## Archive for the ‘books’ Category

### Uğur Şahin, Özlem Türeci and The Vaccine

October 4, 2021

I have just read the book ‘The Vaccine’ by Joe Miller, Uğur Şahin and Özlem Türeci. More precisely, I read the German version which is called ‘Projekt Lightspeed’ but I am assuming that the contents are not too different. The quality of the language in the version I read is high and I conclude from this that it is likely that both the quality of the language in the original and the quality of the translation are high. Miller is a journalist while Şahin and Türeci are the main protagonists of the story told in the book. It is the story of how the husband and wife team of researchers developed the BioNTech vaccine against COVID-19, a story which I found more gripping than fictional thrillers. The geographical centre of the story is Mainz. Şahin and Türeci live there and the headquarters of BioNTech, the company they founded, is also there. In fact when I moved to Mainz in 2013 I lived just a couple of hundred metres from what is now the area occupied by the BioNTech. Since I was interested in biotechnology the building was interesting for me. My first encounter with Şahin was a public lecture he gave about cancer immunotherapy in February 2015 and which I wrote about here. I heard him again in a keynote talk he gave at a conference at EMBL about cancer immunotherapy in February 2017. I was interested to hear his talk but it seems that it did not catch my attention since I did not mention it in the account I wrote of that meeting. One of the last lectures I attended live before the pandemic made such things impossible was at the university medical centre here in Mainz on 13th February 2020. Şahin was the chairman. The speaker was Melanie Brinkmann and the subject the persistence of herpes viruses in the host. I did not detect any trace of the theme COVID-19 in the meeting that day except for the fact that the speaker complained that she was getting asked so many questions on that subject on a daily basis. Later on she attained some public prominence in Germany in the discussion of measures against the pandemic. The book is less about the science of the subject than about the human story involved. I have no doubt that the scientific content is correct but it is not very deep. That is not the main subject of the book.

I now come to the story itself. Şahin and Türeci are both Germans whose parents came to Germany from Turkey. They studied medicine and they met during the practical part of their studies. They were both affected by seeing patients dying of cancer while medicine was helpless to prevent it. They decided they wanted to change the situation and have pursued that goal with remarkable consistency since then. They later came to the University of Mainz. They founded a biotechnology company called Ganymed producing monoclonal antibodies which was eventually sold for several hundred million Euros. They then went on to found BioNTech with the aim of using mRNA technology for cancer immunotherapy. An important role was played by money provided by the Strüngmann brothers. They had become billionaires through their company Hexal which sold generic drugs. They were relatively independent of the usual mechanisms of the financial markets and this was a big advantage for BioNTech. (A side remark: I learned from the book that the capital NT in the middle of the company name stands for ‘new technology’.) In early January 2020 Şahin foresaw the importance of COVID-19 and immediately began a project to apply the mRNA technology of BioNTech to develop a vaccine. The book is the story of many of the obstacles which he and Türeci had to overcome to attain this goal. In the US the vaccine is associated with the name Pfizer and it is important to mention at this point what the role of Pfizer was, namely to provide money and logistics. The main ideas came from Şahin and Türeci. Of course no important scientific development is due to one or two people alone and there are many contributions. In this case a central contribution came from Katalin Karikó.

How does the BioNTech vaccine work? The central idea of an mRNA vaccine is as follows. The aim is to introduce certain proteins into the body which are similar to ones found in the virus. The immune response to these proteins will then also act against the virus. What is actually injected is mRNA and that is then translated into the desired proteins by the cellular machinery. To start with the sequences of relevant proteins must be identified and corresponding mRNA molecules produced in vitro based on a DNA template. The RNA does not only contain the code for the protein but also extra elements which influence the way in which it behaves or is treated within a cell. In addition it is coated with some lipids which protect it from degradation by certain enzymes and help it to enter cells. Karikó played a central role in the development of this lipid technology. After the RNA has been injected it has to get into cells. A good target cell type are the dendritic cells which take up material from their surroundings by macropinocytosis. They then produce proteins based on the RNA template, cut them up into small peptides and display these on their surface. They also move to the lymph nodes. There they can present the antigens to T cells, which get activated. For T cells to get activated a second signal is also necessary and it is fortunate that mRNA can provide such a signal – in the language of vaccines it shows a natural adjuvant activity. In many more popular accounts of the role of the immune system in the vaccination against COVID-19 antibodies are the central subject. In fact according to the book many vaccine developers are somewhat fixated on antibodies and underestimate the role of T cells. There Şahin had to do a lot of convincing. It is nevertheless the case that antibodies are very important in this story and there is one point which I do not understand. Antibodies are produced by B cells and in order to do so they must be activated by the antigen. For this to happen the antigen must be visible outside the cells. So how do proteins produced in dendritic cells get exported so that B cells can see them?

I admire Şahin and Türeci very much. This has two aspects. The first is their amazing achievement in producing the vaccine against COVID-19 in record time. However there is also another aspect which I find very important. It is related to what I have learned about these two people from the book and from other sources. It has to do with a human quality which I find very important and which I believe is not appreciated as it should be in our society. This is humility. In their work Şahin and Türeci have been extremely ambitious but it seems to me that in their private life they have remained humble and this makes them an example to be followed.

### Lisa Eckhart and her novel Omama

October 2, 2020

Lisa Eckhart is a young Austrian known for a type of comedy which is called Kabarett in German-speaking countries. Characteristic features of this form of entertainment are black humour and political content. In her stage performances she likes to break taboos and flout political correctness. I first happened to see her on TV and I was immediately interested by her performance. Since then I saw her on stage in Mainz, shortly before COVID-19 made going to the theatre impossible for some time. I had also previously seen another Austrian proponent of the same type of performance who I appreciate a lot, Josef Hader, on stage in Mainz. Recently Eckhart published her first novel, ‘Omama’, and I now read it. In her stage performances there are some obstacles to understanding. The first is that her humour relies essentially on ambiguity. The second is that the whole thing goes very fast. The third is that she likes to mix in quite a lot of Austrian dialect. I thought that if there is some similarity between the contents of the novel and that of the performances it might help me to understand more. After all, a novel can be read at the speed the reader desires and it is possible to take time to investigate anything which is unclear. Recently there has been some public controversy in Germany around Eckhart. She has been accused of antisemitism, which I do not believe is justified. In August she was supposed to give a reading from her novel at a literature festival in Hamburg. Her invitation was withdrawn because the organisers were afraid that her appearance there might lead to violent protests by left-wing groups which the police would not be able to control. I find the fact that such a thing can happen a disgrace. What happened to free speech? Later the organisers renewed the invitation in a modified form but this time Eckhart refused, which I can understand. On Wednesday evening I went to read the last few pages of the book but before I got properly started I was called by my wife, who was watching TV. When I came into the living room I understood why she had called me since Lisa Eckhart was on the screen. She was participating in a program on the channel ARTE on the subject of decadence. The word decadence was one which had not gone through my mind for many years but it interested me a long time ago. At that time I read ‘A Rebours’ by Huysmans, ‘Le Soleil des Morts’ by Mauclair and, of course, ‘Les Fleurs du Mal’. Looking back it is hard to imagine how different my world was then, a fact that has less to do with a change in the world than with a change in myself. In any case, when I think about it, it is clear that we are now living in a period of decadence.

Let me finally come to the novel itself. It struck me as a curate’s egg. Parts of it are very good. There are passages where I appreciate the humour and I find the author’s use of language impressive. On a more global level I do not find the text attractive. It is the story of the narrator’s grandmother. (Here is a marginal note for the mathematical reader. Walter Rudin, known for his analysis textbooks, was born in Austria. In  a biographical text about him I read that one of his grandmothers was referred to as ‘Omama’.) The expressions are often very crude, with a large dose of excrement and other unpleasant aspects of the human body, and many elements of the story seem to me pointless. There is no single character in the novel who I find attractive. This is in contrast to the novel of Banine which I previously wrote about, where I find the narrator attractive. That novel also contains plenty of crude expressions but there are more than enough positive things to make up for it. I would like to emphasize that just because I find a novel unpleasant to read it does not mean I judge it negatively. A book which I found very unpleasant was ‘Alexis ou le traite du vain combat’ by Marguerite  Yourcenar but in that case my conclusion was that it could only be so unpleasant because it was so well written. I do not have the same feeling about Omama. As to the insight which I hoped I might get for Eckhart’s stage performances I have not seen it yet, but maybe I will notice a benefit the next time I experience a stage performance by her.

### The plague priest of Annaberg

March 26, 2020

I find accounts of epidemics, whether documentary or fictional, fascinating. I appreciated texts of this kind by Camus (La Peste), Defoe (Journal of the Plague Year) and Giono (Le Hussard sur le Toit). This interest is reflected in a number of posts in this blog, for instance this one on the influenza pandemic of 1918. At the moment we all have the opportunity to experience what a pandemic is like, some of us more than others. In such a situation there are two basic points of view, depending on whether you see the events as concerning other people or whether you feel that you are yourself one of the potential victims. The choice of one of these points of view probably does not depend mainly on the external circumstances, except in extreme cases, and is more dependent on individual psychology. I do feel that the present COVID-19 pandemic concerns me personally. This is because Germany, where I live, is one of the countries with the most total cases at the moment, after China, Italy, USA and Spain. Every evening I study the new data in the Situation Reports of the WHO. The numbers to be found in the Internet are sometimes quite inconsistent. This can be explained by the time delays in reporting, the differences in the definitions of classes of infected individuals used by different people or organizations and unfortunately in some cases by poltically motivated lies. My strategy for extracting real information from this data is to stick to one source I believe to be competent and trustworthy (the WHO) and to concentrate on the relative differences between one day and the next and one country and another in order to be able to see trends. I find interesting the extent to which diagrams coming from mathematical models have found their way into the media reporting of this subject. Prediction is a high priority for many people at the moment.

Motivated by this background I started to read a historical novel by Gertrud Busch called ‘Der Pestpfarrer von Annaberg’ [the plague priest of Annaberg] which I got from my wife. The main character in the book is a person who really existed but many of the events reported there are fictional. Annaberg is a town in Germany, in the area called ‘Erzgebirge’, the literal English translation of whose name is ‘Ore mountains’. This mountain range lies on the border between Germany and the Czech republic. People were attracted there by the discovery of valuable mineral deposits. In particular, starting in the late fifteenth century, there was a kind of gold rush there (Berggeschrey), with the difference that the metal which caused it was silver rather than gold. My wife was born and grew up in that area and for this reason I have spent some time in Annaberg and other places close to there. The narrator of the book is Wolfgang Uhle, a priest in the Erzgebirge in the sixteenth century active in Annaberg during the outbreak of plague there. In fact in the end only a small part of the book concerns the plague itself but I am glad I read it. The author has created a striking picture of the point of view of the narrator, at a great distance from the modern world.

During Uhle’s first period as a priest there was a fire in a neighbouring village which destroyed many houses. He saved the life of a young girl, in fact a small child, who was playing in a burning house. Much to the amusement of the adults the girl said she would marry him when she was old enough. In fact she meant it very seriously and when she was old enough it did happen that after some difficulties she got engaged to him. The tragedy of Wolfgang Uhle is that he had a temper which was sometimes uncontrollable. Before the marriage took place he once got into a rage due to the disgraceful behaviour of the judge in his village. Unfortunately at that moment he was holding a large hammer in his hand. A young girl had asked him if a stone she had brought him was valuable. He had some knowledge of geology and he intended to use the hammer to break open the stone and find out more about its composition. In his sudden rage he hit the judge on the head with the hammer and killed him. He went home in a state of shock without any plan but his housekeeper brought him to flee over the border into Bohemia. He was sentenced to death in absentia and hid in the woods for five years. The girl who he was engaged to repudiated him, stamped on his engagement ring and quickly married another man. He partly lived from what he could find in nature, living at first in a cave. Later he started working together with a charcoal burner. I learned something about what that industry was like when I visited those woods myself a few years ago. Eventually he revealed his identity and had to leave.

In the woods he met a man who had got lost and asked him the way. The man wanted to go to Bärenstein, which is the town where my wife spent her childhood. He agreed to show him the way. The man told him that the plague had broken out in Annaberg and that the town was desperately searching for a priest to tend to the spiritual needs of the sick. Uhle decided that he should volunteer, despite the danger. He saw this as God giving him a chance to make amends for his crime. He wrote letters to the local prince and the authorities of the town. The prince agreed to grant him a pardon in return for his service as priest for the people infected with the plague. He then went to Annaberg and tended to the sick, without regard to the danger he was putting himself in. There is not much description of the plague itself in the book. There is a key scene where he meets his former love on her deathbed and it turns out that she had continued to love him and felt guilty for having abandoned him. Uhle survives the plague, gets a new position as a priest, marries and has children. This book was different from what I expected when I started reading it. Actually the fact that it was so different from things I otherwise encounter made it worthwhile for me to read it.

### Sard’s theorem

December 27, 2019

I have recently been reading Smoller’s book ‘Shock Waves and Reaction-Diffusion Equations’ as background for a course on reaction-diffusion equations I am giving. In this context I came across the subject of Sard’s theorem. This is a result which I had more or less forgotten about although I was very familiar with it while writing my PhD thesis more than thirty years ago. I read about it at that time in Hirsch’s book ‘Differential Topology’, which was an important reference for my thesis. Now I had the idea that this might be something which could be useful for my present research, without having an explicit application in mind. It is a technique which has a different flavour from those I usually apply. The theorem concerns a (sufficiently) smooth mapping between $n$-dimensional manifolds. It is a local result so that it is a enough to concentrate on the case where the domain of the mapping is a suitable subset of Euclidean space and the range is the same space. We define a regular value of $f$ to be a point $y$ such that the derivative of $f$ is invertible at each point $x$ with $f(x)=y$. A singular value is a point of the range which is not a regular value. The statement of Sard’s theorem is that the set $Z$ of singular values has measure zero. By covering the domain with a countable family of cubes we can reduce the proof to the case of a cube. Next we write the cube as the union of $N^n$ cubes, by dividing each side of the original cube into $N$ equal parts. We need to estimate the contribution to the measure of $Z$  from each of the small cubes. Suppose that $y_0$ is a singular value, so that there is a point $x_0$ where the derivative of $f$ is not invertible with $f(x_0)=y_0$. Consider now the contribution to the measure of the image from the cube in which $x_0$ lies. On that cube $f$ can be approximated by its first order Taylor polynomial at $x_0$. The image is contained in the product of a subset of a hyperplane whose volume is of the order $N^{-(n-1)}$ and an interval whose length is of the order $\epsilon N^{-1}$ for an $\epsilon$ which we can choose as small as desired. Adding over the at most $N^n$ cubes which contribute gives a bound for the measure of the set of singular values of order $\epsilon$. Since $\epsilon$ was arbitrary this completes the proof. In words we can describe this argument as follows. The volume of the image of a region which intersects the set of singular points under a suitable linear mapping is small compared to the volume of the region itself and the volume of the image under the nonlinear mapping can be bounded by the corresponding quantity for the linear mapping up to an error which is small compared to the volume defined by the linear mapping.

### Ernst Jünger

December 25, 2019

The two German writers I admire most are Ernst Jünger and Hermann Hesse (not necessarily in that order). This might cause some surprise since these two authors are so different. There are, however, some telling similarities. One is that both are appreciated relatively little in their own country and have had a better reception in France. (As some evidence for this I mention that the Magazine Littéraire had a special issue on Hesse (No. 318, February 1994) and that there is an article on Jünger in the issue ‘Ecrire la guerre’ (No. 378, July-August 1999).) Another, which is not unrelated, is that both were individualists who did not fit well into the political categories of their society. In Germany Jünger has a widespread reputation (particularly among people who have not read him) as a Nazi. It is true that he had relations to the party in the very early days but he had sufficient opportunity to regret that later. His book ‘In Stahlgewittern’ was a favourite of Adolf Hitler but an author cannot be held responsible for his readers. This book has more generally been a source of animosity towards Jünger. In this context there is a story which I think is enlightening. Jünger was an officer in the German army which occupied Paris. He attempted to visit André Gide at his home but Gide did not receive him. This was based on prejudice since at that time Gide had read none of Jünger’s books. When he later read ‘In Stahlgewittern’ he called it ‘the best book ever written about war’ and completely changed his attitude to Jünger. Unfortunately, after the first opportunity had been missed, the two never met. (I no longer remember where I read about Gide’s statement and so the quote is only approximate.) I agree with Gide’s judgement on the book. Some people may be put off by the objectivity of the book – this also applies to other writings of Jünger. It does not waste time with general talk about how bad war is. Instead it shows directly how terrible war is for the benefit of those of us fortunate enough never to have experienced it directly.

The book of Jünger which ignited my enthusiasm for his writing is ‘Afrikanische Spiele’. This is a work of fiction but it is based rather closely on Jünger’s own experiences. He was often bored in school and preferred to read adventure stories. For him Africa was the land of adventure and he wanted to go there. He ran away from school and travelled to Verdun, where he enlisted in the Foreign Legion. He was then stationed in Algeria. This was not his real aim and so he deserted and tried to travel further. He was caught and put into prison in solitary confinement. A doctor in the place he was stationed wrote to his father. Since in fact Jünger was not old enough to have joined the foreign legion and had only managed to do so by lying about his age his father was able to get him discharged and took him home. Shortly after he returned the First World War began and Jünger enlisted immediately and had his opportunity for adventure, as related in ‘In Stahlgewittern’. One thing which attracts me to Jüngers writing, in ‘Afrikanische Spiele’ and elsewhere, is the style. At the same time, the content is often remarkable. Here is a striking example. The hero of the book has taken some money with him when he left home. He feels the danger that he might give up and not dare to carry out his plan. To avoid this he takes all the money he has and puts in down a drain in Verdun. In this way he removes the chance of turning back. This reminds me a little of the story of how Nansen became the first to cross the Greenland icecap. He chose the direction of crossing in such a way that failure would have meant almost certain death.

In a previous post I mentioned that I had read a book about Jünger by Banine. I now read her book ‘Rencontres avec Ernst Jünger’. She wrote more than one book about him and I think this is not the same one I read before. The reason is that apart from describing events from the time of the Second World War in Paris she also describes how she visited Jünger in Tübingen after the war. The copy of the book I am reading is from the university library. Interestingly it contains a stamp ‘Don du Gouvernement Français’ [gift of the French government]. It would be interesting to know how that came about. According to the description in the book it was hard for Banine and Jünger to form a warm personal relationship – the positive aspects of their communication during the time in Paris were on a purely intellectual level. It has been a pleasure reading Banine again. She too is a stylist who I appreciate a lot. There are also interesting facts. Banine mentions that Jünger had read neither Proust nor Huxley and that when she gave him their books to read he did not appreciate them. She tells the story of his meeting with Madame Cardot, a Jewish woman who ran a bookshop in Paris throughout the war. The first time he came into her shop (in uniform) the first thing he did was to thank her for having displayed his book ‘Gärten und Strassen’ (in French translation) prominently in her window. This was the start of an unusual friendship. When they met on the street they usually avoiding giving any sign that they knew each other for practical reasons. When they met for the last time it was on the street in July 1944 and Jünger whispered to her ‘in a few weeks you will be rid of us’.

I will mention a passage in ‘Gärten und Strassen’ which particularly struck me and which Banine mentions in her book. In this book Jünger described his experiences during the German invasion of France in the Second World War. This time, in contrast with what happened in the First World War, he was hardly involved in the fighting at all. At one time he was the commanding officer in the town of Laon. Laon has a magnificent gothic cathedral, which I have visited myself. He describes his experience of looking at this cathedral, for whose safety he was responsible at that time, and feeling that this huge building was like a small vulnerable creature. He was successful in preventing treasures from the cathedral being stolen or destroyed, helped by the fact that those who might have done so did not realize how valuable these things were.

Despite my admiration for Jünger’s writings there is one thing which I do not like and which I feel I have to mention. This is a tendency to esotericism which he shows from time to time and which I just try to ignore. Despite this I am sure that I will continue to read Jünger with pleasure in the future.

### Cedric Villani’s autobiography

November 1, 2019

I have just read Cédric Villani’s autobiographical book ‘Théorème Vivant’. I gave the German translation of the book to Eva as a present. I thought it might give her some more insight into what it is like to be a mathematician and give her some fortitude in putting up with a mathematician as a husband. Since I had not read the book before I decided to read it in parallel. I preferred to read the original and so got myself that. With hindsight I do not think it made so much difference that I read it in French instead of German. I think that the book is useful for giving non-experts a picture of the life of a mathematician (and not just that of a mathematician who is as famous as Villani has become). For this I believe that it is useful that the book contains some pieces of mathematical text which are incomprehensible for the lay person and some raw TeX source-code. I think that they convey information even in the absence of an understanding of the content. On the other hand, this does require a high level of tolerance on the part of the reader. Fortunately Eva was able to show this tolerance and I think she did enjoy the book and learn something more about mathematics and mathematicians.

For me the experience was of course different. The central theme of the book is a proof of Villani and Clement Mouhot of the existence of Landau damping, a phenomenon in plasma physics. I have not tried to enter into the details of that proof but it is a subject which is relatively close to things I used to work on in the past and I was familiar with the concept of Landau damping a long time ago. I even invested quite a lot of time into the related phenomenon of the Jeans instability in astrophysics, unfortunately without significant results. Thus I had some relation to the mathematics. It is also the case that I know many of the people mentioned in the book personally. Sometimes when Villani mentions a person without revealing their name I know who is meant. As far as I remember the first time I met Villani was at a conference in the village of Anogia in Crete in the summer of 2001. At that time he struck me as the number one climber of peaks of technical difficulty in the study of the Boltzmann equation. I do not know if at that time he already dressed in the eccentric way he does today. I do not remember anything like that.

For me the book was pleasant to read and entertaining and I can recommend it to mathematicians and non-mathematicians. If I ask myself what I really learned from the book in the end then I am not sure. One thing it has made me think of is how far I have got away from mainstream mathematics. A key element of the book is that the work described there got Villani a Fields medal, the most prestigious of mathematical prizes. These days the work of most Fields medallists is on things to which I do not have the slightest relation. Villani was the last exception to that rule. Of course this is a result of the general fact that communication between different mathematical specialities is so hard. The Fields medal is awarded at the International Congress of Mathematicians which takes place every four years. That conference used to be very attractive for me but now I have not been to one since that in 2006 in Madrid and I imagine that I will not go to another. That one was marked by the special excitement surrounding Perelman’s refusal of the Fields medal which he was offered for his work on the Poincaré conjecture. Another sign of the change in my orientation is that I am no longer even a member of the American Mathematical Society, probably the most important such society in the world. I will continue to follow my dreams, whatever they may be. Villani is also following his dreams. I knew that he had gone into politics, becoming a member of parliament. I was surprised to learn that he has recently become a candidate for the next election to become mayor of Paris.

### Science as a literary pursuit

August 24, 2019

I found something in a footnote in the book of Oliver Sacks I mentioned in the previous post which attracted my attention. There is a citation from a letter of Jonathan Miller to Sacks with the idea of a love of science which is purely literary. Sacks suggests that his own love of science was of this type and that that is the reason that he had no success as a laboratory scientist. I feel that my own love for science has a strong literary component, or at least a strong component which is under the control of language. In molecular biology there are many things which have to be named and people have demonstrated a lot of originality in inventing those names. I find the language of molecular biology very attractive in a way which has a considerable independence from the actual meaning of the words. I expect that there are other people for whom this jungle of terminology acts as a barrier to entering a certain subject. In my case it draws me in. In my basic field, mathematics, the terminology and language is also a source of pleasure for me. I find it stimulating that everyday words are often used with a quite different meaning in mathematics. This bane of many starting students is a charm of the subject for me. Personal taste plays a strong role in these things. String theory is another area where there is a considerable need for inventing names. There too a lot of originality has been invested but in that case the result is not at at all to my taste. I emphasize that when I say that I am not talking about the content, but about the form.

The idea of using the same words with different meanings has a systematic development in mathematics in context of topos theory. I learned about this through a lecture of Ioan James which I heard many years ago with the title ‘topology over a base’. What is the idea? For topological spaces $X$ there are many definitions and many statements which can be formulated using them, true or false. Suppose now we have two topological spaces $X$ and $B$ and a suitable continuous mapping from $X$ to $B$. Given a definition for a topological space $X$ (a topological space is called (A) if it has the property (1)) we may think of a corresponding property for topological spaces over a base. A topological space $X$ over a base $B$ is called (A) if it has property (2). Suppose now that I formulate a true sentence for topological spaces and suppose that each property which is used in the sentence has an analogue for topological spaces over a base. If I now interpret the sentence as relating to topological spaces over a base under what circumstances is it still true? If we have a large supply of statements where the truth of the statement is preserved then this provides a powerful machine for proving new theorems with no extra effort. A similar example which is better known and where it is easier (at least for me) to guess good definitions is where each property is replaced by one including equivariance under the action of a certain group.

Different mathematicians have different channels by which they make contact with their subject. There is an algebraic channel which means starting to calculate, to manipulate symbols, as a route to understanding. There is a geometric channel which means using schematic pictures to aid understanding. There is a combinatoric channel which means arranging the mathematical objects to be studied in a certain way. There is a linguistic channel, where the names of the objects play an important role. There is a logical channel, where formal implications are the centre of the process. There may be many more possibilities. For me the linguistic channel is very important. The intriguing name of a mathematical object can be enough to provide me with a strong motivation to understand what it means. The geometric channel is also very important. In my work schematic pictures which may be purely mental are of key importance for formulating conjectures or carrying out proofs. By contrast the other channels are less accessible to me. The algebraic channel is problematic because I tend to make many mistakes when calculating. I find it difficult enough just to transfer a formula correctly from one piece of paper to another. As a child I was good in mental arithmetic but somehow that and related abilities got lost quite early. The combinatoric channel is one where I have a psychological problem. Sometimes I see myself surrounded by a large number of mathematical objects which should be arranged in a clever way and this leads to a feeling of helplessness. Of course I use the logical channel but that is usually on a relatively concrete level and not the level of building abstract constructs.

Does all this lead to any conclusion? It would make sense for me to think more about my motivations in doing (and teaching) mathematics in one way or another. This might allow me to do better mathematics on the one hand and to have more pleasure in doing so on the other hand.

### Encounter with an aardvark

August 21, 2019

When I was a schoolboy we did not have many books at home. As a result I spent a lot of time reading those which were available to me. One of them was a middle-sized dictionary. It is perhaps not surprising that I attached a special significance to the first word which was defined in that dictionary. At that time it was usual, and I see it as reasonable, that articles did not belong to the list of words which the dictionary was responsible for defining. For this reason ‘a’ was not the first word on the list and instead it was ‘aardvark’. From the dictionary I learned that an aardvark is an animal and roughly what kind of animal it is. I also learned something about its etymology (it was an etymological dictionary) and that it originates from Dutch words meaning ‘earth’ and ‘pig’. Later in life I saw pictures of aardvarks in books and saw them in TV programmes, but without paying special attention to them. The aardvark remained more of an intriguing abstraction for me than an animal.

Yesterday, in Saarbrücken zoo, I walked into a room and saw an aardvark in front of me. Suddenly the abstraction turned into a very concrete animal pacing methodically around its enclosure. I had a certain feeling of unreality. I do not know if aardvarks always walk like that or whether it was just a habit which this individual had acquired by being confined to a limited space. Each time it returned (reappearing after having disappeared into a region not visible to me) the impression of unreality was heightened. I was reminded of the films of dinosaurs which sometimes come on TV, where the computer-reconstructed movements of the animals look very unrealistic to me. Seeing the aardvark I asked myself, ‘if mankind only knew this animal from fossil remains would it ever have been possible to reconstruct the gait I now see before me?’

As a schoolboy I read that dictionary a lot but I did not read it from beginning to end. For comparison, I am reading the autobiography ‘On the Move: A Life’ of Oliver Sacks and he tells the following story. As a student he won a cash prize and used the money to buy a copy of the Oxford English Dictionary in 12 volumes. He read it from beginning to end. I do feel a certain sympathy for him in this matter but it is an example of the fact that he seems to have been excessive in many things, to an extent which creates a distance between him and me. The book is well written and contains a lot of very good stories and I can recommend it. Nevertheless it is not one of those autobiographies which leads me to identify with the author or to admire them greatly. At this point I have only read about a quarter of the book and so my impression may yet change. I had previously read some of his books with pleasure, ‘Awakenings’, The Man Who Mistook His Wife for a Hat’ and ‘An Anthropologist on Mars’ and it was interesting to learn more about the man behind the books.

Another animal I encountered in the Saarbrücken zoo is a species whose existence I did not know of before. This is Pallas’s cat. This is a wild cat with a very unusual and engaging look. The name Pallas has a special meaning for me for the following reason. When I was young and a keen birdwatcher some of the birds which were most exciting for me were rare vagrants from Siberia which had been brought to Europe by unusual weather conditions. A number of these are named after Pallas. I knew almost nothing about the man Pallas. Now I have filled in some background. In particular I learned that he was a German born in Berlin who was sent on expeditions to Siberia by Catherine the Great.

### Light and lighthouses

June 3, 2019

I recently had the idea that I should improve my university web pages. The most important thing was to give a new presentation of my research. At the same time I had the idea that the picture of me on the main page was not very appropriate for attracting people’s attention and I decided to replace it with a different one. Now I have a picture of me in front of the lighthouse ‘Les Éclaireurs’ in the Beagle Channel, taken by my wife. I always felt a special attachment to lighthouses. This was related to the fact that as a child I very much liked the adventure of visiting uninhabited or sparsely inhabited small islands and these islands usually had lighthouses on them. This was in particular true in the case of Auskerry, an island which I visited during several summers to ring birds, especially storm petrels. I wrote some more about this in my very first post on this blog. For me the lighthouse is a symbol of adventure and of things which are far away and not so easy to reach. In this sense it is an appropriate symbol for how I feel about research. There too the goals are far away and hard to reach. In this context I am reminded of a text of Marcel Proust which is quoted by Mikhail Gromov in the preface to his book ‘Metric structures for Riemannian and non-Riemannian spaces’:

‘Même ceux qui furent favorables à ma perception des vérités que je voulais ensuite graver dans le temple, me félicitèrent de les avoir découvertes au microscope, quand je m’étais au contraire servi d’un télescope pour apercevoir des choses, très petites en effet, mais parce qu’elles étaient situées à une grande distance, et qui étaient chacune un monde’

[Even those who were favourable to my perception of the truths which I wanted to engrave in the temple, congratulated me on having discovered them with a microscope, when on the contrary I used a telescope to perceive things, in fact very small, but because they were situated at a great distance, and each of which was a world in itself.]

I feel absolutely in harmony with that text. Returning to lighthouses, I think they are also embedded in my unconscious. Years ago, I was fascinated by lucid dreams. A lucid dream usually includes a key moment, where lucidity begins, i.e. where the dreamer becomes conscious of being in a dream. In one example I experienced this moment was brought about by the fact of simultaneously seeing three lighthouses, those of Copinsay, Auskerry and the Brough of Birsay. Since I knew that in reality it is impossible to see all three at the same time this made it clear to me that I must be dreaming.

The function of a lighthouse is to use light to convey information and to allow people (seafarers) to recognise things which are important for them. Thus a lighthouse is a natural symbol for such concepts as truth, reason, reliability, learning and science. These concepts are of course also associated with the idea of light itself, that which allows us to see things. These are the elements which characterize the phase of history called the enlightenment. Sometimes I fear that we are now entering a phase which is just the opposite of that. Perhaps it could be called the age of obscurity. It is characterized by an increasing amount of lies, deceit, ignorance and superstition. Science continues its progress but sometimes it seems to me like a thin ray among gathering darkness. A future historian might describe the arch leading from the eighteenth to the twenty-first century. I recently watched a video of the Commencement speech of Angela Merkel in Harvard. In a way many of the things she said were commonplaces, nothing new, but listening to her speech and seeing the reactions of the audience it became clear to me that it is important these days to repeat these simple truths. Those of us who have not forgotten them should propagate them. And with some luck, the age of obscurity may yet be averted.

### Book on cancer therapy using immune checkpoints, part 2

April 20, 2019

I now finished reading the book of Graeber I wrote about in the last post. Here are some additional comments. Chapter 7 is about CAR T cells, a topic which I wrote about briefly here. I also mentioned in that post that there is a mathematical model related to this in the literature but I have not got around to studying it. Chapter 8 is a summary of the present state of cancer immunotherapy while the last chapter is mainly concerned with an individual case where PD-1 therapy showed a remarkable success but the patient, while against all odds still alive, is still not cancer-free. It should not be forgotten that the impressive success stories in this field are accompanied by numerous failures and the book also reports at length on what these failures can look like for individual patients.

For me the subject of this book is the most exciting topic in medicine I know at the moment. It is very dynamic with numerous clinical studies taking place. It is suggested in the book that there is a lot of redundancy in this and correspondingly a lot of waste, financial and human. My dream is that progress in this area could be helped by more theoretical input. What do I mean by progress? There are three directions which occur to me. (1) Improving the proportion of patients with a given type of cancer who respond by modifying a therapy or replacing it by a different one. (2) Identifying in advance which patients with a given type of cancer will respond to which therapy, so as to allow rational choices between therapies in individual cases. (3) Identifying new types of cancer which are promising targets for a given therapy. By theoretical input I mean getting a better mechanistic understanding of the ways in which given therapies work and using that to obtain a better understanding of the conditions needed for success. The dream goes further with the hope that this theoretical input could be improved by the formulation and analysis of mathematical models.

What indications are there that this dream can lead to something real? I have already mentioned one mathematical model related to CAR T-cells. I have mentioned a mechanistic model for PD-1 by Mellman and collaborators here. This has been made into a mathematical model in a 2018 article by Arulraj and Barik (PLoS ONE 13(10): e0206232). There is a mathematical model for CTLA-4 by Jansson et al. (J. Immunol. 175, 1575) and it has been extended to model the effects of related immunotherapy in a 2018 paper of Ganesan et al. (BMC Med. Inform. Decis. Mak. 18,37).

I conclude by discussing one topic which is not mentioned in the book. In Mainz (where I live) there is a company called BIONTECH with 850 employees whose business is cancer immunotherapy. The CEO of the company is Ugur Sahin, who is also a professor at the University of Mainz. I have heard a couple of talks by him, which were on a relatively general level. I did not really understand what his speciality is, only that it has something to do with mRNA. I now tried to learn some more about this and I realised that there is a relation to a topic mentioned in the book, that of cold and hot tumours. The most favourable situation for immune checkpoint therapies is where a tumour does in principle generate a strong immune response and has adapted to switch that off. Then the therapy can switch it back on. This is the case of a hot tumour, which exhibits a lot of mutations and where enough of these mutations are visible to the immune system. By contrast for a cold tumour, with no obvious mutations, there is no basis for the therapy to work on. The idea of the type of therapy being developed by Sahin and collaborators is as follows (my preliminary understanding). First analyse DNA and RNA from the tumour of a patient to identify existing mutations. Then try to determine by bioinformatic methods which of these mutations could be presented effectively by the MHC molecules of the patients. This leads to candidate proteins which might stimulate the immune system to attack the tumour cells. Now synthesise mRNA coding for those proteins and use it as a vaccine. The results of the first trials of this technique are reported in a 2017 paper in Nature 547, 222. It has 295 citations in Web of Science which indicates that it has attracted some attention.