Understood
Shen Qi wrote on the blackboard a countable orthogonal set {e1, e2, e3} of Hilbert space H, followed by a Fourier expansion ∑εnen, which is an arbitrary vector such that εn≠0 for all n.
"There is a fascinating conclusion in set theory: there exists a set {Jt} with cardinality * whose elements are infinite subsets of the set of positive integers. Then, for every real number t, let Jt denote the set of infinite rational numbers whose unique cluster is t. For Hilbert space H, we can handle it as follows..."
Shen Qi wielded the chalk with great skill and grace, and the classroom fell silent.
"Please remember that the linear dimension of Hilbert space H is greater than or equal to its orthogonal dimension, an infinite-dimensional Hilbert space H has an orthogonal subset isomorphic to the set of integers, and an infinite-dimensional Hilbert space H is the infinite-dimensional space closest to an n-dimensional Euclidean space Rn. So, Heidi, are you satisfied with my answer? Ladies and gentlemen, what about you?" Shen Qi answered Heidi's question using language and formulas that everyone could understand.
"Professor Shen, I'm very satisfied. I have no further questions." Heidi understood.
"I see." Everyone understood.
"Do you really understand?" Shen Qi asked casually.
Students: "We totally understand!"
"OK, you guys are great." Shen Qi showed a pleased expression, and then wrote on the blackboard: C0,ρ(I, C)={u: I→u is continuous, limρ(τ)u(τ)=0}
"Now that you fully understand the relationship between Hilbert space and Euclidean space, I'll leave you with my only Functional Analysis problem this semester." A professor who doesn't hang a blackboard has the right to assign homework, and Shen Qi was doing just that.
"Over the past decade or so, the study of hypercycles in C0-semigroups on Banach space has been a hot topic. Please think about how to handle strongly mixed C0-semigroups on Banach space after class."
"Before the semester ends, I hope someone can tell me the answer. If someone solves my question, his or her Functional Analysis will directly yield an A. Okay, thanks for listening, class dismissed." Shen Qi patted the chalk dust off his hands and left.
A classroom full of students stared blankly at the blackboard; this was the consequence of their attempt to get Professor Shen to hang the blackboard.
"A strongly mixed C0-semigroup on Banach space? That's a very difficult assignment." Yu Lei's expression was serious; every student had the ambition to get all A's.
"Yu Lei, you should leave the group." Zhou Yu'an learned a lot of skills from Shen Qi; this lesson was worthwhile.
Heidi handed the pen back to Yu Lei: "Yu, Professor Shen chose you as his graduate student; you are truly very lucky."
"Of course, I'm the luckiest one." Yu Lei spending a lot of time with Shen Qi, Yu Lei realized that although Shen Qi adopted a hands-off approach, the pressure of being Little Brother Qi's graduate student was really immense.
A strong general has no weak soldiers under his command. With everyone watching Yu Lei, how could he not be under pressure?
"Heidi, it's my good fortune to know you too. I should buy you a drink." Yu Lei is very adaptable to new environments. This generation of young Chinese people grew up in an era of rapid development and global expansion of their motherland. They are more confident and optimistic, and are willing to embrace the world with open arms.
"Why not?" Heidi readily accepted Yu Lei's invitation.
"Little Brother Yu, wanna come along? You can bring your girlfriend," Yu Lei asked Zhou Yu'an warmly.
"I don't have a girlfriend, have fun." Zhou Yu'an patted Yu Lei the shoulder and left. This guy Yu Lei has only been at Princeton for a few months and he's already picking up pretty girls. Looks are everything, it's a global trend, and it's getting stronger and stronger.
Then Yu Lei and his pretty girl went off to have fun, while Zhou Yu'an buried himself in preparing his master's thesis.
Shen Qi wanted to focus on his Condensed Matter Physics research, but he also had some other miscellaneous things to deal with recently.
The American Mathematical Society invited Shen Qi to attend the Steele Prize award ceremony. This prize was established in 1970 with a donation from Still to reward mathematicians who have made significant contributions to mathematics.
The evaluation criteria are a book of significant value, a review article, or a paper with fundamental or long-term impact.
The laureate can be a non-U. S. citizen mathematician, but must be a member of the American Mathematical Society.
When Shen Qi received the Ford Prize a few years ago, he paid a $20,000 participation fee to the American Mathematical Society, becoming a foreign member of the American Mathematical Society.
From any perspective, Shen Qi fully meets the criteria for the Steele Prize.
The American Mathematical Society awarded the Steele Prize to Shen Qi for the following reasoning. "From the proof of the Wash Conjecture to the Muller -Shen theorem in Banach space, the Shen Proximity Theorem in Banach space, and the proof of the Riemann Hypothesis based on the 'twin matching method', Professor Shen Qi could have won the Steele Prize with any one of his papers published in the Top Four Journals in recent years."
"To date, Professor Shen Qi's most valuable academic achievement is undoubtedly his 'History of Number Theory,' in which the 'Theory of Prime Distribution of Riemann zeta function' is published in its complete form for the first time, and its influence will continue into the next millennium. Without a doubt, this year's Steele Prize belongs to Professor Shen Qi."
Since he would be spending some time in the United States, Shen Qi maintained a harmonious relationship with the American Mathematical Society and received the Steele Prize.
After the Fields Medal, Shen Qi received a string of other Math Prize, with the Steele Prize Math Prize his eighth.
System: "New achievement! The host has won the international mathematics grand prize, the A-level Math Prize, the Steele Prize. The basic reward is 850,000 academic points, multiplied by the primary mathematical talent coefficient of 2.0, resulting in a final reward of 1,700,000 academic points."
Host, Shen Qi
Age: 23
Mathematics Level 13, 472/20 million
Physics Level 10, 101/1.2 million
Sports Level 5, 3129/50,000
English Level 5, 2501/50,000
Chinese Language Level 5, 2598/50,000
Politics Level 5, 9460/50,000
Chemistry Level 3, 599/5000
Biology Level 3, 586/5000
History Level 2, 1231/3000
Geography Level 2, 828/3000
Remaining Academic Points: 31,028,693
Progress towards Math Level 14: 472/20 million (Remaining top-performing student points can satisfy condition one).
Condition 2 progress: 3/5 (Obtain the S-level Fields Medal, and the A-level Ramanujan Prize and Steele Prize)
Condition 3 progress: 0/1
Through his daily mathematical studies, Shen Qi can accumulate a small amount of daily experience points.
The most reasonable approach is to wait until conditions two and three are both at 100% before investing in condition one to reach 20 million. This will prevent the overflow of tens to hundreds of daily experience points.
Frugality is a virtue of mathematicians. At Shen Qi's level of mathematics, it takes a considerable amount of time to accumulate tens to hundreds of mathematical experience points on a daily basis.
At the Steele Prize award ceremony, Shen Qi thanked the American Mathematical Society and his colleagues in mathematics across the United States for their support and affection.
Of the eight Math Prize Shen Qi has received, four were awarded by American mathematics institutions (Steele Prize, Breakthrough Prize, Clay Research Award, and Ford Prize).
International mathematical organizations awarded two prizes: the Fields Medal and the Ramanujan Prize.
Chinese mathematical institutions awarded two prizes: the Chern Prize in Mathematics and the Zhong Jiaqing Mathematics Prize.
Shen Qi will definitely complete the three conditions for advancing to Math Level 14 with high quality and quantity. He will also need to win two more A-level mathematics awards to make his total number of trophies and medals a round number. Then, condition two will be met.