parentshiftbook Chapter 28 The Gift of Genius
Chapter 28 The Gift of Genius
With great effort, Kayla controlled her expression and said, "Li Ang, what you just said involves relatively obscure knowledge in algebraic geometry, some of which even touch upon areas typically only encountered by philosophy PhDs. So-called mathematical tools, such as ring theory in algebraic geometry, do indeed have methods that can help you quickly get closer to the right direction."
"Professor Nolan, could you explain in more detail?" Li Ang asked humbly.
Kayla nodded, spread out a sheet of draft paper, and began to scribble on it with her slender fingers, holding a pen. "Here, your understanding of Schur complement is still stuck on a matrix defined by a formula, which is a static algebraic perspective. Li Ang, have you ever thought about how S changes when matrix A changes? If we consider the Schur complement operation as a mapping, what kind of geometric properties does it have?"
What is the change in S when A has a small perturbation δA?
"Good. Let's consider the simplest scenario and study the set of n-order symmetric positive definite matrices..."
The two were chatting away, and judging by the setting and their appearances alone, no one would guess that they were discussing profound algebraic geometry.
Li Ang felt he had gained a great deal.
His mathematical knowledge is increasing at a rate two or even three times faster than he usually does when he reads books.
After discussing the extensions of Gaussian elimination for block matrices, Kayla Nolan and Li Ang exchanged views on the content of today's exam.
"Teacher..." Nicole whispered, "Didn't you just say you were going to have a meeting? It's almost time."
Kayla glanced at the time and continued, "No rush, it's only a little past eleven, there's still plenty of time."
After thinking for a moment, Kayla turned to Nicole and said, "Nicole, could you use the landline in front of us to call the FDA and tell them I'll be late? They can just say what they need to say and don't need to wait for me."
"Yes, teacher."
……
Time ticked by, and after Nicole finished her call and had a quick cup of coffee, Kayla came out from the inner room.
She quickly put down her cup and stepped forward to ask, "Teacher?"
Kayla glanced outside and gestured for them to go outside to talk. The two pushed open the clinic door and went to the side of Maxwell Street.
"So, teacher, Li Ang is going to study at the University of Chicago, right?"
After a moment of silence, Kayla shook her head and said, "No, Leon said he would consider it."
"Consider it? What's there to consider! I understand, teacher. Didn't you apply for a tuition waiver for Li Ang? With his exceptional mathematical talent, he wouldn't have to pay tuition if he went to the University of Chicago, right?"
"Nicole, your aunt can tell you like Li Ang... Don't rush to disagree, I think Li Ang is good too. But I want to say, for someone as smart as Li Ang, you shouldn't try to make decisions for him. Whether he goes to the University of Chicago or not should be his own decision. Most importantly, when it comes to money, he should rely on his own efforts."
"Teacher... Li Ang is working very hard to earn money, but you know that university tuition, living expenses, and book fees are not a small amount. I believe that as long as the money problem can be solved, Li Ang will definitely go to university without hesitation. Then, you can directly take him as your student, and wouldn't it be a good thing if he gets good results?"
Kayla shook her head, glancing back in the direction of the Danube Clinic. "Li Ang has an exceptional talent for mathematics; even outside of university, he has a chance to succeed. Anyway, there's no need to rush this; let's wait and see. I have other things to do, so I'll be going now."
"Teacher..." Nicole watched as Kayla got into the Cadillac and disappeared from sight.
……
After finishing his day at the clinic, Li Ang went home as usual.
After several days of intensive study and morning discussions, Li Ang's math subject experience has reached 183 points.
If I study normally, I should be able to level up 2 levels and complete the system task by the morning after tomorrow.
Li Ang was very concerned about his 0.3 intelligence attribute.
Thinking about math-related tasks, Li Ang couldn't help but recall his conversation with Kayla Nolan.
"Professor Nolan, do you mean that the example I just mentioned is related to the theoretical research in abstract mathematics?"
"Of course. In mathematics, many profound research advances stem from such concrete geometric observations, and the example you provided is precisely what mathematical research needs. I think we can collaborate on a short paper as a direction for your future research."
"Unfortunately, I haven't fully grasped many of the points you mentioned here."
"It's alright, otherwise what would be the point of having me as a professor? With the mathematical intuition and exploratory spirit you've shown, you're more than capable of doing mathematical research. You can take your time to learn the more advanced mathematical foundations, but this insight into abstracting universal laws from concrete examples is a gift unique to mathematical geniuses."
It's hard to imagine.
Professor Nolan, who is usually so aloof and serious in front of Nicole, can be surprisingly charming when he compliments someone.
Li Ang admitted that he was indeed tempted at the time.
If Keira Nolan had tried a little harder...
In fact, Professor Nolan pressed his advantage, saying, "Li Ang, if you'd like, I can guide you step-by-step through the necessary knowledge. You don't need to take the SAT; you can come directly to the University of Chicago's mathematics department."
After some thought, Li Ang still did not agree directly.
The main issue is that he hasn't fully determined the pros and cons of going to university.
There are many benefits to going to college. He can systematically learn cultural knowledge, enjoy the advanced resources of the University of Chicago, meet outstanding alumni, and even enter the upper circles of America.
However, there are also many downsides. Many courses that he is not interested in will inevitably distract him and waste his time.
To put it bluntly, subjects not available in the academic system and not used in the Aiolia magic model are not worth wasting a single moment of Li Ang's time on.
Besides that, there are various university fees.
Unlike American University in 1960, where tuition averaged a few hundred dollars a year, the University of Chicago, as a private research university, had a total annual cost of up to $3000.
Including expensive textbooks and various other miscellaneous fees, many college students have to take on heavy loans in order to attend university, and there are even reports of people selling their blood to pay for tuition.
Of course, with the help of the old charlatan Martin Wood, or the promise to help him distribute drugs and make money, several thousand dollars may soon be no problem for Li Ang.
The various interests involved require careful consideration.
Anyway, as long as Keira Nolan is around, there will be opportunities.
Even if Kayla Nolan retracts this promise, Li Ang believes that with his rapid advancement to Level 2 in mathematics, he will be able to make a name for himself in the American mathematics community.
"Professor Nolan, I think I need to think about this carefully. I'll give you an answer in a couple of days, okay?"
"Oh, of course. If you've made up your mind, just have Nicole call me."
Thank you.