Questioning Infinity, Touching Eternity — A Conversation with Every Soul Seeking Immortality
Prelude: Setting Out from Finitude
We are all finite beings.
Our lives span only a few decades, mere instants on the cosmic scale. Our bodies age, memories blur, and ultimately we return to dust. What we can do, whom we can love, where we can reach—all are pitifully limited.
Yet we persistently desire infinity.
We desire love to be eternal, work to be immortal, names to be remembered, life to have meaning. This desire is innate, encoded in our genes, inscribed in our souls.
Why does finite life desire infinity?
Because we are human.
Because humans have consciousness, can recognize their own finitude, and thus yearn for infinity. Because humans have reason, can comprehend the long river of time, and thus crave eternity. Because humans have spirit, can transcend bodily limitations, and thus pursue immortality.
This is the human condition: dwelling in finitude, heart turning toward infinity.
How to resolve this predicament? Where is the way out?
Thinkers across ages and cultures have offered their respective answers. Today, let us follow a special path—the path of mathematicians who devoted their lives to questioning the "Riemann Hypothesis"—to explore this question. Their lives may tell us: how to set out from finitude, question infinity, and ultimately touch eternity.
Volume One: Questioning
Chapter One: The Birth of the Problem
Every great inquiry begins with a question.
In 300 BCE, Euclid wrote in Elements: there are infinitely many primes. This was humanity's earliest profound understanding of primes. But what comes after infinity? How are they distributed? Are there patterns?
This question, for two thousand years after Euclid, no one could answer.
In 1737, Euler discovered a formula:
The left side is a sum over natural numbers; the right side is a product over primes. This formula first revealed the profound connection between primes and all natural numbers. But it still did not tell us the distribution pattern of primes.
In 1792, the 15-year-old Gauss casually wrote at the dinner table: the number of primes not exceeding x is approximately equal to x divided by the natural logarithm. This was a conjecture from observing prime tables. He did not prove it; he only conjectured. But this conjecture later became known as the "Prime Number Theorem," becoming the central problem of 19th-century mathematics.
In 1859, Riemann was elected as a corresponding member of the Berlin Academy of Sciences. By convention, he submitted a report. This report was only eight pages, titled "On the Number of Primes Less Than a Given Magnitude."
In these eight pages, Riemann did three things:
First, he analytically continued Euler's zeta function to the entire complex plane. The function originally defined only on the real axis was extended to the complex domain. This extension opened up an entirely new world.
Second, he discovered a symmetry in this function: if you replace s with 1-s, the function values satisfy a certain relation. This symmetry forces the zeros to be symmetrically distributed on both sides of a line—the line where the real part equals 1/2.
Third, he computed the first few zeros and found they all lay on this line. So he wrote a sentence:
"It would seem plausible that these roots are probably all real. Of course, one would wish for a rigorous proof here; after a few brief, futile attempts, I have temporarily set aside the search for such a proof, as it appears unnecessary for the immediate objective of my investigation."
This is the Riemann Hypothesis: all non-trivial zeros of the zeta function have a real part equal to 1/2.
167 years have passed, and this question remains unresolved.
This is how a great question is born: from Euclid's infinity of primes, to Euler's product formula, to Gauss's observation, to Riemann's eight-page paper. It did not appear from nowhere, but was the crystallization of two thousand years of human thought. Once born, it acquired an independent life, beginning to summon generation after generation of followers.
Chapter Two: Portraits of the Questioners
From 1859 to today, countless people have been summoned by this question. They came from different countries, spoke different languages, had different personalities, but were all drawn by the same problem.
Let us meet a few.
Gram, Danish mathematician. In 1903, he computed 15 zeros. This was humanity's first glimpse of concrete evidence for the Riemann Hypothesis. His method was crude, his results limited, but he took the first step. His name was forever recorded in the history of mathematics, not because he solved the problem, but because he began the computation.
Hardy, British mathematician. In 1914, he proved that infinitely many zeros lie on the critical line. This was not the final answer, but it was the first breakthrough. Hardy was a pure mathematician; he once said, "I have never done anything useful." But his contribution to the Riemann Hypothesis made him an immortal legend. His story tells us: pursuing "useless" knowledge is itself the highest form of "usefulness."
Turing, British mathematician, father of computer science. In 1953, he used a machine he designed to compute 1,104 zeros. Turing's life was full of legend: cracking the Enigma code, laying the foundations of artificial intelligence, being forced to undergo chemical castration due to his homosexuality, ultimately taking his own life. In his brief and tragic life, computing Riemann zeros was a small part of his many contributions. But this small part tells us: even the greatest minds are drawn by the charm of this question.
Lehmer, American mathematician. In 1956, he computed 25,000 zeros. He invented the concept of "Lehmer pairs," used to describe special relationships between zeros. This concept was later employed in estimating the de Bruijn-Newman constant, becoming a key tool in proving that constant non-negative. He did not know the ultimate purpose of his work; he simply did what he could, approaching that ultimate question.
Gourdon and Demichel, French mathematicians. In 2004, they verified the first 10^13 zeros. This means they checked 10 trillion cases, each conforming to the hypothesis. This work took years, requiring immense patience and meticulousness. But they did it, because they honored their commitment to their vocation.
Guth and Maynard, contemporary mathematicians. In May 2024, they released new zero-density estimates, improving records dating back to 1940. Guth is a harmonic analysis expert; Maynard is a number theory expert. They brought techniques from their respective fields and applied them to number theory problems. Terence Tao commented: "The first few steps are standard; many analytic number theorists, including myself, have tried to break through the Ingham bound and would recognize these steps. But from there onward, Maynard and Guth performed many clever and unexpected maneuvers."
What do these people share in common?
They all knew they might not be able to solve the ultimate problem. They all knew they might be merely a wave in the long river of history. Yet they still chose to inquire, still chose to contribute, still chose to become one link in the chain.
This is the spirit of the questioner: not seeking that success be mine, but seeking that I be part of success.
Chapter Three: Why Question Unsolvable Problems?
This is a fundamental question: why would someone spend their entire life questioning a problem that may never be solved?
Secular eyes cannot comprehend: if the ultimate answer is never obtained, isn't all effort wasted?
But questioners have a different view.
First, questioning itself is meaning.
Mathematicians do not know whether the Riemann Hypothesis can be proven within their lifetimes, but they know: every inquiry deepens understanding of the problem; every attempt enhances thinking ability; every failure serves as a warning to later seekers.
The meaning of life lies not in reaching the destination, but in the process of walking. If only the destination held meaning, then what comes after arrival? If the Riemann Hypothesis were solved, what would mathematicians do next? Continue questioning the next problem. Questioning never ceases. Therefore, meaning lies not in the destination, but on the road.
Second, the greater the problem, the deeper the nourishment.
The Riemann Hypothesis is great not because it is solvable, but because it connects seemingly unrelated domains: number theory, complex analysis, random matrix theory, quantum chaos, statistical physics. Those who pursue this question are compelled to learn the knowledge of these fields, compelled to build connections between these domains, compelled to expand the boundaries of their own thinking.
The degree to which a problem can nourish you is proportional to its magnitude. Small problems yield small gains; great problems yield great growth. A problem like the Riemann Hypothesis can nourish a person for a lifetime, because it always has new angles, new layers, new connections waiting to be discovered.
Third, the individual is finite, the enterprise is infinite.
Connes, in his 2022 lecture, demonstrated a startling result: using only primes less than 13—an extremely small subset of information—one can approximate the first 50 zeros with astonishing accuracy. The approximation error for the first zero is about 10^-4, for the 50th about 10^-3. All approximations lie on the critical line.
What does this mean? It means that finite information already encodes infinite truth. You do not need to solve the entire problem to touch its core.
Similarly, you do not need to live forever to leave something eternal. Every contribution you make becomes a stepping-stone for later seekers; every thought of yours continues growing in others' minds. The individual is finite, but the enterprise is infinite. When you merge your life into an infinite enterprise, you transcend finitude.
This is the questioner's answer: because questioning itself is meaning, because problems nourish life, because enterprise transcends the individual.
Volume Two: Wisdom
Chapter Four: What Is Wisdom?
Before questioning infinity, we must first understand: what is wisdom?
Wisdom is not knowledge. Knowledge is knowing facts; wisdom is understanding meaning. Knowledge is knowing what the Riemann Hypothesis is; wisdom is understanding why this question is worth pursuing. Knowledge is knowing the content of the Prime Number Theorem; wisdom is feeling the beauty of order behind it.
Wisdom is not intelligence either. Intelligence is the ability to solve problems; wisdom is the ability to choose problems. Intelligence can help you solve any problem, but only wisdom can tell you: which problems are worth solving, which are not.
The mathematicians studying the Riemann Hypothesis demonstrate profound wisdom.
They chose not a quickly solvable "small problem," but a "great problem" that may never have an answer. They know the value of this question lies not in being "solvable," but in being "worth solving." They know that even if they cannot solve it, later seekers will continue advancing. They know that every approach is progress, every failure is experience.
This is wisdom: knowing what is worth pursuing.
Chapter Five: How to Find a Question Worth Pursuing?
Rogers, in his letter to his daughters, wrote: "Focus on what you love. The fastest way to succeed is to do what you love to do, and then give it everything you have."
This statement is not motivational platitudes, but profound wisdom. Only what you truly love can sustain you through long years. Only questions you truly care about can keep you from lightly giving up when facing difficulties.
But love alone is not enough. Love must be combined with three characteristics:
First, the question must be sufficiently deep.
Deep enough to require constant learning, constant growth. If the question is too shallow, solvable in a few months, then what comes after resolution? You fall into emptiness. Only sufficiently deep questions can keep you occupied for a lifetime, growing for a lifetime.
Second, the question must be sufficiently large.
Large enough to make you aware of your own insignificance, thus maintaining humility. If the question is too small, you overestimate your abilities; only when the question is sufficiently large can you experience the state of "learning and then knowing what is still lacking." Facing the Riemann Hypothesis, even the most brilliant mathematicians feel humble—this is precisely how it nourishes people.
Third, the question must have "approachability."
Allowing you to feel some progress every day. If the problem is completely elusive, with no interim results, people will give up in despair. A good question should have countless small questions orbiting it, so you can gain something every day.
Wisdom is finding such a question, then pursuing it for a lifetime.
Chapter Six: Wisdom in Daily Life
You need not be a mathematician to practice this wisdom. In daily life, you can:
Find depth in your profession. Whatever work you do, you can question: how to do it better? How to understand it more deeply? How to innovate? These questions have no ultimate answers, but every day's questioning makes you a better professional.
Find meaning in relationships. With family, friends, colleagues, you can question: how to love more deeply? How to understand more thoroughly? How to support more effectively? These questions have no perfect answers, but every questioning deepens the relationship.
Find truth within yourself. Facing your own heart, you can question: what do I truly want? What do I fear? What do I avoid? These questions have no simple answers, but every direct confrontation makes you better understand yourself.
This is wisdom in daily life: turning every ordinary question into a topic worth pursuing.
Volume Three: Benevolence
Chapter Seven: Solitary Questioning and Shared Enterprise
In the popular imagination, questioning is solitary: one person facing the unknown, one person facing difficulty, one person facing failure.
But mathematicians studying the Riemann Hypothesis tell us: questioning can also be shared.
1737: Euler wrote the product formula, laying the foundation for Riemann's work. 1859: Riemann posed the conjecture, inaugurating a century of research direction. 1896: Hadamard and de la Vallée Poussin proved the Prime Number Theorem, taking a crucial step. 1914: Hardy proved infinitely many zeros lie on the critical line, achieving a major breakthrough. 1940: Ingham gave zero-density estimates, establishing an analytical framework. 1973: Montgomery discovered the connection with random matrices, opening new horizons. 2004: Gourdon verified the first 10^13 zeros, providing powerful evidence. 2024: Guth and Maynard improved density estimates, once again advancing the boundary.
This is a relay spanning three centuries. Each person stood on the shoulders of predecessors; each person paved the way for successors. They are not solitary individuals, but one link in the long river of human knowledge.
This is benevolence: merging one's work into humanity's shared enterprise.
Chapter Eight: Marx's Teaching
At seventeen, Marx wrote an essay titled "Reflections of a Young Man on the Choice of a Profession." One passage stands as perhaps the most profound discourse on benevolence:
"If a person works only for himself, he may perhaps become a famous scholar, a great sage, an excellent poet, but he can never be a perfect, truly great human being. History calls those who exalt themselves by working for a common goal the greatest of all people; experience praises those who bring happiness to the majority as the happiest of all people; religion itself teaches us that the ideal everyone admires has sacrificed himself for humanity—who would dare to deny such teachings?"
This passage reveals the true meaning of benevolence: not charity, not pity, but connecting one's life to a greater enterprise.
Mathematicians study the Riemann Hypothesis not for fame or fortune—pure mathematics research offers limited income and scarce public attention. What do they pursue?
To understand the order of the universe. To satisfy human curiosity. To pave the way for later seekers. To become one link in the chain of knowledge.
This is benevolence: transforming personal inquiry into human inquiry; merging finite life into infinite enterprise.
Chapter Nine: Benevolence in Daily Life
You need not be a mathematician to practice benevolence.
When you earnestly complete your work and share the burden with colleagues, you practice benevolence. When you patiently teach children and invest in the next generation's growth, you practice benevolence. When you participate in community service, making neighbors' lives better, you practice benevolence. When you share knowledge and experience, helping others grow, you practice benevolence.
Every such action connects your personal life with others. Every such connection transcends your self's limitations, making you part of something larger.
Rogers says: "Bring the world within your scope. Go out and see the world, keep an open mind, be a citizen of the world." Benevolence is shifting from self-focus to attending to others and the world.
Volume Four: Courage
Chapter Ten: Courage in Facing the Unknown
How much courage does studying the Riemann Hypothesis require?
Consider: you invest a lifetime of effort, possibly achieving nothing in the end. You face a problem that the most brilliant minds of 167 years could not solve. You may fail at any time, may be proven wrong in direction at any time.
But mathematicians still choose to proceed.
In 1903, Gram computed 15 zeros. His method was crude, his results limited, but he took the first step. He did not know how far he could go, but he chose to begin.
In 1914, Hardy proved infinitely many zeros lie on the critical line. This was not the final answer, but it inspired later seekers. He did not know whether he could solve it, but he chose to try.
In 2024, Guth and Maynard improved zero-density estimates. They did not know whether this led to the ultimate proof, but they chose to advance.
They did not fail to recognize the difficulty; they proceeded despite knowing it. This is courage.
Chapter Eleven: Courage Is Not the Absence of Fear
We often misunderstand courage: assuming courageous people do not feel fear. The truth is precisely the opposite: courageous people also feel fear, but they choose not to be controlled by it.
Mathematicians also fear failure. They worry their proofs have flaws, worry their research direction is wrong, worry about wasting years of their lives. But they still choose to try.
Rogers says: "Do not let others influence you. Your life is your own; do not let others influence your decisions. Going against the crowd requires courage, but success often belongs to those who dare to walk their own path."
Courage is walking your own path, even if few walk it, even if it is full of unknowns.
Mathematicians studying the Riemann Hypothesis walk precisely such a path. They do not chase trendy fields, do not pursue short-term results, do not cater to review panel tastes. They follow only one question, only the inner calling. This requires immense courage.
Chapter Twelve: Courage in Daily Life
Courage exists not only in mathematicians' studies. It exists in everyone's daily life:
- Choosing a profession you love, rather than the "stable job" your parents expect
- Speaking your true thoughts, even if they may not be accepted
- Admitting your mistakes and taking responsibility
- Trying new things, even if you might fail
- Persisting in doing what is right, even under pressure
Every such choice is a practice of courage. Every practice makes courage a habit.
Volume Five: Temperance
Chapter Thirteen: Accepting Finitude
The most fascinating aspect of the Riemann Hypothesis is: it may be unprovable.
Mathematicians must face this possibility: the question they pursue for a lifetime may never have an answer. This is not failure, but the nature of the question.
What lesson does this offer us?
Life too is finite. We cannot accomplish all we wish, cannot reach all heights we aspire to. We must accept this finitude.
But accepting finitude does not mean abandoning pursuit. On the contrary, precisely after recognizing finitude, we can better arrange our finite lives.
Chapter Fourteen: The Wisdom of Temperance
Temperance is not doing nothing, but knowing what to do and what not to do.
Mathematicians studying the Riemann Hypothesis understand this well. They do not attempt to solve all problems simultaneously, but focus on one small direction. They do not expect overnight breakthroughs, but accumulate day by day. They do not greedily seek fame and fortune, but take satisfaction in every small advance.
This temperance enables them to persist for decades without exhaustion.
Rogers says: "Fortune only favors those who persist in effort. Study hard; the more you learn, the more you realize how little you know. Without extra effort and dedication, success will not fall upon you."
The opposite of temperance is not laziness, but greed. Greedily wanting everything, ultimately gaining nothing. Temperately focusing on one point on the contrary may reach distant horizons.
Chapter Fifteen: Temperance in Daily Life
How to practice temperance in life?
- Do not overindulge: Do one thing at a time, do it well
- Do not rush: Accept that progress requires time, do not seek quick results
- Do not compare: Walk your own path, do not compare speed with others
- Do not waste: Treasure time and energy, do not invest in pointless consumption
- Know priorities: Know what is important, what is not
Temperance liberates you from the anxiety of "wanting everything," enabling focus on what truly matters.
Volume Six: Justice
Chapter Sixteen: Loyalty to Truth
Mathematics has an iron rule: you may make mistakes, but you may not fabricate. Erroneous proofs can be forgiven; deliberate deception gets you expelled from the community.
The history of studying the Riemann Hypothesis includes many failed attempts:
1885: Stieltjes claimed to have proved a stronger conclusion but never published the proof; it was later deemed erroneous. 1945: Rademacher submitted a proof, discovered the error, and voluntarily withdrew the paper. Since the 1980s: de Branges has multiple times announced proofs, none accepted.
These failed attempts were not erased. They were recorded, becoming warnings and experience for later seekers. This is loyalty to truth: not concealing failure, not exaggerating achievement.
Chapter Seventeen: The True Meaning of Justice
Justice applies not only to others, but also to oneself.
Mathematicians must be honest with themselves: does this proof truly hold? Are there still gaps? Have I overlooked something?
They must also be honest with others: acknowledge predecessors' contributions, make public one's own methods, accept peers' scrutiny.
This double honesty constitutes the cornerstone of the academic community.
Rogers says: "Common sense is not so common. What the mass society believes is often wrong. You must learn to think independently for yourself, examine everything personally, and do not blindly trust what others say."
The prerequisite for independent thinking is honesty with oneself. Only by admitting you do not know can you begin learning; only by admitting you might be wrong can you find what is right.
Chapter Eighteen: Justice in Daily Life
How does justice manifest in daily life?
- Be honest with yourself: Do not deceive yourself; face your strengths and weaknesses squarely
- Be honest with others: Do not lie, do not deceive, do not exploit others
- Be responsible in work: Fulfill your commitments, do not cut corners
- Admit mistakes: When wrong, own it; do not make excuses
- Respect rules: Compete fairly, do not take shortcuts
Justice grants us inner peace, because nothing needs to be hidden.
Volume Seven: Integrity
Chapter Nineteen: Persistence to the End
What kind of integrity do mathematicians studying the Riemann Hypothesis need?
They need loyalty to the path they have chosen. Not for a day or two, not for a year or two, but for a lifetime.
In 2004, Gourdon and Demichel verified the first 10^13 zeros. This means they checked 10 trillion cases, each conforming to the hypothesis. This work took years, requiring immense patience and meticulousness. But they did it, because they honored their commitment to their vocation.
Even more touching are the mathematicians who left no names. They may have had no major breakthrough in their lifetimes, yet they persisted in research, taught and mentored, transmitted knowledge. Their names did not appear in papers, but their students later made contributions. Their integrity is manifested in day-after-day steadfastness.
Chapter Twenty: The Essence of Integrity
Integrity is first and foremost a covenant with oneself: having chosen this path, I shall persist in walking it.
Rogers says: "Focus on what you love. The fastest way to succeed is to do what you love, and then give it everything you have." Giving everything is the manifestation of integrity. Having chosen love, one must be worthy of that love.
Integrity does not mean never changing direction, but before changing, first trying one's utmost. If after genuine effort one indeed discovers the direction is wrong, one may adjust. But giving up without having tried one's best is dishonest to oneself.
Chapter Twenty-One: Integrity in Daily Life
How does integrity manifest in daily life?
- Honor commitments: What you promise, strive to fulfill
- Uphold principles: Do not abandon them due to difficulty
- Persist in effort: Do not give up because of short-term ineffectiveness
- Be responsible to yourself: Do not make excuses, do not deflect responsibility
- Keep agreements: Even when inconvenient, fulfill your commitments
Integrity makes us reliable people. Others can depend on us, and we can depend on ourselves.
Volume Eight: Transcendence
Chapter Twenty-Two: From Finite to Infinite
What do mathematicians studying the Riemann Hypothesis ultimately gain?
If they prove the conjecture, their names will be immortalized in history. But what if they fail to prove it? Is their life then wasted?
No.
Because they have already transcended personal gain and loss. Their work has merged into the ocean of human knowledge. Even if they did not solve the ultimate problem, they became one link in the chain. Later seekers will continue advancing on their foundation.
The appendix of the paper contains a long table recording the progress of zero computation from 1903 to 2004:
1903, Gram: 15 zeros 1914, Backlund: 79 zeros 1925, Hutchinson: 138 zeros 1935, Titchmarsh: 1,041 zeros 1953, Turing: 1,104 zeros 1956, Lehmer: 25,000 zeros 1958, Meller: 35,337 zeros 1966, Lehman: 250,000 zeros 1969, Rosser et al.: 3,500,000 zeros 1979, Brent: 81,000,001 zeros 1982, Brent et al.: 200,000,001 zeros 1986, van de Lune et al.: 1,500,000,001 zeros 2004, Gourdon and Demichel: 10,000,000,000,000 zeros
Every name, every number, is a contribution. Among these people, the vast majority were not remembered by the public, but collectively they advanced humanity's understanding of mathematics.
This is transcendence: merging finite life into infinite enterprise.
Chapter Twenty-Three: The Path of Transcendence
Transcendence is not personal ascension, but the transformation from "I" to "we."
When you realize you are one link in a relay across generations, when you feel your work will pave the way for later seekers, when you see personal effort merging into collective enterprise—you transcend personal limitations.
Marx wrote: "History calls those who exalt themselves by working for a common goal the greatest of all people; experience praises those who bring happiness to the majority as the happiest of all people; religion itself teaches us that the ideal everyone admires has sacrificed himself for humanity."
Sacrifice is not loss, but transcendence. Merging the individual into the collective, merging the fleeting into the eternal.
Chapter Twenty-Four: How to Achieve Transcendence
You need not be a great person to achieve transcendence. In daily life, you can:
- Care for the next generation: Transmit your experience to young people
- Protect the environment: Leave a better planet for future generations
- Engage in public service: Create value for people you do not know
- Create works: Leave something meaningful behind
- Carry forward culture: Learn and propagate valuable traditions
Every such action is a transcendence of personal limitations.
Volume Nine: Eternity
Chapter Twenty-Five: What Is Eternity?
What is eternity?
For the ancients, eternity was the immortal soul, the dwelling of gods, a realm beyond time.
For modern people, eternity might be leaving a name, being remembered by history, achievements that endure.
But the mathematicians' story offers us another understanding: eternity is not existing forever, but having existed in a way sufficient to influence forever.
Gram lived only 56 years, computing 15 zeros. But his name was recorded in the history of mathematics, his methods improved by later seekers, his work becoming one link in the chain. His life was finite, but his influence extends to forever.
Lehmer lived 84 years, computing 25,000 zeros, inventing the concept of "Lehmer pairs." This concept was later used in estimating the de Bruijn-Newman constant, becoming a key tool for proving that constant non-negative. He did not know his work would have such applications, but the fact is: his work influenced later research, unto forever.
Turing lived only 41 years; in his brief life, he cracked Enigma, laid the foundations of AI, computed 1,104 zeros. His life was cut short, but his ideas continued growing, until today, until forever.
Eternity is not living long, but living in a way sufficient to transcend time.
Chapter Twenty-Six: Ways to Touch Eternity
Then, how do we touch eternity?
Mathematicians tell us: through questioning infinity.
When you question a sufficiently large problem, when you connect your life with humanity's enterprise, when you become one link in the chain of knowledge—you touch eternity.
Because that question will continue to exist, even after you are gone. Because that enterprise will continue advancing, even after you depart. Because that chain will continue extending, even after you have completed your segment.
You need not live forever; your work will make you live forever.
You need not be remembered by everyone; your contributions will be remembered by those who need them.
You need not complete everything; the portion you complete is enough.
This is the way to touch eternity: with finite life, do infinite enterprise.
Chapter Twenty-Seven: Conversing with Eternity
In 1859, Riemann wrote down that conjecture.
In 2022, Connes delivered a lecture at the French Academy of Sciences titled "The Riemann Hypothesis: A Letter to Riemann." He told Riemann: 167 years later, we are still pursuing your question.
This is not metaphor; this is a real conversation. Connes, using mathematical language, converses with Riemann from half a century ago. He says: look, we have approached your conjecture with methods you could not imagine. Look, your question still nourishes us. Look, your enterprise continues.
This is conversing with eternity. When you join an inquiry spanning time and space, when you respond to a summons from the past, when you leave clues for future seekers to continue questioning—you are conversing with eternity.
Rogers says: "Learn history. You need a macro-level worldview, and studying history lets you know what forces drive markets." History allows us to converse with the past. Similarly, questioning allows us to converse with the future.
Volume Ten: Return
Chapter Twenty-Eight: Returning to the Original Question
Now, let us return to the original question: how should we spend our lives?
Poiman wrote:
Arriving here by chance Wandering in doubt What lies ahead What lies behind No one can say No one can resolve What is truth! Who can attain it?
No one can say, no one can resolve. Truth lies not elsewhere, but in the process of our questioning. The way to attain it is to spend a lifetime approaching a question worthy of our pursuit.
The mathematicians' story tells us: that question can be very large, so large that a lifetime cannot complete it; that question can be very small, so small that one feels progress every day. The key is that it must be your question—a question you truly love, a question you are willing to approach for a lifetime.
Chapter Twenty-Nine: The Fusion of Seven Qualities
Wisdom, benevolence, courage, temperance, justice, integrity, transcendence—these seven qualities are not isolated, but mutually supporting.
Without wisdom, courage may become recklessness. Without benevolence, justice may become indifference. Without temperance, transcendence may become greed. Without courage, wisdom may become empty fantasy. Without justice, integrity may become blind conformity. Without integrity, benevolence may become performance. Without transcendence, everything remains trapped in finitude.
Mathematicians studying the Riemann Hypothesis embody the fusion of these seven qualities:
- They used wisdom to choose a question worth pursuing
- They used benevolence to dedicate their work to humanity's enterprise
- They used courage to face the unknown and possible failure
- They used temperance to accept finitude and focus on one point
- They used justice to treat truth and colleagues fairly
- They used integrity to persist in lifelong pursuit
- They used transcendence to merge the individual into humanity's long river
This is the complete picture of a life.
Chapter Thirty: An Answer for Everyone
You need not be a mathematician to practice these seven qualities.
You need not study the Riemann Hypothesis to question infinity.
You only need to find your question—that question that keeps you awake at night still pondering, that question you are willing to invest time and energy in, that question that makes you feel life has meaning.
Then, use wisdom to choose it, benevolence to nourish it, courage to face it, temperance to focus on it, justice to treat it, integrity to persist in it, transcendence to elevate it.
Then, pursue it for a lifetime.
Even without a final answer, your life already has direction. Even without final completion, your effort has already merged into humanity's long river.
Marx wrote at seventeen:
"If we have chosen the position in life in which we can most of all work for mankind, no burdens can bow us down, because they are sacrifices for the benefit of all; then we shall experience no petty, limited, selfish joy, but our happiness will belong to millions, our deeds will quietly live on and increasingly bear fruit, and over our ashes noble tears will be shed by those who attain higher development."
This is our answer.
Finale: Living Toward Infinity
In 1859, Riemann wrote down that conjecture in an eight-page paper.
In 2026, we are still questioning.
In these 167 years, countless people came, loved, questioned. Not many among them solved the ultimate problem, but all contributed strength to the questioning. Their lives were fulfilled because of questioning; their names were remembered because of contribution.
Now, it is our turn.
Each of us has our own "Riemann Hypothesis"—that question worth pursuing for a lifetime. It may be very large, or very small; it may concern all humanity, or only a small community. But as long as it is worth questioning, as long as we are willing to approach it for a lifetime, it can endow life with direction.
So, find your question.
Then pursue it for a lifetime.
Even without a final answer, your life already has meaning. Even without final completion, your effort has already merged into eternity.
Because questioning itself is meaning.
Because problems nourish life.
Because enterprise transcends the individual.
Because finitude merges into infinity.
Bid farewell to finite life.
Pay tribute to infinite questioning.
A life lived this way is sufficient.
Appendix: A Questioner's Self-Inquiry
If you wish, at the end of each day, you can ask yourself a few questions:
Wisdom What new thing did I learn today? What question did I understand more deeply? Did I discover any new questions worth pursuing?
Benevolence Whom did I help today? What value did I create for others? Did I connect my work to a larger enterprise?
Courage What difficulty did I face today? How did I respond? Did I abandon what I should have done out of fear?
Temperance Did I spend time on the most important things today? Was any wasted on pointless matters? Did I seek too much, too fast?
Justice Was I honest with myself today? Was I honest with others? Did I violate any principles?
Integrity Did I honor my commitments today? Did I give up because of difficulty? Did I lie to myself?
Transcendence Did what I did today transcend personal gain and loss? Did I leave anything for the future? Did I feel myself as one link in the chain?
These questions have no standard answers, but they can help you examine your day's life, allowing the seven qualities to gradually merge into your being.
Day by day, accumulating over time, you will discover: the question that once vexed you—"how should I spend my life"—already has an answer.
The answer lies not elsewhere, but in each of your daily choices.
Copyright Notice: This is a preview translation — Chinese original is the authoritative version. Copyright belongs to Guangzhou Phaenarete AI Technology Co., Ltd. Unauthorized reproduction, citation, or distribution is prohibited.