuancebydefault 2y ago
While they are not studying maths, they can grow and improve themselves in other ways, not?
dwaltrip 2y ago
There’s a world of difference between that and beating yourself up for not being in the top 0.01% of performance.
- MichaelZuo 2y ago
  To coast through a serious program (physics, engineering physics, pure math, etc…) at a major university while barely doing any work and also simultaneously getting high marks takes a lot more than 0.01% performance. More like 0.001%, at the very least, with some extra luck needed too.
pxc 2y ago
Worse still, we lead kids to believe that 'doing math' is performing computations. And so even many kids that can calculate passably grow up thinking that 'math' is boring and they hate it.
- nuancebydefault 2y ago
  Pretty early after kids learn about numbers and computations, they learn about sets, units, lengths, surfaces, weights etc. Where i live, mathematical formulas are already thought to 7-8 year olds. Also real world questions are asked for which they need to find a solution, and where they need to explain how they found it. > grow up thinking that 'math' is boring How can it be thought in a less boring way, i do not immediately see it.
  - pxc 2y ago
    > real world questions are asked for which they need to find a solution, and where they need to explain how they found it. This could be fun if the questions are predictable enough, but typically in my own early education 'word problems' just ended up being computation problems with the single extra step of translating the question into one of a very small handful of known formulas. > mathematical formulas are already taught to 7-8 year olds That's great, but applying memorized formulas is still just computation. > How can it be thought in a less boring way, i do not immediately see it. Mathematics is the work mathematicians do. That work is fundamentally creative: it's about exploring, defining, and constructing abstract structures and conducted through writing. Mathematics as it's taught before college is typically presented almost exclusively as a mere instrument in service of engineering or the empirical sciences. This is like teaching physics purely as a parade of unexplained facts about past results and never giving students a chance to conduct experiments! There should be way less emphasis on the notion of a single track of linear progress from arithmetic to calculus. Formulas should be derived by students rather than just presented to them for memorization. Formal logic should be introduced about as early as arithmetic; first-order logic certainly isn't any more complicated than addition and multiplication. Teachers should prove the principles they expect students to rely on. Mathematical topics which do not require great facility with engineering computations (e.g., calculus, linear algebra, trigonometry), like propositional logic, discrete math, and basic geometry, should be used as opportunities to get students reading and writing proofs for themselves in multiple mathematical contexts as early as possible. The more students have a sense of the foundations of what they're learning, the more meaningful it can be to them. The more deeply they understand their formulae, the less memorization is required. And the sooner they engage with proofs, the sooner they have a chance to engage with mathematical as a creative and collaborative process.
IOT_Apprentice 2y ago
We have not acknowledged an approach that teaches the majority math properly. Find approaches that do and also have some problems that resonate to children in an age appropriate way set for their environment.

KronisLV 2y ago

> There are many things to learn and ways to grow as a person, why beat ourselves up for not being very good at this or that particular thing? I'd say that this takes a lot of work to unlearn, be it social media or whatever else seems to teach us to compare ourselves against others. Even though there are people way more brilliant than me out there (maybe they're naturally gifted, maybe they have a better work ethic, or different circumstances), it is definitely possible to be happy for their success, rather than lean into being jealous or what have you. Of course, they will often achieve more than I will and will lead better lives as a result of that, but that's also something to accept and take in stride, rather than for example believing that I'm some temporarily embarrassed soon-to-be millionaire who's one good idea away from a lavish lifestyle. Not that it should discourage me from being curious about new ideas, even if writing my own particle simulation quite quickly ran into the n-body problem and also the issues with floating point numbers when the particles get close and the forces between them great.

MichaelZuo 2y ago
What made you believe you were in the 99.999th percentile when going into university? (As opposed to something more realistic like the 99th percentile) Unless you were literally outsmarting your teachers every day at age 16, it seems difficult to successfully fool yourself in this way.
- biotinker 2y ago
  There are a lot of things that one can be in the absolute top of, and overall academic achievement need not be one of them. Speaking personally, when these articles come out, there are always a lot of comments about "I didn't really try super hard in high school, but college was a huge wakeup call for me and I had to learn to learn." That wasn't me at all. I somewhat lazily skated through high school, and got a mix of 4s and 5s on AP exams. I did the exact same thing in college, with no change to my work/learning ethic, and lazily skated my way to finishing my 4-year molecular bio degree in 3 years, with a GPA of like 3.5 or so. Then I went to grad school, did more of the same for two years, and won an award for having the 2nd best masters thesis produced by the university that year. Then I got a great job in my field doing cancer research, did that for 5 years, then jumped careers entirely and now work in robotics. But you know what? I feel like I'm constantly surrounded by people smarter than me. I'm not some brilliant person, I'm just some dude that when presented with some problem, things just seem to make sense for a path forwards, and maybe my special thing is that I just always go explore that path and learn that either I was right or why I was wrong and that just pays dividends. When I see people around me who work hard at things, who study and memorize and read papers, they impress the heck out of me, because I really struggle to do the same thing. And when I do, I really struggle to absorb any information; if something doesn't make sense to me, it's like it just passes out of my head. I have to do/build/try it to make it make sense a lot of the time, or at least have things framed in a way that just intuitively makes sense for me. Anyway, my point is that maybe I was the top 99.99% of something, because, clearly I was/am pretty good at some things that apparently most "gifted" people struggle with. But I never got a 4.0, I never aced all my classes, and I never really cared to as long as I felt I was getting what I needed to out of the classes. I did the work I needed to do to gain the information and skills I felt I was there for, and as long as the number assigned to me by the professor for doing so was at least an 80, I was happy.

vasco 2y ago

The difference is that math is the only field of study of things that are 100% true about the universe. It's the most pure knowledge that humanity has, so it's normal people recognize it. You can read 100 philosophy books and maybe you will learn a few things that are correct among all the rambling, but everything you learn from the basics of math proof by proof all the way "up", you can be assured everything is true. There's something special about this field of knowledge that nothing else has.

badpun 2y ago
Math is not about the universe, it would be true even if the universe didn’t exist at all.
- riwsky 2y ago
  It is, however, about turtles.
- vasco 2y ago
  There must be a word for everything, so just replace with whatever you want instead, if universe triggers you.
  - badpun 2y ago
    ?
tsurba 2y ago
In a sense even this is not true, as in any sufficiently complex (which turns out to be quite simple) formal system you can create proofs that are true and untrue at the same time creating a contradiction. In other words, mathematics works by setting up useful axioms and following up on the logical consequences, but they usually can be used to create contradictory proofs even if useful in many problems. I recommend learning about Gödel’s incompleteness theorem behind it all. For a pop science book that explains it nicely I recommend ”I am a strange loop”. The wiki intro is also quite good https://en.m.wikipedia.org/wiki/G%C3%B6del%27s_incompleteness_theorems https://en.m.wikipedia.org/wiki/G%C3%B6del%27s_incompletenes...