Whenever a new Numberphile podcast drops, I get excited, download it and start listening in my car while navigating traffic. The Numberphile podcast actually makes a traffic jam a good thing as I get to listen to the entire episode before I get home.
Dear Brady I am relatively new to these videos, a middle-aged dad who studied maths at uni. These videos are a delight and an inspiration. Thanks also for lovely people you are interviewing! May much good come from them and your videos.
I'm inspired and so pleased to hear someone acknowledging the subcon/intuition side of what they do/work out/create connections. That articulation is gold. Thank you! 😁
A lot of his process he describes for doing research mathematics sounds strikingly similar to what I do in a creative field, especially the analogy of fumbling around in the dark for a long time looking for that inspiration light switch.
Hey Brady and numberphile! Saw an asshole on here telling you to stop posting these because they don’t like the notification. Just wanted to let you know I really appreciate that the podcasts are on RUclips. I get to watch them at work since RUclips isn’t blocked by the firewall. So thanks! Keep up the good work!
If you want to understand what it's like to know a math 'genius' and what they 'do all day', you must listen to this! (And if you want to see a genius interviewer at his best, listen to Brady's questions as well as the answers!!) Professor Maynard is a great man and a great thinker, humble, very articulate. It's so great to know that he's in the world!
Very interesting interview :) As a teacher I hope I have inspired some of my kids to get deeper into maths as well :) It is a lot about building up confidence and showing them, that this is a "thing" they could spend their lifes with....
Minor note on primes: suppose q is a prime > 3, then prime t multiples of q where t > 3 is a solution of |6n+1|. These multiples are predicted with a singular linear equation based on the n that generates q. Ie: 5 is generated by -1, the values of y=5x-1when x is an integer used as n in|6n+1| seem to all be prime multiples of 5.
I call primes 'The unlucky numbers". If you imagine numbers as walking creatures and their multiples as the stones where they step on, then you will see primes as unlucky numbers or special numbers if you like. Imagine a prime number with billions of digits. That number being prime means that no other number that comes before it puts a leg on it! And there are billions and billions and billions that come before it. So weird how much unluckiness there is.
I know this isn't a proof or anything, but it's why I believe the TPC. Imagine, if you will, a numberline. Start ticking the hole numbers off. You hit your first prime number with 2. Immediately, with no thought, you eliminate every second number. Now your number line has 1, 2 and every odd number. All of those numbers are two apart and some unknown number of them are twin-primes. Keep going, the next number you hit is 3 and now get rid of all the numbers evenly divisible by three. About half of them are already gone because we got rid of the even numbers greater than 2, but now we have 1, 2, 3 and all the odd numbers that can't be evenly divisible by 3. Because 3 is not evenly divisible by 2, there is still an infinate number of numbers that are two apart albeing a smaller number of them. Some are twin primes. Keep going. 5, 7, 11, 13, for as far as you can. This is an iterative process to get rid of composit numbers and leave only primes. At no point no matter how long you do this,, are all of the numbers 2 apart eliminated and because this is a system to get rid of composit numbers, sone of them will be twin primes. This is because anythign else would indiate a pattern with the number 2 and primes are what happens when you get rid of all the patterns. Anyway, that's why I believe it.
@@catprincess9 Because there would have to be some connection between 2 why there are no twin primes to get rid of all the pairs of odd numbers that are two apart.
This argument seems so strong, it even took me a few minutes to realize why this line of argument can’t just be directly turned in to a rigorous proof. To me, it seems that the only way this can’t be made rigorous is if primes “blocked off” twin primes faster than you can arrive at them. This argument, however, seems to be extremely strong intuition that can help show why mathematicians think this is so likely.
Idk but I'm having a desperate crush on this man, like, really, a crush. I'm even thinking of quickly finishing my MSc. and apply for a PhD in Britain so I can have a sliiiimmmmm chance of meeting him. God knows I've never crush on anyone this hard ;_;
Does the 246 bottle neck boil down to it being 2x3x41, and 41 being that special number where n^2 - n + 41 = P, where P is prime and n is any value from 0 through 40? That's got no gaps in it in some glaring way. And obviously in a similar way, 2 and 3 are the only consecutive primes
Every time I hear "2" being treated differently I start questioning why that is the case. Is it because in Base 10 we can easily identify the last digit of a really big number and decide if it is divisible by 2? We can do the same with 5 so why isn't it treated differently? And if we had a really easy means of determining divisibility by 7 would we also treat it as special? We have an easy one for 3 but we didn't choose special names for '1st third', '2nd third', and '3rd third' like we did for '1st half' = 'Odd' and '2nd half' = 'Even'. Just thinking out loud. No great revelation to be found here.
Well even numbers make up exactly half of all numbers, and numbers are even iff 2 is a factor, so it's automatically pretty important. It's also the smallest prime, so bound to lead to excepts just by sticking out (after all, there is no "largest"!). It will also be the most common factor in any number.
We have bilateral symmetry. We recognize bilateral symmetry as beautiful, and even musically tones that relate to each other 1:2 are recognized in our minds as being an octave apart. Likewise we intellectually recognize many binary pairings. Heaven/Earth, Day/Night, Sun/Moon, Order/Chaos. The origins of mathematics within the ancient world, numbers are viewed symbolically as well as mathematically, so the number 1 had supreme primacy, followed by two which is not only 2 as a number but the idea of duality and complementarity. 3, or the triad also has significance, but lacks that primacy of 2. Also, we use base 10 as the dominant number base. 3 does not divide nicely into 10. The Babylonians used base 60, they may have had a different relationship to 3 than we do. Now an interesting tangent from your question is if the understandings of numbers inherently so in the nature of things or we would understand reality vastly differently given a different biology; one with 6 fold or 8 fold symmetry. Would we use a different base number system, and thereby have different relationship to their numbers?
Joel Addie if you’re already quite strong at math (at least a strong calculus student) and don’t mind your math RUclips being a bit... “spicy” then flammable maths probably has the most interesting math problems explained well on RUclips
9 is not prime... 9 is not prime... 9 is not prime... 9 is not prime... 9 is not prime... 9 is not prime... 9 is not prime... oh good, they've switched to 11.
podcasts on RUclips are terrible idea, we cant even turn of the screen because on the phone ..either make video podcasts or use different platform: Acast is great for podcasts
@@numberphile2 Why isn't it on a separate channel though? Its very different content from bonus videos on Numberphile2 and I would really like to unsubscribe from podcast here
Congratulations for the Fields Medal!
I appreciate this being posted on the channel. The exposure this podcast gets on here is the only reason I came across this interview
Cheers!
Could you please put these podcasts on Stitcher too?
Keep doing podcasts, it's the format that is lacking in Mathematics.
Thank you Brady for this amazing podcast. It is a privilege to hear from James Maynard.
Whenever a new Numberphile podcast drops, I get excited, download it and start listening in my car while navigating traffic. The Numberphile podcast actually makes a traffic jam a good thing as I get to listen to the entire episode before I get home.
Dear Brady I am relatively new to these videos, a middle-aged dad who studied maths at uni. These videos are a delight and an inspiration. Thanks also for lovely people you are interviewing! May much good come from them and your videos.
I'm inspired and so pleased to hear someone acknowledging the subcon/intuition side of what they do/work out/create connections. That articulation is gold. Thank you! 😁
A lot of his process he describes for doing research mathematics sounds strikingly similar to what I do in a creative field, especially the analogy of fumbling around in the dark for a long time looking for that inspiration light switch.
And he's outstanding to learn from and listen to.
GREAT!!! Probably the greatest interview of a mathematician!!!
Hey Brady and numberphile! Saw an asshole on here telling you to stop posting these because they don’t like the notification. Just wanted to let you know I really appreciate that the podcasts are on RUclips. I get to watch them at work since RUclips isn’t blocked by the firewall. So thanks! Keep up the good work!
It's great that they are on here.
If you want to understand what it's like to know a math 'genius' and what they 'do all day', you must listen to this! (And if you want to see a genius interviewer at his best, listen to Brady's questions as well as the answers!!)
Professor Maynard is a great man and a great thinker, humble, very articulate. It's so great to know that he's in the world!
Today I learn that James Maynard will receive Fields Medal (year 2022), so I'm here to listen to him more.
Very interesting interview :) As a teacher I hope I have inspired some of my kids to get deeper into maths as well :) It is a lot about building up confidence and showing them, that this is a "thing" they could spend their lifes with....
Minor note on primes: suppose q is a prime > 3, then prime t multiples of q where t > 3 is a solution of |6n+1|. These multiples are predicted with a singular linear equation based on the n that generates q. Ie: 5 is generated by -1, the values of y=5x-1when x is an integer used as n in|6n+1| seem to all be prime multiples of 5.
I'm fascinated by what he means by the interaction between addition and multiplication. I've heard Holly Krieger use the same expression.
Very odd, walking, drinking water, short sporadic breaks, this resonates very very deeply..
I am wondering whether you are planning to interview with some young mathematicians like Peter Scholze... I think Scholze is an amazing figure
For the record, James is only a few months older than Peter. :)
Great podcast! He's such a likable and clearly knowledgeable guy
Thank you sooooo much brady for this interview !!!
Dr James Maynard won the fields medal this year
I call primes 'The unlucky numbers". If you imagine numbers as walking creatures and their multiples as the stones where they step on, then you will see primes as unlucky numbers or special numbers if you like. Imagine a prime number with billions of digits. That number being prime means that no other number that comes before it puts a leg on it! And there are billions and billions and billions that come before it. So weird how much unluckiness there is.
The story about the biology text book is awesome! :D
I know this isn't a proof or anything, but it's why I believe the TPC.
Imagine, if you will, a numberline. Start ticking the hole numbers off. You hit your first prime number with 2. Immediately, with no thought, you eliminate every second number. Now your number line has 1, 2 and every odd number. All of those numbers are two apart and some unknown number of them are twin-primes.
Keep going, the next number you hit is 3 and now get rid of all the numbers evenly divisible by three. About half of them are already gone because we got rid of the even numbers greater than 2, but now we have 1, 2, 3 and all the odd numbers that can't be evenly divisible by 3. Because 3 is not evenly divisible by 2, there is still an infinate number of numbers that are two apart albeing a smaller number of them. Some are twin primes.
Keep going. 5, 7, 11, 13, for as far as you can. This is an iterative process to get rid of composit numbers and leave only primes. At no point no matter how long you do this,, are all of the numbers 2 apart eliminated and because this is a system to get rid of composit numbers, sone of them will be twin primes. This is because anythign else would indiate a pattern with the number 2 and primes are what happens when you get rid of all the patterns.
Anyway, that's why I believe it.
What do you mean by :"This is because anything else would indicate a pattern with the number 2."?
@@catprincess9
Because there would have to be some connection between 2 why there are no twin primes to get rid of all the pairs of odd numbers that are two apart.
This argument seems so strong, it even took me a few minutes to realize why this line of argument can’t just be directly turned in to a rigorous proof. To me, it seems that the only way this can’t be made rigorous is if primes “blocked off” twin primes faster than you can arrive at them. This argument, however, seems to be extremely strong intuition that can help show why mathematicians think this is so likely.
Are there any special properties of non prime numbers adjacent to two twin primes?
apart from 4 it is always divisible by 6
When you add one to the number or subtract one to the number it’s always a prime (shocking, I know)
Idk but I'm having a desperate crush on this man, like, really, a crush. I'm even thinking of quickly finishing my MSc. and apply for a PhD in Britain so I can have a sliiiimmmmm chance of meeting him.
God knows I've never crush on anyone this hard ;_;
Does the 246 bottle neck boil down to it being 2x3x41, and 41 being that special number where n^2 - n + 41 = P, where P is prime and n is any value from 0 through 40? That's got no gaps in it in some glaring way. And obviously in a similar way, 2 and 3 are the only consecutive primes
Woo, I have the same favourite number as James Maynard!
This man knows his maths
Every time I hear "2" being treated differently I start questioning why that is the case. Is it because in Base 10 we can easily identify the last digit of a really big number and decide if it is divisible by 2? We can do the same with 5 so why isn't it treated differently? And if we had a really easy means of determining divisibility by 7 would we also treat it as special? We have an easy one for 3 but we didn't choose special names for '1st third', '2nd third', and '3rd third' like we did for '1st half' = 'Odd' and '2nd half' = 'Even'. Just thinking out loud. No great revelation to be found here.
Well even numbers make up exactly half of all numbers, and numbers are even iff 2 is a factor, so it's automatically pretty important. It's also the smallest prime, so bound to lead to excepts just by sticking out (after all, there is no "largest"!). It will also be the most common factor in any number.
We have bilateral symmetry. We recognize bilateral symmetry as beautiful, and even musically tones that relate to each other 1:2 are recognized in our minds as being an octave apart. Likewise we intellectually recognize many binary pairings. Heaven/Earth, Day/Night, Sun/Moon, Order/Chaos. The origins of mathematics within the ancient world, numbers are viewed symbolically as well as mathematically, so the number 1 had supreme primacy, followed by two which is not only 2 as a number but the idea of duality and complementarity. 3, or the triad also has significance, but lacks that primacy of 2. Also, we use base 10 as the dominant number base. 3 does not divide nicely into 10. The Babylonians used base 60, they may have had a different relationship to 3 than we do. Now an interesting tangent from your question is if the understandings of numbers inherently so in the nature of things or we would understand reality vastly differently given a different biology; one with 6 fold or 8 fold symmetry. Would we use a different base number system, and thereby have different relationship to their numbers?
How can i reach James Maynard. I wanna share my thoughts of prime numbers.
You can find him on the Oxford maths department, but I'm interested, what are your thoughts?
I think they are great.
Beautiful just beautiful
Regarding twin primes; can we say, "one and only one is the sum of 2 squares"
Can anybody suggest other channels as good as @numberphile2 ?
apart from @Numberphile (1)
Three blue one brown
Mathologer
Joel Addie if you’re already quite strong at math (at least a strong calculus student) and don’t mind your math RUclips being a bit... “spicy” then flammable maths probably has the most interesting math problems explained well on RUclips
9 is not prime... 9 is not prime... 9 is not prime... 9 is not prime... 9 is not prime... 9 is not prime... 9 is not prime... oh good, they've switched to 11.
👑
GG
Yay
This is the wrong James Maynard
TL;DR 2
trying hard to thing of a bad tool joke to make. His names and his interest in numbers man.. there's something there.
First
podcasts on RUclips are terrible idea, we cant even turn of the screen because on the phone ..either make video podcasts or use different platform: Acast is great for podcasts
The Numberphile podcast exists on podcast players. It is just put here on Numberphile2 as a bonus feature for people who don’t use a podcast player.
You can download it through any podcast app... (including Acast)
@@numberphile2 Why isn't it on a separate channel though? Its very different content from bonus videos on Numberphile2 and I would really like to unsubscribe from podcast here
@@numberphile2 Also thanks for letting me know its on acast, Ill go listen to it there :)
@@holeysh You could always not click the video. I like that it's here because I mostly use RUclips for podcasts.