I am not sure why anyone would mistaken this achievement for genius. Not to say this student isn't a genius because I don't know him or her. For all I know maybe this student has built a perpetual motion machine but getting into an Ivy league and/or scoring well on the USAMO doesn't indicate anything other than a talented math student which is not uncommon unlike genius which is uncommon. If these were interchangeable, every year MIT would dot the landscape with geniuses which obviously doesn't happen and has never happened. Students attending Stanford or the other top schools are no brighter than their peers of yesteryear who also attended these schools (and one could very well argue quite a bit less bright overall though they may be more of a standout in one particular area). This means brighter than average but most do not have the type of genus that make one an Einstein. If they did, then Einstein wouldn't have been Einstein. Look at Stanford or Harvard or even MIT. The students that attend seem highly compliant as can be seen by the uptake of the covid-19 vaccines. Do they really foster or even desire genius? Seems from what I see that they highly discourage it. Noam Chomsky said it best when he talked about the goal of the US education system (which I am paraphrasing) - they want people bright enough and obedient enough to do the work but not so bright that they ask questions. This seems to describe the typical college grad but most especially the ones from Ivy leagues:
The difference between the top students now vs those in the past? The jobs themselves rather than the intelligence of the student. There are many highly technical fields out there than ever before which require far more math literacy to earn the same position in society that one earned in the past without such math knowledge. It is akin to many athletic fields. Compare the top figure skaters of the 60's to the top today and they're not in the same ballpark but that is because the ones today spend far more time and energy but there is also so much known about the techniques and how to teach them compared to the past. The best back then would probably not be able to compete with the worst in the class today. That doesn't elevate all new figure skaters to another class compared to their brethren such as genius. Also, the amount of time and energy they spend to improve their skating means far less time on all other matters which may make them a super-specialist when it comes to skating but they may not be very well equipped to handle other matters of life which is often the complaint some who work in these schools have of the incoming students who may have some talent but are often immature compared with former graduates. Many are not even able to cope with differing opinions. Genius can't be measured on a test or a score board and it seems to require thinking outside the box which is not a trait these schools have any interest in cultivating.
I'm really fascinated by your posts on education, and how much they contrast with the view of the 'IQ determinists'. Do you have a sense of the relative contribution of heritable factors vs environmental factors (including parenting and educational setting) to children's capacity for intellectual development? My kids attended a Montessori school for the first several years of their formal education, and I was fascinated by the 'origin story' of the Montessori method i.e. kids who were considered 'mentally deficient' were able to blitz entrance exams when taught by the methods Maria Montessori developed.
Have you ever hear of the Institute for the Achievement of Human Potential? The founder, Glen Doman, wrote Teach Your Baby to Read in 1962, and went on to identify the "genius" capabilities of all children, when impediments to learning were removed and thirst for knowledge was met by parents. What a child's brain can perceive before it is "vaccinated into antigens sin" by our rote classes is amazing, numeracy included. IAHP still operates today, 49 weeks a year teaching parents to restore the full function of brain-injured children, and 3 weeks with "normal children, whose parents have a home schooling web worldwide" I was lucky enough to attend, and it helped my kids tremendously.
The annoying requirement is that A is not allowed to have leading zeros, right? If this is dropped, the problem becomes symmetric and is just about drawing a black ball (last digit of A) from the ubiquitous urn, which contains one black ball (last digit of B), and six balls that might be white or black with probability 1/2.
It must be so gratifying to receive such correspondence. It’s certainly heartening to see critical thinking still exists in some small way. However, it’s incredibly disheartening to know that this student chose to attend an institution that mandates the jab! I guess cognitive dissonance usurps critical thinking once again.
A good question that resounds down the millennia. Sadly there are few with your depth of ability and motivation to teach and inspire by example. This is why it remains a mystery. Not just in math. But in all fields of endeavor.
Whether you know it or not you are also informing and inspiring us who follow your substack. For me I have wondered for over 50 years why basic health (mental, emotional and physical) that can only come from taking care of the Earth is also far from common knowledge.
If we look at the movies and tv dramas we find that the emphasis is on strength, cunning and manipulation, rather than nurture, loving kindness or compassion and wisdom. There are few people in the public eye that model those qualities. Instead we are given President Biden as a model.
I have had but one mathematics mentor. But I have been abundantly cared for with those wise and compassionate people that modeled those qualities in the way they engaged me. I am not easy, but I have been touched by that depth of caring. That caring changed me over time. I have a long way to go.
Mathew - you are still teaching lots of students. your subject is now life or death, not some math contest.
Brilliant. I hope he isn’t disappointed by Stanford. It’s turned out to be the wokeist university administration in the country.
I am not sure why anyone would mistaken this achievement for genius. Not to say this student isn't a genius because I don't know him or her. For all I know maybe this student has built a perpetual motion machine but getting into an Ivy league and/or scoring well on the USAMO doesn't indicate anything other than a talented math student which is not uncommon unlike genius which is uncommon. If these were interchangeable, every year MIT would dot the landscape with geniuses which obviously doesn't happen and has never happened. Students attending Stanford or the other top schools are no brighter than their peers of yesteryear who also attended these schools (and one could very well argue quite a bit less bright overall though they may be more of a standout in one particular area). This means brighter than average but most do not have the type of genus that make one an Einstein. If they did, then Einstein wouldn't have been Einstein. Look at Stanford or Harvard or even MIT. The students that attend seem highly compliant as can be seen by the uptake of the covid-19 vaccines. Do they really foster or even desire genius? Seems from what I see that they highly discourage it. Noam Chomsky said it best when he talked about the goal of the US education system (which I am paraphrasing) - they want people bright enough and obedient enough to do the work but not so bright that they ask questions. This seems to describe the typical college grad but most especially the ones from Ivy leagues:
https://www.youtube.com/watch?v=tgXZuGIMuwQ
The difference between the top students now vs those in the past? The jobs themselves rather than the intelligence of the student. There are many highly technical fields out there than ever before which require far more math literacy to earn the same position in society that one earned in the past without such math knowledge. It is akin to many athletic fields. Compare the top figure skaters of the 60's to the top today and they're not in the same ballpark but that is because the ones today spend far more time and energy but there is also so much known about the techniques and how to teach them compared to the past. The best back then would probably not be able to compete with the worst in the class today. That doesn't elevate all new figure skaters to another class compared to their brethren such as genius. Also, the amount of time and energy they spend to improve their skating means far less time on all other matters which may make them a super-specialist when it comes to skating but they may not be very well equipped to handle other matters of life which is often the complaint some who work in these schools have of the incoming students who may have some talent but are often immature compared with former graduates. Many are not even able to cope with differing opinions. Genius can't be measured on a test or a score board and it seems to require thinking outside the box which is not a trait these schools have any interest in cultivating.
Inspiring, Mathew! Thanks!
I'm really fascinated by your posts on education, and how much they contrast with the view of the 'IQ determinists'. Do you have a sense of the relative contribution of heritable factors vs environmental factors (including parenting and educational setting) to children's capacity for intellectual development? My kids attended a Montessori school for the first several years of their formal education, and I was fascinated by the 'origin story' of the Montessori method i.e. kids who were considered 'mentally deficient' were able to blitz entrance exams when taught by the methods Maria Montessori developed.
How is he dealing with Stanford's "vaccine" mandate (see https://docs.google.com/spreadsheets/d/11BrDadiUGN-vQBe7Jolcb_-aWhLT7S2AkWOkSX49M40/edit#gid=532284473), which includes a booster?
Have you ever hear of the Institute for the Achievement of Human Potential? The founder, Glen Doman, wrote Teach Your Baby to Read in 1962, and went on to identify the "genius" capabilities of all children, when impediments to learning were removed and thirst for knowledge was met by parents. What a child's brain can perceive before it is "vaccinated into antigens sin" by our rote classes is amazing, numeracy included. IAHP still operates today, 49 weeks a year teaching parents to restore the full function of brain-injured children, and 3 weeks with "normal children, whose parents have a home schooling web worldwide" I was lucky enough to attend, and it helped my kids tremendously.
The annoying requirement is that A is not allowed to have leading zeros, right? If this is dropped, the problem becomes symmetric and is just about drawing a black ball (last digit of A) from the ubiquitous urn, which contains one black ball (last digit of B), and six balls that might be white or black with probability 1/2.
1/7 + 6/7 * 1/2 = 4/7.
This is why human connection eye to eye will save the world.
Everytime you write on this topic you open the world to the idea that more is possible.
Would really encourage you to again consider teaching math to a larger group. Even if you place it on YouTube. Fantastic approach you have there.
Stanford and critical thinking are sadly incompatible
It must be so gratifying to receive such correspondence. It’s certainly heartening to see critical thinking still exists in some small way. However, it’s incredibly disheartening to know that this student chose to attend an institution that mandates the jab! I guess cognitive dissonance usurps critical thinking once again.
> "Why doesn't everybody know this is possible?"
A good question that resounds down the millennia. Sadly there are few with your depth of ability and motivation to teach and inspire by example. This is why it remains a mystery. Not just in math. But in all fields of endeavor.
Whether you know it or not you are also informing and inspiring us who follow your substack. For me I have wondered for over 50 years why basic health (mental, emotional and physical) that can only come from taking care of the Earth is also far from common knowledge.
If we look at the movies and tv dramas we find that the emphasis is on strength, cunning and manipulation, rather than nurture, loving kindness or compassion and wisdom. There are few people in the public eye that model those qualities. Instead we are given President Biden as a model.
I have had but one mathematics mentor. But I have been abundantly cared for with those wise and compassionate people that modeled those qualities in the way they engaged me. I am not easy, but I have been touched by that depth of caring. That caring changed me over time. I have a long way to go.
Keep up the inspired work you do!