St. Lamberti Church Oldenburg 27 April 2014 (Quasimodogeniti)

Reading of the Gospel (also sermon text): John 20, 24-29

Now Thomas, who is called the Twin, one of the Twelve, was not with them when Jesus came. Then the other disciples said to him, "We have seen the Lord. But he said to them: Unless I see in his hands the prints of the nails, and put my finger into the prints of the nails, and put my hand into his side, I cannot believe it. And after eight days his disciples were gathered together again, and Thomas was with them. When the doors were shut, Jesus came and stood among them and said, ' Peace be with you! Then he said to Thomas, "Reach out your finger and see my hands, and reach out your hand and put it in my side, and do not be unbelieving, but believing. Thomas answered and said to him, " My Lord and my God! Jesus said to him, "Because you have seen me, Thomas, therefore you believe. Blessed are those who do not see and yet believe.
Jesus performed many other signs before his disciples, which are not written in this book. But these are written so that you may believe that Jesus is the Christ, the Son of God, and that by believing you may have life in his name.

From: Hope for all - The Bible. Brunnen Verlag, Basel, 2003.

Thomas, one of the twelve disciples, who was also called the twin, was not there. That is why the disciples later told him: "We have seen the Lord." But Thomas doubted: "I don't believe it! I'll only believe it when I've seen his pierced hands. I will feel them with my fingers, and I will put my hand into the wound in his side."
Eight days later, the disciples had gathered again. This time Thomas was with them. And although they had locked the doors again, Jesus suddenly stood in their midst and greeted them: "Peace be with you." Then he turned to Thomas: "Put your finger on my pierced hands! Give me your hand and place it in the wound at my side. Doubt no longer, but believe!" Thomas replied: "My Lord and my God!" Jesus said to him: "You believe because you have seen me. How happy can those be who do not see me and yet believe!"

Sermon

Dear congregation, I would like to welcome you to the 3rd university service, which we are holding in the 40th anniversary year of the University of Oldenburg. We are at the beginning of the Easter season of joy and can feel carried by the hope that all will be well and that our path will lead us into the light. Today is the 1st Sunday after Easter, in the church year Quasimodogeniti, which means: like new-born children. Can we believe this today, have trust and accept love, unconditionally and without mistrust, like a child who has just come into the world and allows himself to be enveloped in the love of his parents and neighbours? For my son, who has just turned seven, the matter is still clear: "I don't know yet whether I will believe one day, but I do believe!" And that says a lot about trust in God, which perhaps often doesn't come so easily to us grown-ups. "Because believing means taking something for true that you can't see, trusting in something that may never exist. In the age of reason, believing in God seems not only unreasonable, but naïve. "1 However, the children's words also address the doubts that overcome each and every one of us when we do not see what we want to believe in, when what we experience does not match our experience, when we were not there and were not able to see what happened with our own eyes. In this respect, Doubting Thomas, whom I got to know as the unbelieving Thomas when I was at school, is a modern figure who points the way for faith in our time: Questioning is allowed! Thomas heard about the resurrection and yet did not understand it. He could not believe that Jesus had conquered death. So he asked doubting questions and asked for proof. Jesus allows this request without rebuking Thomas, and even more: He pays special attention to the doubting Thomas2. Jesus himself offers Thomas the proof he is asking for: "Put your finger on my pierced hands! Give me your hand and place it in the wound at my side." And to his own surprise, Thomas suddenly no longer needs the proof that had just seemed so central to him in order to trust and believe. It is not reported whether Thomas actually touches the Risen Lord. Centuries of Christian art show Thomas putting his finger in the wound. The text says nothing about this. For me, Ernst Barlach's sculpture "Christ and Thomas" captures the essence of the situation well when he lets Thomas sink into Jesus' arms: My Lord and my God.

¹ DIE ZEIT, 19.12.2013. Faith.
^{2 Dr A. Rinn-Maurer, Mainz}

Asking questions, not just accepting everything, understanding for yourself before believing others - these are the cornerstones of what I would like to pass on to my students of mathematics or those who need mathematics as a tool, even today, in the benefit-orientated, rushed times of Bachelor's and Master's degree programmes. In this respect, I like the doubting Thomas. Perhaps he would have turned to maths in another barrier-free society and studied philosophy. After all, maths, my subject and my passion, is more of a humanities and certainly not a natural science. A formal language, in search of beautiful patterns and repetitive structures that are used for characterisation. Numbers are a prominent actor, but not the only one and not the most important one either. And no, maths is not arithmetic with letters instead of numbers, as many of my non-maths students put it when they want to put into words their fear of the error-free abstract thinking that I demand of them. In this way, school, no doubt unconsciously, gives children and young people images to take with them that become ingrained. My son when asked by his godfather what school was like: "I actually like all the subjects, except religion, we always have to draw! Unfortunately, music has replaced maths as his favourite subject, and Mr Götting's organ has played its part in this, as have the "boring" arithmetic packets in the book. So let's dive into mathematical thinking together. Let's start with the numbers we are surrounded by, the ones we need to measure. I'm sure many of you have already dealt with the question of the largest number. The children's question: "How big is the biggest number?" I rephrase it quite correctly as "Does the set of natural numbers have an upper bound?" and I have already brought out the image of "I always found maths incomprehensible" (if not worse) in many of you. But we can prove the whole thing with a game. We take our counting numbers 1,2,3,4,5 ... (maths calls them natural), and you think of a large number from this set that you think is the largest. You and I know that no matter which number you take, adding 1 will result in a larger number. So I simply choose your number plus 1, and your number has already lost the winning position of "the largest" on the podium. This type of proof is called indirect, and with our little game we have proven the opposite of the statement "There is one largest number". Well, I would now explain to the students in the first semester that this is more of a heuristic preliminary stage and that you have to write everything down again from the back for the correct proof so that it is also formally correct. Many people felt the need to continue doing maths with this infinitely large object, which is not a number. As early as the 17th century, Mr Wallis assigned it the symbol of a horizontal eight ∞. It seems tempting to do a little maths with this non-number, for example to look at "1 through infinity", i.e. the reciprocal value. If everything is correct, the result must be an infinitely small non-number. We can describe such infinitesimal numbers by the fact that they are closer to zero than any other non-zero number. The amazing thing is that with a somewhat shirt-sleeved approach, which we like to attribute to physicists, you can formally calculate quite well with them. Even an entire theory, that of non-standard calculus, can be based on this infinitesimal non-number object. The contentious and controversial contemporary historian of mathematics Detlef Spalt has pointed out that the historical changes that the nature of mathematical objects undergo3 must be taken into account (and this is too rarely done) in order to appreciate earlier mathematical works. With this approach to infinitesimals, he succeeds in rescuing supposedly false results from Cauchy, who was actually a recognised great mathematician of the early 19th century. This subjective historical element is irritating. Mathematical truth requires a proof that deduces what is postulated from assumptions (in short: it is) and permissible logical rules of inference or refutes it by means of a counterexample. How the proof is carried out follows from the idea, the creativity of the mathematician, who is a child of his time in terms of language and figurative imagination. (In the 1930s strictly formal from the school of Bourbaki, today increasingly supported by colourful images from the computer). What is accepted as a proof is a social convention of the mathematical community and for many of us also has to do with a sense of mathematical elegance and aesthetics4. The proof, an indisputable sign of mathematical truth, therefore has to do with the people who write and recognise it, just as we can ask about the author, the historical and social context and the narrative mission of linguistic texts, including biblical texts. I would like to surprise you once again with how entertaining mathematical questions and proofs can be. We all think we know for sure: If you give away half, you have less than before. Is that really always true? Instead of numbers, let's turn our attention to counting. This cultural technique is related to measuring, but the answer to the questions is the same, less or more? My daughter's school readiness (among other things, of course) was determined in this way: You see a row of cars and a row of beads here - are there more cars or more beads? One solution is to add a bead to each car and see if and where (among the cars or the beads) there is a remainder. And thus we have imitated Georg Cantor's ingenious idea: with a one-to-one relationship between cars and pearls, there are the same number.

³ D. Spalt, Completeness as the goal of historical explication. A case study. Collegium Logicum 1, 1995, pp. 26-36
^{4 DIE ZEIT, 27 April 2006, WISSEN: Das bittere Ende der Logik}

And so back to the (infinitely many!) counting numbers. Even and odd numbers differ in whether they can be divided by two with or without a remainder. And since every even number has exactly one odd partner, you could say because of this one-to-one relationship: there are as many even as odd numbers. Does this mean that half of all counting numbers are even? After all, every second (odd) number is missing. Surprisingly, you can number all even numbers and numbering means: There is a one-to-one relationship, so there are just as many even numbers as there are counting numbers. Terms such as "fewer" or "half as many" must therefore be interpreted differently when it comes to sets with an infinite number of elements. Mathematics calls the number of elements in a set its power. In the case of counting numbers, we call the power and speak of "countably infinite". Infinity is therefore quite large, ∞ or - and irritatingly different. We understand what it is not and yet, despite proof, we can't quite grasp it exactly. If we allow ourselves to look at theological science at this point, we realise that the question of the true person of Jesus, i.e. the coexistence of the divine and human nature of Jesus, faces a similar dilemma. And we once again understand Thomas, who first wants to have the earthly Jesus back with whom he had been travelling before he can accept the new nature, before he can trust and believe. The Council of Chalcedon in 4515 ended years of theological controversy about the natures of Jesus Christ with the words "Only-begotten in two natures unmixed, unchanged, undivided and undivided". And behind the paraphrase of what is not, we also see in the choice of words the historical situation from which it was formulated, and we go one better mathematically with the question: Is the number of counting numbers actually the greatest infinity that is mathematically conceivable? Or to put it more formally: Are there quantities that cannot be counted in the sense just introduced? If your school lessons were positively memorable for you, you will remember that all fractions (consisting of positive counting numbers) can also be numbered if you count them over the diagonal paths in an infinitely large square grid. To answer our question: Can it get any bigger? let's look at a nice illustration known in maths as Hilbert's hotel. This has an infinite number of (consecutively numbered) single rooms arranged in a long row. Another guest who knocks can easily find a room by moving all of them one to the right. Using the same argument as with the even numbers, an infinite number of guests travelling in an infinitely long bus can be accommodated in the rooms with odd room numbers (e.g.).

⁵ I owe this tip to Dr R. Hennings, Oldenburg

But even buses, each filled with guests, find space by leaving larger and larger gaps between the guests who have already disembarked (first one room, then two, then three free and so on). This means that the arithmetic of power = , and one could come up with the idea that any infinite set could have power. It is the achievement of Georg Cantor, a mathematician of the late 19th century, to have shown that there are indeed much larger sets that are called uncountable and have the power (and which we need, for example, to give the circle number π a home). The obvious question is: if this continues, can we perhaps demonstrate consistency, i.e. the non-contradiction of mathematics, by operating formally correctly with the proofs themselves as mathematical objects? Questions like these were posed by the burgeoning field of logic at the beginning of the twentieth century, and not only by David Hilbert, who gave his name to the hotel. As early as 1930, Kurt Gödel was able to demonstrate the limits of logic and present an incompleteness theorem at a specialist conference, which led a colleague, John von Neumann, to formulate the following in a letter to Gödel a few months later: "I was able to show that the non-contradiction of mathematics is unprovable." So there are true, albeit unprovable statements, and this gap between provability and truth enables us to prove that there is a gap. This proved that there are always undecidable statements in sufficiently complex theories, i.e. propositions that can neither be proven nor disproven. What could have caused a serious crisis left most mathematicians untouched, even though examples of undecidable theorems were found. Most simply carried on. On the other hand, proving with the computer by checking a large number of special cases, as practised in 1976 with the proof of the four-colour theorem, faced great doubts. In contrast to the confusing machine code, a good proof always shows why something is true. At least that was the case for a long time. Today, many problems have reached such a level of complexity that the mathematical community can no longer check proofs with certainty as to whether they are true or not. If you have now gained an impression of the fact that mathematics as a science is not about utility, but about gaining knowledge within mathematics, you can smile with me at the following anecdote: "A man in a balloon loses his bearings. To find out where he is, the balloonist rappels down to a walker below and asks: "Please, tell me where I am." The walker thinks for a while and replies: "You are under your balloon." It follows from this: The walker must be a pure mathematician, because he has thought before answering, his statement is undoubtedly true, and you can't do anything with the statement." This attitude towards truth may also be considered naïve in today's world, but without it, mathematics would not exist. Incidentally, the anecdote was told on the fringes of one of the legendary conferences of the Max Planck Institute of Mathematics in Bonn, one of the places where even today people are still allowed to think about mathematical questions without using them. Bettina Heintz, who was allowed to conduct what must be called a field study6 on the mathematician species at the MPI, was surprised at how strongly this quest for knowledge takes place in dialogue with other mathematicians and how openly (at a time when many researchers only conduct research in the shadow of their patent attorneys) mathematicians share and discuss results with their community. My own research is about modelling the financial market. The aim is to measure the risk of large financial portfolios with the aim of minimising the total loss (ruin) of companies. We provide models and empirical analyses for financial securities whose future development is uncertain, but (and this is in contrast to natural science) whose current value is already a consequence of mathematical valuation. The modelling of uncertainty on the financial market (for example, due to the psychology of market participants, technological innovation, but also external "shocks" such as natural disasters) is essential. A mathematical model is never real, but is a (hopefully helpful) representation of reality. Even if the correctness of the methods used can of course be proven, there are still limiting theoretical assumptions that I make for my thought experiment. As one of the pioneers in the field, Emanuel Derman7 , puts it, the confusion between the real financial market and the model must lead to disaster and, as blind faith in the model, has in fact already caused more than one banking crisis. What is new and unique in this field is that European policy prescribes standardised models via supervisory law and thus a way of reading existing, i.e. past, data. This is a huge job driver for financial mathematicians, but sets narrow limits to healthy mathematical doubt and the endeavour to do as well as one's mathematical knowledge and individual ability allow. With a cross-comparison to exegesis, one could compare this - admittedly luridly - with a relapse to the time of the Enlightenment and Reformation, and at the very end the question remains: Do you now know how big infinity is? Can you see and touch it? And above all, do you have to? In the course of our lives, we all acquire different ideas about many things, images become fixed in our minds and sometimes we have the opportunity to clear up a few things. Not everything we are taught by the normal realities of life holds true. This applies to maths as well as faith.

⁶ B. Heintz, The inner world of mathematics. On the culture and practice of a proving discipline. Springer, 2000
^{7 E. Derman, Models Behaving Badly. Hoffmann and Campe.2013}

Mathematics remains exciting every day if you persistently keep asking: Why? and in this sense, the attitude of the doubting Thomas is perfectly suited to our profession. And in our time, because the time when the Church did not allow doubts is fortunately far behind us. We can therefore all confidently ask questions and doubt with the tenacity of the mathematician seeking truth, as long as we do not do so in a pessimistic manner, but give the new a chance. Even if, like mathematical infinity, we cannot experience theological eternity haptically. And so - just like Thomas - we don't need the certainty of the lurid headline from Spiegel online on 9 September 2013 "Mathematicians confirm proof of God", in which we meet our friend Kurt Gödel again, who formulated the existence of God as a proven logical theorem as early as 1941 and whose proof could now be carried out without gaps using computers. The ability to believe sometimes comes as a surprise, may be accompanied by doubts and unites - without contradiction - thinking and feeling. I hope that we can all confess with Thomas "My Lord and my God" and that we can enter a bright week together, open to new things and full of trust, in which many things will turn out well. Amen.