Mathematicians From The United States

"This morning's meeting went very well. We also discussed the need to make the Church more collegial. He is an excellent Pope and received well over 100 votes."

"Please join me in thanking Our Lord for the election of Pope Leo XIV, Successor of St. Peter, as Shepherd of the Church throughout the world.The Shrine of Our Lady of Guadalupe in La Crosse has a particularly strong bond with the Roman Pontiff, especially through its affiliation with the Papal Basilica of St. Mary Major. I urge all pilgrims and friends of the Shrine to pray fervently for Pope Leo XIV that Our Lord, through the intercession of Our Lady of Guadalupe, St. Peter the Apostle and Pope St. Leo the Great, may grant him abundant wisdom, strength and courage to do all that Our Lord asks of him in these tumultuous times. May God bless Pope Leo and grant him many years."

"War does not solve problems; on the contrary, it amplifies them and inflicts deep wounds on the history of peoples, which take generations to heal. No armed victory can compensate for the pain of mothers, the fear of children, or stolen futures. May diplomacy silence the weapons! May nations chart their futures with works of peace, not with violence and bloodstained conflicts!"

"I don't think I'm revealing any secrets when I write that a long and warm round of applause followed that ‘I accept,’ which made him the 267th Pope of the Catholic Church. [...] I met Cardinal Prevost years ago, in connection with a thorny issue involving the Church in Peru. Even then, I saw in him a sense of balance, calmness, love for people and attention to detail. [...] Pope Leo XIV, he continues, is well aware of the world's problems, as he demonstrated from his very first words from the Loggia, evoking a ‘disarmed and disarming’ peace. [...] I am certain that he will find strength in the grace of the Lord, in his experience as a religious and in the example of the great Father Augustine, whom he mentioned in his first speech. We are close to him with our affection, our obedience and our prayers."

"I met Leo XIV in Peru, and I was struck by his serenity. He is the right man to lead the Church."

"We still keep in our ears that weak but always courageous voice of Pope Francis who blessed Rome! The Pope who blessed Rome gave his blessing to the world, to the whole world, that morning of Easter Day. Allow me to follow up that same blessing: God loves us, God loves you all, and evil will not prevail! We are all in God’s hands. Therefore, without fear, united hand in hand with God and we move forward with each other. We are disciples of Christ. Christ is before us. The world needs its light. Humanity needs Him as the bridge to be reached by God and His love. Help us too, then one another to build bridges, with dialogue, with encounter, all by uniting us to be one people always at peace. Thank you to Pope Francis!"

"I also want to thank all my brother cardinals who chose me to be Peter's successor and to walk with you as a united Church, always seeking peace, justice, always trying to work as men and women faithful to Jesus Christ, without fear, to proclaim the Gospel, to be missionaries."

"Today is the day of the Supplication to the Madonna of Pompeii. Our Mother Mary always wants to walk with us, to be close, to help us with her intercession and her love. Then I would like to pray with you. Let us pray together for this new mission, for the whole Church, for peace in the world and let us ask this special grace from Mary, our mother."

"°I consider myself an amateur tennis player. [...] I really enjoy reading, going for long walks, travelling, seeing new places and enjoying the countryside in a different environment. I like to relax with friends and get to know people who are so different from me, whose gifts I learn from and appreciate greatly."

"Peace be with you all! Dear brothers and sisters, this is the first greeting of the Risen Christ, the good shepherd who gave his life for the flock of God. I too would like this greeting of peace to enter your heart, to reach your families, to all people, wherever they are, to all peoples, to all the earth. Peace be with you! This is the peace of the Risen Christ, an unarmed peace and a disarming, humble and persevering peace. He comes from God, God who loves us all unconditionally."

"I am a son of St. Augustine, an Augustinian, who said: “I am a Christian with you and a bishop for you.” In this sense we can all walk together towards that homeland that God has prepared for us. A special greeting to the Church of Rome! We must seek together how to be a missionary Church, a Church that builds bridges, dialogue, always open to receive like this square with open arms. All of them, all those who need our charity, our presence, dialogue and love."

"Brother Cardinals, I greet and thank you all for this meeting and for the days that preceded it, days that were painful because of the loss of the Holy Father Francis, demanding because of the responsibilities we face together, and at the same time, according to the promise Jesus himself made to us, rich in grace and consolation in the Spirit. Your presence reminds me that the Lord who entrusted this mission to me does not leave me alone in bearing its responsibility. I know, first of all, that I can always, always count on his help, the help of the Lord, and, by his grace and providence, on your closeness and that of so many brothers and sisters throughout the world who believe in God, love the Church, and support the Vicar of Christ with their prayers and good works."

"Sinner: The ball, there it is. If you want to play a little. Pope Leo XIV: But we'll break something here! We'd better not."

"God's charity, which makes us brothers and sisters, is at the heart of the Gospel, and with Leo XIII, we can ask ourselves today: if this criterion ‘were to prevail in the world, would not all strife cease and peace return?’ (Encyclical Letter Rerum novarum, 21). With the light and strength of the Holy Spirit, let us build a Church founded on God's love and a sign of unity, a missionary Church that opens its arms to the world, proclaims the Word, allows itself to be unsettled by history, and becomes a leaven of harmony for humanity. Together, as one people, as Fratelli tutti [brothers and sisters], let us walk towards God and love one another."

"To all of you, brothers and sisters of Rome, of Italy, of the whole world, we want to be a synodal Church, a Church that walks, a Church that always seeks peace, that always seeks charity, which always seeks to be close especially to those who suffer."

"Being a good shepherd means being able to accompany God's people and live close to them, not being isolated. Pope Francis has said this clearly many times. He does not want bishops who live in palaces. He wants bishops who live in relationship with God, with the rest of the episcopate, with priests and, above all, with the people of God in a way that reflects the compassion and love of Christ, creating community, learning to live what it means to be part of the Church in an integral way that includes much listening and dialogue."

"The priorities of pastoral work will always be different in one place or another, but recognising the great richness of the diversity of the People of God is tremendously helpful because it makes us more sensitive to reaching out and responding better to what is expected of us."

"Ideologies have become more powerful than humanity's real experience, faith, and the different values we live by. Some will misunderstand unity as uniformity: ‘You must be like us.’ No, it cannot be so. Nor can diversity be understood as a way of living without criteria or order. The latter lose sight of the fact that since the very creation of the world, the gift of nature, the gift of human life, the gift of so many different things that we experience and celebrate, cannot be sustained by inventing my own rules and doing things my way. These are ideological positions. When an ideology becomes, so to speak, the master of my life, then I can no longer dialogue with another person because I have already decided how things will be. Therefore, I am closed to encounter and transformation cannot take place. And this can happen anywhere in the world, on any subject. This obviously makes it very difficult to be Church, to be community, to be brothers and sisters."

"(Concerning Nostra Aetate) And so I, too, confirm that the church does not tolerate antisemitism and fights against it, on the basis of the Gospel itself. We cannot deny that there have been misunderstandings, difficulties and conflicts in this period, but these have never prevented the dialogue from continuing. Even today, we must not allow political circumstances and the injustices of some to divert us from friendship, especially since we have achieved so much so far. Even in these difficult times, marked by conflicts and misunderstandings, it is necessary to continue the momentum of this precious dialogue of ours. Never in the relationship of Catholics and Jews since ‘Nostra Aetate’ has the Jewish people been more in need of friends who commit themselves to combating antisemitism with every fiber of their being. The Catholic Church has one of the largest megaphones available. It has moral suasion that is unparalleled. We hope that they will use all of the tools in their arsenal to double down in that effort."

"Do you know how many stars there are in the observable universe? An impressive and marvellous number: a sextillion stars – a 1 followed by 24 zeros! If we divided them among the 8 billion inhabitants of Earth, each person would have hundreds of billions of stars to themselves. With the naked eye, on clear nights, we can see about five thousand of them. However, they show us a direction, just like when sailing at sea. Travellers have always found their way using the stars. Sailors followed the North Star; Polynesians crossed the ocean by memorising star charts. According to the farmers of the Andes, whom I met as a missionary in Peru, the sky is an open book that marks the seasons of sowing, shearing, and the cycles of life. Even the Magi followed a star to get to Bethlehem and worship the Baby Jesus."

"Perseverance is a great gift that the Lord is ready to offer us. But we must learn to welcome it and make it come alive, to be strong. It is one of those gifts that are built up over time, in the small trials of the beginning that help us to be stronger, to be able to carry the Cross when it becomes heavier. It is what enables us and makes us capable of moving forward."

"The Universal Declaration of Human Rights , approved and proclaimed by the United Nations on 10 December 1948, is now part of humanity’s cultural heritage. That text, which is always relevant, can contribute greatly to placing the human person, in his or her inviolable integrity, at the foundation of the quest for truth, thus restoring dignity to those who do not feel respected in their inmost being and in the dictates of their conscience."

"Trusting in the assistance of the almighty, I pledge to continue and strengthen the Church’s dialogue and cooperation with the Jewish people in the spirit of the Second Vatican Council’s declaration Nostea Aetate."

"We continue to follow carefully and with hope the developments in Iran, Israel and Palestine. The words of the prophet Isaiah resound with urgent relevance: “Nation shall not lift up sword against nation, neither shall they learn war any more” (Is 2:4)."

"Today we desolately witness the unjust use of hunger as a weapon of war. Starving the population is a very cheap way of waging war. That is why today, when most conflicts are not fought by regular armies but by groups of armed civilians with few means, burning land, stealing livestock, blocking aid are tactics increasingly used by those who wish to control entire defenceless populations. Thus, in this type of conflict, the first military targets become the water supply networks and communication routes.Farmers cannot sell their produce in contexts threatened by violence and inflation skyrockets. This leads to huge numbers of people succumbing to the scourge of hunger and dying, with the aggravating factor that, while civilians are weakened by misery, the political summits grow fat on corruption and impunity."

"(Meeting the cardinals in Vatican) Dear brothers, I would like to conclude this first part of our meeting by making my own – and proposing to you as well – the wish that Saint Paul VI expressed at the beginning of his Petrine Ministry in 1963: ‘May it pass over the whole world like a great flame of faith and love, kindling all people of good will, illuminating the paths of mutual cooperation, and drawing upon humanity, again and always, the abundance of divine favours, the very strength of God, without whose help nothing is valid, nothing is holy.’"

"One of the things that comes to mind when I think of St Augustine, his vision and his understanding of what it means to belong to the Church, is what he says about not being able to say you are a follower of Christ without being part of the Church. Christ is part of the Church. He is the head. So anyone who thinks they can follow Christ ‘in their own way’ without being part of the body is, unfortunately, a distortion of what is an authentic experience. St Augustine has an omnipresent wisdom that helps us to live in communion. Unity and communion are essential charisms of the life of the Order and a fundamental part of understanding what the Church is and what it means to be in the Church."

"A bishop must not be a little prince sitting in his kingdom."

"Interviewer: You are an Augustinian. How does Augustinian spirituality characterise your ministry? Cardinal Prevost: We could say several things... As my episcopal motto suggests, unity and communion are part of the charism of the Order of Saint Augustine and also of my way of acting and thinking. I think it is very important to promote communion in the Church, and we know well that communion, participation and mission are the three key words of the Synod. So, as an Augustinian, promoting unity and communion is fundamental for me. St Augustine also speaks a lot about unity in the Church and the need to live it, about the fact that there is a certain guarantee of unity in listening to the Bishop of Rome, in being part of the Church of Rome. In this sense too, therefore, I feel that the Pope's new call is a way of living my unity and participation in the Church, in obedience to the Holy Father. This too is very Augustinian. Interviewer: How much does the figure of Augustine inspire your choices, your steps, your service in the Church? Cardinal Prevost: St Augustine is certainly a great figure not only for the order but for everyone. I wish I had more time to study and read him. He has so much to offer the Church, even the Church of today. Then there is what I said before: unity in the Church and fidelity to the Bishop of Rome, always seeking to promote communion. Living unity in the Church, as Augustine recommends, means living united in Christ."

"Pope Francis has spoken of four types of closeness: closeness to God, to brother bishops, to priests and to all God's people. One must not give in to the temptation to live isolated, separated in a palace, satisfied with a certain social level or a certain level within the church. And we must not hide behind an idea of authority that no longer makes sense today. The authority we have is to serve, to accompany priests, to be pastors and teachers."

"Sometimes the bishop risks focusing only on the local dimension. But a bishop should have a much broader vision of the Church and reality, and experience the universality of the Church. He also needs the ability to listen to his neighbour and seek advice, as well as psychological and spiritual maturity. A fundamental element of the portrait of a bishop is being a pastor, capable of being close to the members of the community."

"Q: Can the process for the appointment of new bishops be improved? Praedicate Evangelium states that "members of the people of God" must be involved. Is this happening? A: We had an interesting reflection among the members of the Dicastery on this issue. For some time now, not only some bishops or some priests, but also other members of the people of God are being heard. This is very important, because the bishop is called to serve a particular Church. Therefore, listening to the people of God is also important. If a candidate is not known by anyone among his people, it is difficult—not impossible, but difficult—for him to truly become pastor of a community, of a local Church. So, it is important that the process is a little more open to listening to different members of the community. This does not mean that it is the local Church that has to choose its pastor, as if being called to be a bishop was the result of a democratic vote, of an almost ‘political’ process. A much broader view is needed, and the apostolic nunciatures help a lot in this. I believe that, little by little, we need to open up more, to listen a little more to the religious, the laity."

"I always had the impression of a man who wanted to live the Gospel authentically, consistently. In the days when I was Prior General of the Augustinians, several times during visits to my brothers in Argentina, when he was still a cardinal, I had the opportunity to meet him and speak with him, informally and on more institutional matters'."

"Even today, there are many contexts in which the Christian faith is considered absurd, for weak and unintelligent people; contexts in which other forms of security are preferred, such as technology, money, success, power, and pleasure. These are environments where it is not easy to bear witness to and proclaim the Gospel, and where believers are mocked, opposed, despised, or at best tolerated and pitied. Yet, precisely for this reason, they are places where mission is urgent, because the lack of faith often brings with it tragedies such as the loss of the meaning of life, the forgetting of mercy, the violation of human dignity in its most dramatic forms, the crisis of the family and other wounds from which our society suffers greatly."

"It will be a pontificate in continuity with the magisterium of Pope Francis. I am very happy about that. This is what the majority of the cardinals wanted ... but with a style of their own. [...] Pope Leo XIV, in his first message, spoke of a “synodal Church.” Having participated in the work of the Synod, we have a Pope who knows synodality, who understands it, who dares to be synodal. There will not be a revolution, but an evolution."

"... I think Walther Mayer got a designation that has never been used for anyone else. He was the only associate professor the Institute has ever had. He was called "associate professor." Yes, and the reason was: Einstein wanted him very much. Clearly the mathematicians did not feel that he really should be a full-fledged faculty member. This was at an early stage, so they took a designation that was used in American universities. Only later did it occur to them to create a new thing called "permanent member.""

"The duality theorems for a manifold will be derived from the corresponding ones for nets and co-nets of group systems ... Of the two types of duality theorems — the and s — the first could be obtained more easily from the corresponding one for a group system and its character system ... But when applied to the Alexander type this method fails. Also in using the net and co-net theory for both types, the less complicated Poincaré theorem serves as an introduction for the Alexander theorem."

"In 1972 announced a remarkable connection between the distribution of the zeros of the Riemann zeta-function and the distribution of eigenvalues of large random Hermitian matrices. Since then a number of startling developments have occurred making this connection more profound. In particular, random matrix theory has been found to be an extremely useful predictive tool in the theory of L-functions."

"A major difficulty in trying to construct a proof of RH through analysis is that the zeros of L-functions behave so much differently from zeros of many of the s we are used to seeing in mathematics and mathematical physics. For example, it is known that the zeta-function does not satisfy any differential equation. The functions which do arise as solutions of some of the classical differential equations, such as s, s, etc., have zeros which are fairly regularly spaced. A similar remark holds for the zeros of solutions of classical differential equations regarded as a function of a parameter in the differential equation."

"The Riemann Hypothesis is a statement about a deep connection between addition and multiplication that we do not yet understand."

"The ultimate goal of the Hindu was to free himself from the endless cycle of pain found in continual reincarnation and reconnect with the Nothingness that is the source and fundament of the All. For Indians, the void of Sunya was the very font of all- potential; nothingness was liberation. No surprise then that it is from this sophisticated culture that we inherit the mathematical analog of nothing, zero"

"It is notoriously difficult to convey the proper impression of the frontiers of mathematics to nonspecialists. Ultimately the difficulty stems from the fact that mathematics is an easier subject than the other sciences. Consequently, many of the important primary problems of the subject‍—‌that is, problems which can be understood by an intelligent outsider‍—‌have either been solved or carried to a point where an indirect approach is clearly required. The great bulk of pure mathematical research is concerned with secondary, tertiary, or higher-order problem, the very statement of which can hardly be understood until one has mastered a great deal of technical mathematics."

"Early in his college days, Minsky had had the good fortune to encounter Andrew Gleason. Gleason was only six years older than Minsky, but he was already recognized as one of the world’s premier problem-solvers in mathematics; he seemed able to solve any well-formulated mathematics problem almost instantly... “I couldn’t understand how anyone that age could know so much mathematics,” Minsky told me. “But the most remarkable thing about him was his plan. When we were talking once, I asked him what he was doing. He told me that he was working on Hilbert’s fifth problem.” Gleason said he had a plan that consisted of three steps, each of which he thought would take him three years to work out. Our conversation must have taken place in 1947, when I was a sophomore. Well, the solution took him only about five more years... I couldn’t understand how anyone that age could understand the subject well enough to have such a plan and to have an estimate of the difficulty in filling in each of the steps. Now that I’m older, I still can’t understand it. Anyway, Gleason made me realize for the first time that mathematics was a landscape with discernible canyons and mountain passes, and things like that. In high school, I had seen mathematics simply as a bunch of skills that were fun to master—but I had never thought of it as a journey and a universe to explore. No one else I knew at that time had that vision, either."

"Who came up with ethno-nationalism? [Is] swedes caring about Sweden ethno-nationalism? FU! You know, people have a right to be in their country without somebody saying "Oh, that's just blood and soil like from the nazis.""

"There is a jewish strategy. The great part of the jewish strategy is that most of it is pretty much open source. If you want to push your children really, really hard to survive and if you want to tell them "You've got a dragon breathing fire down the back of your neck because you've always been oppressed and you never know when you have to leave very quickly on short notice", you can duplicate the jewish experience. Good luck!"

"Black Lives Matter was a piece of genus called declarative marketing. I don't know if you've ever heard of it via products in the 1970's called "Gee, Your Hair Smells Terrific" or "I Can't Believe It's Not Butter!" was the name of the product. So the name of the product is called Black Lives Matter. How can you disagree with that?"

"… In her new book, “The Shame Machine,” the writer and data scientist Cathy O’Neil, writing with Stephen Baker, examines how shame has been both commodified and weaponized by a society that is increasingly estranged from real life. Who stands to profit from our ubiquitous shame-driven culture wars? she wonders. And is there anything to be gained from them? … … O’Neil suggests that we enter treacherous waters when we start -ing people online; it is a fantasy to believe that it does anything other than enrich ."

"The tech giants are paying millions of dollars to the operators of clickbait pages, bankrolling the deterioration of information ecosystems around the world. Shame is a potent mechanism to turn a systemic injustice against the targets of the injustice. Someone might say, “This is your fault” (for poor people or people with addictions), or “This is beyond you” (for algorithms), and that label of unworthiness often is sufficient to get the people targeted with that shame to stop asking questions."

"... She is an academic mathematician turned Wall Street quant turned data scientist who has been involved in and recently started an algorithmic auditing company. She is one of the strongest voices speaking out for limiting the ways we allow algorithms to influence our lives and against the notion that an algorithm, because it is implemented by an unemotional machine, cannot perpetrate bias or injustice."

"For shame machines, there is nothing more profitable than a painful and intractable scourge shrouded in mystery. False promises sell, and since they don’t work, the market stays strong. Failure, in fact, is central to the dieting business model, fueling earnings for giants like and . They profit from a never-ending stream of shame-addled, self-loathing repeat customers. Weight Watchers’ former chief financial officer, Richard Samber, told ' that 84 percent of the customers failed in their diets and cycled back to the company. “That’s where your business comes from,” he said."