Here are the timestamps for this conversation. If you have questions for Dr. Berndt, please write them below. 0:00 - Introduction 0:39 - Mock Theta Functions 3:06 - Ramanujan's Big Leaps 5:08 - Ramanujan's Divinity 7:45 - Ramanujan's Early Life 14:16 - Ramanujan arrives in England 16:22 - How Berndt found Ramanujan 26:55 - Ramanujan's Home 30:24 - Ramanujan's Slate 36:04 - The Lost Notebook 48:43 - How Ramanujan found Berndt 54:48 - India's perspective of Ramanujan 56:30 - What would you ask Ramanujan? 1:02:58 - Ramanujan's obsession & pressures to be "well-rounded" 1:07:04 - We need new systems to allow people to follow their obsessions 1:10:00 - College Admissions & Ramanujan would not be accepted at UIUC 1:14:00 - Advice for young people 1:20:59 - Favorite UIUC Memories 1:28:00 - What would be the greatest mathematics discovery? 1:33:18 - Ramanujan and Complex Analysis 🚥Overrated or Underrated Section 🚥 1:35:28 - 🚕 1729 1:38:20 - 🏆 Millennium Prize Problems 1:39:02 - 👨🏫 Small Colleges 1:43:38 - 🏀 UIUC Basketball 1:44:40 - Closing Words
For the question on "how did ramanujan figure out properties, made auch great leaps", exactly how. This is a great question. My guess is, his mind being so nimble with numbers and so flexible with operations on this numbers, and visualizing these numbers and functions or feeling them in his gut, he could probably feel and sense certain functions or identities tending towards all the numbers of interest up to some very high number. He was right because usually if it works for a bunch of numbers, it works for all. This is where the rigor of proofs was necessary for him, because thats of course not always true by design... Im guessing, he felt the numbers, he felt the errors were low / arbitrary or there was no error between the numbers he was after and the identity or parts of that expression. Remember, all his work was with real numbers if im not mistaken - meaning he was dealing with numbers you can easily add , multiply and just simply count. If you had such enormous facility with these operations on numbers, you can juggle, split apart parts of these numbers, approximate them, etc. He is doing calculations of these numbers in a way that is visceral, connected in his mind and pattern specific. Probably some "apophenia" with numbers themselves, which comes from thinking through patterns until something probably harmonious "pops" our at you. These identities are simply waiting to be found, and he is always thinking and stumbled across ones that make sense. Almost in a synesthetic way probably. Im completely speculating, but i bet its how he "mechanistically" arrived at "such great leaps". They leapt out at him, as the numbers revealed all these patterns to him, because he knew them so intimately (can rearrange them, juggle them with no effort etc )
Certain minds simply have such beauty to them! This certainly seems possible and accurate as if he had a way of feelings what most don't feel when it comes to numbers, etc. A beautiful and unique mind, that's for sure.
Goddess Namagiri (consort of god Vishnu also named Laxmi, Saraswathi) taught him mathematical methods with which he proved partition function and taught him to use q-series, with which he proved many theorems. Recently modern mathematicians deduced string theorem.
![[กูเพิ่งซื้อมึงปิดหนี] 20 นาที ผมรีวิวเกมที่แย่ที่สุดในโลก CONCORD](http://i.ytimg.com/vi/XhC-3q3Ii7I/mqdefault.jpg)
Here are the timestamps for this conversation. If you have questions for Dr. Berndt, please write them below.
0:00 - Introduction
0:39 - Mock Theta Functions
3:06 - Ramanujan's Big Leaps
5:08 - Ramanujan's Divinity
7:45 - Ramanujan's Early Life
14:16 - Ramanujan arrives in England
16:22 - How Berndt found Ramanujan
26:55 - Ramanujan's Home
30:24 - Ramanujan's Slate
36:04 - The Lost Notebook
48:43 - How Ramanujan found Berndt
54:48 - India's perspective of Ramanujan
56:30 - What would you ask Ramanujan?
1:02:58 - Ramanujan's obsession & pressures to be "well-rounded"
1:07:04 - We need new systems to allow people to follow their obsessions
1:10:00 - College Admissions & Ramanujan would not be accepted at UIUC
1:14:00 - Advice for young people
1:20:59 - Favorite UIUC Memories
1:28:00 - What would be the greatest mathematics discovery?
1:33:18 - Ramanujan and Complex Analysis
🚥Overrated or Underrated Section 🚥
1:35:28 - 🚕 1729
1:38:20 - 🏆 Millennium Prize Problems
1:39:02 - 👨🏫 Small Colleges
1:43:38 - 🏀 UIUC Basketball
1:44:40 - Closing Words
For the question on "how did ramanujan figure out properties, made auch great leaps", exactly how. This is a great question.
My guess is, his mind being so nimble with numbers and so flexible with operations on this numbers, and visualizing these numbers and functions or feeling them in his gut, he could probably feel and sense certain functions or identities tending towards all the numbers of interest up to some very high number. He was right because usually if it works for a bunch of numbers, it works for all. This is where the rigor of proofs was necessary for him, because thats of course not always true by design... Im guessing, he felt the numbers, he felt the errors were low / arbitrary or there was no error between the numbers he was after and the identity or parts of that expression. Remember, all his work was with real numbers if im not mistaken - meaning he was dealing with numbers you can easily add , multiply and just simply count. If you had such enormous facility with these operations on numbers, you can juggle, split apart parts of these numbers, approximate them, etc. He is doing calculations of these numbers in a way that is visceral, connected in his mind and pattern specific. Probably some "apophenia" with numbers themselves, which comes from thinking through patterns until something probably harmonious "pops" our at you. These identities are simply waiting to be found, and he is always thinking and stumbled across ones that make sense. Almost in a synesthetic way probably. Im completely speculating, but i bet its how he "mechanistically" arrived at "such great leaps". They leapt out at him, as the numbers revealed all these patterns to him, because he knew them so intimately (can rearrange them, juggle them with no effort etc )
thank you for sharing such a thought-out comment! Enjoyed reading it!
Certain minds simply have such beauty to them! This certainly seems possible and accurate as if he had a way of feelings what most don't feel when it comes to numbers, etc. A beautiful and unique mind, that's for sure.
Great video. Dr Berndt has some really interesting stories
Hey Eron! What's up! How's your summer?
Goddess Namagiri (consort of god Vishnu also named Laxmi, Saraswathi) taught him mathematical methods with which he proved partition function and taught him to use q-series, with which he proved many theorems. Recently modern mathematicians deduced string theorem.
❤❤❤❤❤
The man was literally waiting for you to question him after his answers.
Dr. Berndt is a great person to talk to.