This is nice initiative and any attempt to make mathematics more accessible is a value added to society in my book. However, saying you will learn "mathematical thinking" by watching 1.5 hours of passively watching, even Professor Tao, is quite an overpromise. I don't think there's a subject that requires more hands on practice and thinking than math, especially higher level math, so this is more along the lines of edutainment. So in my mind, how valuable this course is depends on what this content replaces for you. If watching this series replaces something distracting then its great, but if it replaces actually doing problems and working out proofs, then it's not worth it.
Finally there's a celebrity aspect to Masterclass that's a bit strange. Like these guys are famous, and because they're famous, they are the most worthy to teach you something.
Some series you should check out that are free and IMO provide much better value for time:
Academy of Achievement: https://achievement.org/
* Some good lessons with Eric Lander, Larry Page, Sergey Brin, Bill Gates, Jeff Bezos and Demis Hassabis
I fully agree on the celebrity worship, but am a bit confused with how you then align
> Finally there's a celebrity aspect to Masterclass that's a bit strange. Like these guys are famous, and because they're famous, they are the most worthy to teach you something.
with the recommendation
> Academy of Achievement: https://achievement.org/ * Some good lessons with Eric Lander, Larry Page, Sergey Brin, Bill Gates, Jeff Bezos and Demis Hassabis
You're right, that is somewhat contradictory. On the other hand those interviews don't profess to teach you a skill, but more of an outlook on life that led to success.
The 3B1B videos on 1) the Fourier transform, and 2) the determinant
were eye-opening for me to understand what all the math actually meant physically, 20 years after learning about that stuff in a book. Sometimes it really does take explaining it from a different angle.
on the other hand, i took a general relativity class solely because Prof Penrose was teaching it, did none of the homeworks, and still walked away having learned a lot from the many comments Penrose made that conveyed a big picture understanding; an experience of illumination that so many maths classes fail to provide. and unlike the famous business people you cite, Prof Tao has done a lot of actual maths.
I've taken a course by Dr. Keith Devlin (professor at Standford) through coursera: _Introduction to Mathematical Thinking_, which I found quite interesting. However, I studied medicine, so perhaps it may be too basic for someone who has studied mathematics in university.
Watching the trailer, makes me think that people who may enjoy this series will also enjoy a book called "Aha" by Martin Gardner (from probably 40 years ago)[0].
It has a lot of amusingly illustrated insight problems that show you how thinking about a problem differently simplifies getting to the answer a lot. It's probably aimed at advanced teenagers, but in fact the lessons there are some that even many adults probably have not come across before. I mean, I haven't watched the Masterclass, but I imagine Terrence Tao isn't teaching multimanifold group theory or something anyway, so this is the kind of insightful more daily-math problems he's helping people to understand how to think about.
[0] search your favorite, ahem, LIBrary GENeric source of books to find it.
Do you mean Aha! Insight? I don't see a book just labeled "Aha".
There is another Gardner book, Aha! Gotcha, which has a different emphasis than what I think you're talking about, but is excellent. I loved it as a kid. Gotcha is more about mathematical paradoxes and intuition-breaking concepts. Hotel Infinity, "who shaves the barber who does not shave himself?", the 'unexpected tiger', Zeno's paradox is included I think..., the difference between average and median, Newcomb's problem, etc...
Actually both books, but I was particularly thinking first of the "Aha Insight!" book, which has like 100 different problems where some clever thinking/turning around the problem statement helps to solve it.
The other one ("Aha Gotcha"), you are right is more about paradoxes that arise when applying logic that seems to lead to contradictory outcomes. But it also has a lot of "change the way of thinking" answers.
My first reaction to this blog post was kind of negative because Master Class is not free. I watched the teaser video and it's actually pretty inspiring. As someone who has done undergraduate Computer Science level Math, but completely forgotten most things about Math except for simple Algebra, I am going to try this.
The cost is €16/month which is cheaper than Netflix. I just cancelled my Spotify recently so this is affordable for me right now.
EDIT: The problem I see with Master Class as a subcription service is... if you watch Master classes on everything you are getting a broad education rather than a deep dive. I guess it's more for entertainment though.
In case anyone missed the response to a similar comment on the blog:
> Terence Tao on 27 January, 2022 at 10:31 am
The production values of the lecture series given by Masterclass would not be possible for me to replicate by myself. (For instance, the film shoot alone involved well over a dozen people, including makeup, prop design, camera and lighting crew, director, editing, etc., in a custom studio with professional-quality recording equipment. The professional scriptwriting services were also very valuable, improving the selection and arrangement of material in ways I would not have thought of.)
Plenty of Youtube teachers put out good quality stuff without access to any of that. People would listen to Terrence Tao using a cheap ass webcam and drawing on screen using a Wacom tablet. It's a justification for something that doesn't add value for learning mathematical thinking. To me it sounds more like he gets paid a passive income and a lump sum to make infotainment.
I think the gratuitous cynicism toward the mathematician is uncalled for. Terence Tao has devoted a lot of time writing educational articles on his blog. [1] If he mainly cares for passive income, he could divert a bit of time to hire a production company and film a few courses. He would own 100% of the contents and make millions simply out of his global name recognition.
Going with Masterclass is probably the path of least resistance for him to create high-quality video content while continuing to spend most time on research and other educational activities.
Another possible factor: Many good mathematicians are quite perfectionistic and would not want to create homemade-quality videos if they can avoid it.
> He would own 100% of the contents and make millions simply out of his global name recognition.
I think you overestimate how commercially viable actual teaching is as opposed to infotainment. Either way, infotainment allows him to earn money and talk about a subject he loves. Good for him and people love infotainment, it tickles their brains just enough but not too much to require actual thinking.
There are large groups of people who do care about their own’s and their kids’ mathematical education — some in North America and other continents and a huge number in Asia.
“Teaching pays: Cha said he earned $8m last year. “I’m madly in love with maths,” he said, looking the height of trendiness in his crimson shirt and trousers and tweed jacket, in his office in Gangnam – a wealthy part of Seoul famous for its conspicuous consumption and featured in the song Gangnam Style.”
> Plenty of Youtube teachers put out good quality stuff without access to any of that. People would listen to Terrence Tao using a cheap ass webcam and drawing on screen using a Wacom tablet. It's a justification for something that doesn't add value for learning mathematical thinking. To me it sounds more like he gets paid a passive income and a lump sum to make infotainment.
That's possible. It's also possible that Terrance Tao is correct in his judgement that using Masterclass was worth it for him. Personally I'd give him the benefit of the doubt that he's not lying.
Well he knows what he's capable of and knows what the crew is capable of. I think it makes more sense to assume he know what he's talking about rather than not. I mean he might literally never have done this without Masterclass at all.
Sure, if you're a full time youtuber already with years of experience knowing how to script, film, light, edit, do post production, etc. etc. etc.
A lot of these youtubers who put out fantastic videos do essentially all the same things as the Masterclass production crew, but just on a smaller scale. Countless hours are poured into producing these youtube videos that are maybe just as short as 10 minutes.
And even if Terrance Tao wants to make some infotainment, what's wrong with that?
> To me it sounds more like he gets paid a passive income and a lump sum to make infotainment.
Whether or not something's infotainment and whether or not it could be done more cheaply are orthogonal. There's no reason for him to make this on Youtube, any more than there's a reason for plumbers to do plumbing for nothing in their spare time.
I didn't claim they were related.
The justification for the cost of MasterClass was that they have a huge crew that produces these professional looking video's. Which is probably true, but I think the value added is not big enough to justify the cost. There's no reason to make it on Youtube because he doesn't make money that way, I agree. We don't live forever after all. I mainly see it as a way for him to make some extra money and there is nothing wrong with that.
I don't think you understand the pressure he is under. Being a mathematician is not a joke, they project a fear-aura and can never tell a lie. It's the closest you can come to finding aliens on the planet.
I'm a mathematician who joined Masterclass to improve my cooking. I look forward to checking out the class by Terence Tao, as a diversion.
I held off joining for the longest time because I didn't want twenty hours of each person telling me "You can do this!" The cooks such as Thomas Keller simply aren't capable of staying in affirmation mode that long (think of their kitchens!) and they do get down to business. I learned a lot, even as an experienced cook.
(Math meets Keller: I still don't believe they use a 10% brine in the restaurant. I think he's confused as to what they do.)
I think of it like "listen to an expert in X talk about why they love X" instead of "learn the basics of X". It's sort of more like an interview than a lecture.
I wish people would avoid suffixing porn to give a negative connotation to anything they disagree with. As a non-native English speaker, I truly hate the way some Americans butcher the language.
True. They had this cooking classes from some Michelin 3-star restaurant chef. Apart from some slick flourishes these are not usually about learning some practical skills.
We've had Masterclass for a bit over a year now. It's not deep, for sure, not going to replace any kind of study or exercise.
However, the production value is not only visually high, it is generally well done so I find myself watching something I might otherwise not be interested in. It's not like TED talks, which I often find too showy, too heavy on the presentation.
I think Masterclass is a good platform for this kind of thing: get experts to introduce people to watch something they otherwise wouldn't.
Same for me, I also appreciated that he responded to the question on his blog of why it is paid - production value / editing / professional equipment etc... it makes sense.
I had a similar negative knee jerk reaction upon learning that Yo-Yo Ma gives one of the courses from MasterClass. The whole MasterClass business seems like entertainment as you've noted. Music could be entertainment but there's some deep subjects just like mathematics. One cannot just sit back and gain deep understanding.
On that note, I wonder if anyone has suggestions for paid video content that is good? That is, "non fiction" or educational stuff like this series is supposed to be. I feel like I spend too much time watching YouTube (mostly free) and Netflix (very cheap, quality varies).
This is a vague question but I'm interested in all kinds of suggestions... including meta suggestions to recommendation sites. I sometimes look at various subreddits like /r/netflix but I don't find much there.
CuriosityStream [0] has non-fiction documentaries on a broad range of subjects that can be educational, and is relatively cheaper than similar services. I have been a subscriber for a few years, and it's easy to default to it over YouTube, when you feel you're watching too much of YouTube and not really getting much in return.
I've also heard good things about The Great Courses Plus [1], but have not tried them out yet.
And there look for non-US universities or the older courses by US universities (when MOOCs were still a thing idealists did). For US universities providing such online courses are now either part of marketing or an attempt to sell overpriced masters. For the European state-run universities they instead mostly deliver good content but without the rip off. They lack slick design and editing but they usually make up for it with substance. For example look at TU Delft for the absolutely best aeronautics and engineering courses.
Which actually adds value to Masterclass because really what kind of an education could one get from Netflix?
I’ve thought for years that netflix could/should really do something interesting with education. I’d love some high quality lectures and courses from them. Like actually legit ones.
I've never seriously considered subscribing to Masterclass, but this has gotten the gears turning in my head a little. So I'm curious: does anyone here subscribe, and could you comment on whether or not you feel like it's worthwhile, given the available content?
I subscribe, but will probably be ending my sub at the end of this year.
It's a mixed bag, but more positive than the phrase implies. The great ones are great, even if they are just infotainment, but there are some deeper ones as well. At the very least it's a great way to sample different creative fields and find out more about them.
My two main observations are:
1. There's a reason most of them say "So-and-so teaching <vague phrase>". You're not going to learn scales from any musicians, how to make jokes from any comedians, or how to write good from any writers. The craft part is up to you; they'll teach concepts, ideas, abstractions, etc relevant to their field, and ways to apply that craft effectively.
2. They all have elements of "Strong educational content" (EDU) and "infotainment / autobiography / motivational speaking" (TAIN), but some of them swing much harder in one direction than the other.
---
Here's some hand-wavy opinions of the ones I've watched. (Obviously the TAIN value will be higher if you're already interested in that person) -
- Aaron Sorkin teaches Screenwriting (Strong EDU and TAIN)
- Tom Morello teaches Electric Guitar (Strong EDU and TAIN)
- Tony Hawk teaches Skateboarding (Strong EDU and TAIN)
- Daniel Negreanu teaches Poker (Strong EDU and TAIN)
- Niki Nakayama teaches Modern Japanese Cooking (Strong EDU, Medium TAIN)
- Bob Iger teaches Business Strategy and Leadership (Read his book)
- Dan Brown teaches Writing Thrillers (Strong EDU, Medium TAIN)
- Hans Zimmer teaches Film Scoring (Medium EDU, Strong TAIN)
- Neil Gaiman teaches the Art of Storytelling (Medium EDU, Strong TAIN)
- St Vincent teaches Creativity (Medium EDU, Strong TAIN)
- Danny Elfman teaches Music for Film (Medium EDU and TAIN)
- Itzhak Perlman teaches Violin (Medium EDU and TAIN)
- Steve Martin teaches Comedy (Read his book)
- Billy Collins teaches Poetry (Medium EDU, Low TAIN)
- Herbie Hancock teaches Jazz (Low EDU, Medium TAIN)
- Yo-Yo Ma teaches Music and Connection (Low EDU, Medium TAIN)
Cinematography is a hobby of mine and I got gifted the "Ron Howard teaches Directing" Masterclass a few years back. I did not check the other Masterclasses, although I've considered watching a few others.
I've really enjoyed it but as it's already been said it's a lot better to approach the class as an extended interview and reflections from a world-class practitioner about their craft and career. Directing was an especially relevant discipline for the Masterclass formula as it is a mix of hard and soft skills, and there are a lot of resources for the hard skills, especially at an indie level. Ron Howard instead focused more on the soft skills and I gained something from it, especially as some of it is just plain old project management that I could also apply at my (engineering) work.
There was also a long, uncut practical session where Howard directed a scene on a set with an entire team of actors and crew, and I found it really interesting to watch them all work together like I was a fly on the wall.
So if you view Masterclass as a way to pick the brain of a celebrity practitioner you genuinely admire, I think it is 100% worthwhile. If you're instead looking for a regular tutorial about a discipline without having any interest in the instructor themselves, I'm less sure.
It's totally worthwhile, but it depends on your interests.
I originally subbed, for all things, to see Penn & Teller teach the basics of magic. I've since moved on to learning about cooking and how movies are made from the best in the business.
I also enjoyed the book. A very nice addition of the course are some mock negotiations that I think really help illustrate many of the points. I would recommend at least you watch those, the rest is true that are mostly highlights (I watched them anyway, it was a nice refresher).
I just watched the first 8 out of 12 episodes and I was disappointed. There were certainly a couple good nuggets but I'm afraid that Masterclass puts too much emphasis on making things simple such that he spends most of the time talking about really simple ideas.
Have you seen the EdX course Effective Thinking Through Mathematics (free) [0]? I really enjoyed it and found the principles really do transfer beyond the domain of math, as the title suggests.
The production values are nowhere near what you get with Masterclass (thus, why it's free) but the content can't be beat.
Tao said that they assumed no math knowledge, not even high school math. So .. um, absolutely no. It's probably a nice story/narrative involving a famous mathematician.
It's probably a nice watch, but not for the math value :)
Basically the math equivalent of all those quantum-blackhole-stringtheory videos from the last ~20 years.
Looks good. It reminds me of The Great Courses and its streaming service Wondrium [1]. They have (from the top of my head [1]) at least two courses that would be the equivalent to this one.
The courses are taught by experts in a field who also happen to be great teachers (usually teaching award winning professors).
I would like to second this recommendation. For a long time I thought their content was low quality edutainment because of the generally 90s website design and the generic stock photos used for courses(admittedly, that's...a pretty shallow line of reasoning). The courses are usually taught by university professors, have a well thought out lesson plan and have helpful accompanying guidebooks (you can also request course transcripts, I believe). For example, the course linked above is taught by Paul Zeitz based on his book, "The Art and Craft of Problem Solving", which is a classic for learning Olympiad-level problem solving techniques. I've also learned a lot from their history courses.
partially agree, but I also think that it is in many cases worthwhile entertainment compared to many other entertainment options available.
but also I think that understanding paradigms and thought processes outside your usual comfort zone is education, albeit not the formal one. And this is what Masterclass does great imho.
Try not to take this as me being mean, but I can't help but feel that for profit math education grands very hard against the basic concepts of math and math education("No royal road to math" and all that). I understand that someone of Tao's stature in the popular math community is likely very enticing to masterclass. However Tao himself benefited tremendously from being noticed at a young age and having his skills nurtured. It feels a bit wrong for any one in his position to be aiding a for profit institution, especially when the content is not free. I understand that they approached him, and I and everyone haven't to produce a free good quality version of this. But it does still FEEL wrong. I of course say this as a very privileged elite educated person.
EDIT: in the comments Prithvi has some interesting suggestions for doing a patreon at a higher level to be released freely. If possible and that eventually exists support that,
1. Masterclass is $20/month. The "masses" can absolutely afford it. It's not really a barrier for entry.
2. There's tons of free lecture content already. Khan Academy is a great example and it'll actually dive deeper than a short episodes.
3. If you're an American, $20/month is laughable for an education. Getting a post-secondary education is like getting a mortgage.
4. Why do we have to knock on highly produced commercial edutainment? It is not a threat to any other form of education by any stretch. At least someone watching this may get inspired or motivated to keep learning more Math.
> 1. Masterclass is $20/month. The "masses" can absolutely afford it. It's not really a barrier for entry.
Agree with your other points, but disagree on this - there are plenty of people who can't afford this kind of subscription (e.g. most materially poor countries in the world, which make up billions of people).
probably helps also to have a 1 in 100 million IQ too, but sounds like fun anyway. I am not sure how some of thee masterclasses are useful. Like the one by the astronaut . I don't plan on going into space anytime soon. Maybe Elon Musk would enjoy that one. No amount of videos will make even a typical PhD in math even as close to as good as him. It's 90% genes , 10% other factors.
Is it really common opinion that TT is smart because of his genes? I would think having a helpful and engaged math-fluent father and lots of encouragement from an early age has way more to do with it. You can't seriously believe that an introduction into mathematical thinking from an early age and close advision from math-fluent parents is only 10% of the reason that TT is where he is today.
> Tao exhibited extraordinary mathematical abilities from an early age, attending university-level mathematics courses at the age of 9. He is one of only two children in the history of the Johns Hopkins' Study of Exceptional Talent program to have achieved a score of 700 or greater on the SAT math section while just eight years old; Tao scored a 760
I think genetics have more to do with this level of achievement than encouragement from an engaged father. Tao has 2 brothers - why aren't they mathematical supergeniuses too? Either he was born with a brain that has extraordinary analytical ability, or he was born with an insane work ethic not commonly associated with young kids. But even then, are there reports of him having to work super hard to understand things? If you can do advanced algebra at age 5, I'd say your brain is something extraordinary. Whether the underlying reason for that extraordinary brain is due to genes or some other trigger, it likely was not mainly due to an "encouraging father", IMO.
Regarding his brothers, imagine if IQ is like a bunch of switches. TT was born with all his switches flipped 'on' out of some maximum. His brothers were born with most of them flipped on, as were his parents. Having high IQ parents increases the odds of more switches being flipped on, but having all of them flipped is still innate.
You can't (your germ line mutations are fixed, and even if you could change your genes in place your brain has already developed according to the previous genetic code and environment). You can only choose where to direct the output of your already flipped switches.
People on Reddit are taking pills to try and do that. Sometimes you hear about them getting aggressive cancers. Other times you hear about them semi-successfully treating damage they did to their brains with past drug use. Randomized controlled trials never show anything, but if you're being held back from being a genius by one protein that you got a bad gene for, you'd be one of the positive testimonials without showing up above the noise in a trial. Who knows.
Ask again in 2122.
In the meantime, I guess, we all need to learn that our worth as a person is determined by who we are, not what we are.
Very impressive no doubt, and again, they are brothers, so genetics plays a part. But their achievements aren't even close.
His (younger) brother, Nigel achieved two bronze medals (placing 132nd and 114th overall) at the age of 15 and 16 [0]. Quite good, specially at a younger age than most participants.
Terence [1] got a gold medal (13th place) right before completing 13 years of age. He achieved a similar feat (28th place) around his 12th birthday and a more humble performance (87th place, but still better than his brother's best) around his 11th birthday. At 11, better than 58% of his competition, some of the best 17 and 18 year olds at competitive math in the world.
He is cited as "the youngest bronze, silver, and gold medalist, respectively, in IMO history." [2]
If I were to guess, his brothers and parents pushed him, and had more experience with teaching compared to their older son. They got him interested, and he went from there.
He was probably lucky to be the younger brother growing up.
Oh, then I was completely wrong :D I would think the youngest kids are generally the more academically advanced. (But this is coming from someone who has 0 kids :D)
I don't think you understand the difference between being good at math and being at his level. Good parents can make the difference between being good at math or mediocre at math, but not knowing higher level concepts at the age of 15 or so . Or PhD at 22 or something. There are thousands of professors in the US even in math, how many produce super genius math kids with similar ability? Two 120-IQ parents a more more likely to produce a 110 IQ kids than someone with a 170+ IQ like TT; that is something else.
My favorite part is when he was asked, at age 8 minus epsilon, whether addition distributes over multiplication (after having established that multiplication distributing over addition is an example of a distributive law), and he said, "only for Boolean algebras."
(Disclosure: I was also a child prodigy, so much of this story resonated with me. I'm now a research software engineer at Google, working on lots of mathematically intensive topics in 2D graphics, but obviously nowhere nearly as accomplished as Prof Tao)
The entire Q&A is great. My favorite part is the snippet of his basic program for fibonacci computation.
300 print "mr. fibonacci is leaving now,"
310 print "and wishes to see you again sometime in the future"
312 print
313 print
315 print "here goes his car!!!!!!!!"
320 print "(brmmmm-brmmmm-putt-putt-vraow-chatter-chatter bye mr. fibonacci!)"
I don't think I come across as an alien. For example, I'm very deeply involved in my local Quaker meeting, and I don't think any of that is particularly different than others. That said, I can nerd out extremely deeply into a problem, to a point where I've noticed other people's eyes glaze over. Case in point, I've become interested in memory models for GPUs, and while most people in the field would be content to leave it there, I've actually dug into the Alloy code for the formalization of the Vulkan memory model (and found some issues along the way). I'd estimate there are probably less than two dozen other people in the world who have dug that deep, and, thinking about it now, I can see a pretty direct line to what child-prodigy-me would do in a similar situation.
Very cool. Thanks for the response. I may be reaching but maybe genius is a combination of curiosity, processing speed, mental RAM and focus. Maybe each of those can be improved in regular people...
As a human high in curiosity and processing speed but low in RAM and focus, my personal experience is that diet+prescription drugs can unlock the rest.
At least for me, this also comes with costs. Some of these costs are immediately observable to me (much lower levels of broad-insight / Gordian-Knot-slicing, and I am less patient with others). Other costs are only presumed…I have guesses about associated long-term health risks both direct and indirect.
Anyway, all this to say, I think it can be done artificially. Since these things take time to play out towards mastery, you better hope you can get it right. Just like in software, some things can be a Pareto improvement, but some things can be prematurely optimized, and some things really never needed to be built in the first place.
I hadn't thought of it but I see that I'm high RAM, high curiosity. Haha we should make a Meyers-Brigg for this.
I agree about inputs. I have a list project I'm working on called "This I Believe". I'm trying to decode my deeply held beliefs so that I understand mself and can change those beliefs. The very first thing I put on it was "Better living through chemistry."
> You can't seriously believe that an introduction into mathematical thinking from an early age and close advision from math-fluent parents is only 10% of the reason
Are you implying that if there isn't a mostly-genetic basis for his intelligence, the career success of his family members must be a complete coincidence?
He was a demonstrating adult level math ability even at the age of 5. Also, he was genius level at other subjects too. How would it not be genetic. Think of how hard parents push their kids in today's super-competitive economy and high-stakes higher ed system, how many turn out even close to as talented as him?
Not sure why you think the split is so tilted towards genetics. If TT had been born in some 3rd world country with poor nutrition and crappy education system, how would he be exposed to all the higher level math topics? It's clear you need that exposure, you aren't just going to know things about what mathematicians have thought about and consider important without coming into contact with some.
We have a sample size of 600 + million ppl between the US and Western Europe with full access to food, electricity, and other modern necessities, not third world countries. How many are as smart as him.
I'll accept that nobody is, but his mom was a math teacher. Few of us get that kind of leg up, certainly not 600m+. When I was 5, "don't get shot" was already getting a significant share of my brain's power, and I had it better than most. Sure, he's got a brain like gasoline, but don't discount the spark and oxygen that allowed the genius to deflagrate. And don't just throw numbers around like that if you don't have proof. If you respect the mathematics, act like it.
And how many of them were able to dust up a person who could explain to them not only how algebra works, but why one should study it? At the age where they can actually do it and not get bored?
Math education comes up here regularly, and we have lots of smart math people here, but the story is often that some commentator was simply never shown anything interesting in their whole schooling. I'd never have given it much thought were it not for one particular math teacher who put a lot of effort into me and a few other interested kids. I still keep in touch with him.
If you’re asking about math talent as in child prodigies, then one can browse previous winners of the math Olympiad.
But I have a feeling his success as a professional mathematician involves the interaction of such math talent with hard work and good mathematical taste.
One can read his PhD qualifying exams to observe he was actually not an outlier amongst his peers in his early career.
So in other words, the answer to your parent's question is "No, you don't have any evidence."
You are providing questions as a substitute for actual evidence. Your questions are worthy of being asked, but they are still questions.
Basically a variant of "I cannot explain ... therefore it must be Y! How could it not be Y?"
Just because people don't have adequate explanations for nurture doesn't make it an automatic "genetics". All it means is that they don't have adequate explanations. This does not make your stance any stronger or more likely to be correct.
(Disclaimer: I can easily believe genetics is the answer. I won't, however, be sure of it).
Really? Do you have proof of this is result of extraordinary nurture. Because nurture would be far more easy to see/document and match against against other examples.
> Really? Do you have proof of this is result of extraordinary nurture.
> Just because people don't have adequate explanations for nurture doesn't make it an automatic "genetics". All it means is that they don't have adequate explanations.
Your question is the equivalent of "Since you cannot provide evidence, I must be right." This is a fallacy. The other party's lack of evidence does not strengthen your position.
> Think of how hard parents push their kids in today's super-competitive economy and high-stakes higher ed system, how many turn out even close to as talented as him?
Maybe they don't know how to do it. Maybe TT got lucky.
The genetic model for the occurrence of supreme levels of ability more accurately matches reality than an environmental model. We know that polygentic traits in a population follow a normal distribution[1], which entails a regression to the mean for traits in offspring[2]. This means the occurrence of extreme ability is a function of the ability of the parents. While being rare, it becomes more likely if the parents themselves have some extreme traits.
This dynamic matches what we see in the case of Terrence Tao and his brothers, the Polgar sisters, and other cases of savants/virtuosos that come to mind. Usually one child has extraordinary ability while their siblings are much less remarkable. If the environmental model were accurate, we should see many cases where families produce more than one extreme talent of equal skill. But we don't see that in practice.
Genes must have something to do with it. Take the case of Srinivasa Ramanujan
No formal training in math. Made insane contributions to mathematics including solving "unsolvable" problems.
> A child prodigy by age 11, he had exhausted the mathematical knowledge of two college students who were lodgers at his home. He was later lent a book written by S. L. Loney on advanced trigonometry.[18][19] He mastered this by the age of 13 while discovering sophisticated theorems on his own. By 14, he received merit certificates and academic awards that continued throughout his school career, and he assisted the school in the logistics of assigning its 1,200 students (each with differing needs) to its approximately 35 teachers.[14]: 27 He completed mathematical exams in half the allotted time, and showed a familiarity with geometry and infinite series. Ramanujan was shown how to solve cubic equations in 1902; he developed his own method to solve the quartic. In the following year, he tried to solve the quintic, not knowing that it could not be solved by radicals.
If there was a method of raising kids like this "scientifically" , I bet a good portion of the worlds GDP would be put into this field of research
I'm not sure why people feel so allergic to the idea of a genetic intelligence boost.
Our genes encode the layout of physical race tracks on which marbles of matter and information travel. Some people's bodies have a bunch of muscle tracks, so as they grow, their body benefits from the activity on those. They grow up to find it easier to gain muscle than other people.
For geniuses, I imagine that the brain is a perfectly laid out super highway. Any information that comes in gets to where it needs to go because there's signs and signals and traffic cops patrolling. If some piece of information can't find where to go, well, damned if we don't have a construction worker and a navigator jumping in the passenger seat with you to help out.
Ultimately, I think the brain is so plastic that each of us can one day decide to elect a new mayor to our body town. The new mayor can decide to tear up roads and fix potholes etc. Yeah, it would have been great if we had founded the town with a plan and hadn't had that college riot but here we are. Time to pave some roads.
> I'm not sure why people feel so allergic to the idea of a genetic intelligence boost.
Because it kinda puncture this feel good marketing bull that "you can be anything you want". It could also shut endless flowing money into extra-coaching classes outside normal schools which promise to "help child to reach their fullest potential".
That does make sense. I think the reality is somewhere in the middle. I personally plan on hiring professional tutors for my children when I have them. Hopefully they're born with a lot of moldable clay, but either way, there are additional evidence-based education methods to utilize that promote mastery.
The studies trying to find the link between genetics and IQ are flawed in that they don't have a way to handle the interactions between genes. Instead they are based on correlations.
If you will be good at baseball if you have A and B, OK with neither, but terrible with only one, those genes will be identified in most studies as having nothing to do with baseball, maybe even identified as harmful.
I can offer a concrete example. Autism is more often found in high-IQ families, but itself is associated with decreased IQ. That suggests one case where either A and B alone are harmful, having neither makes you fine (and unlikely to bear children with A or B), and having both makes you smart.
I am not sure if we want people to figure out how to make connections involving specific genes, because a lot of us benefit from living in a world where we can game LeetCode by working longer and harder in a way that's unrelated to what Google is looking for.
These are like world class atheletes, gifted and they put in the hard work to get to where they are today. That is what it takes to be one of these once in a decade type of mathematician.
Probably getting to his level is highly genetically dependent but that’s not what watching a Masterclass vid is about. Probably really interesting but I would likely forget to cancel and i am planning on living forever so I’d end up paying an infinite amount of money for this.
Finally there's a celebrity aspect to Masterclass that's a bit strange. Like these guys are famous, and because they're famous, they are the most worthy to teach you something.
Some series you should check out that are free and IMO provide much better value for time:
Academy of Achievement: https://achievement.org/ * Some good lessons with Eric Lander, Larry Page, Sergey Brin, Bill Gates, Jeff Bezos and Demis Hassabis
3B1B: https://www.3blue1brown.com/
Numberphile: https://www.youtube.com/channel/UCoxcjq-8xIDTYp3uz647V5A