Biography of Perelman by Masha Gessen

Masha Gessen first came to my attention because of the controversy caused by her being awarded the Hannah Arendt Prize in 2023. A week before the planned award ceremony Gessen published an essay in the New Yorker with the title ‘In the Shadow of the Holocaust’. In this essay she portrays the Israeli military actions in the Gaza Strip as being comparable to Nazi liquidations of Jewish ghettos. I have written about this issue elsewhere (in German) and I will say no more about it here. While trying to find out more about this person I discovered that she had written a biography of Grigori Perelman with the title ‘Perfect Rigor’. Perelman is one of the most remarkable mathematicians of recent years. He resolved one of the most famous open problems in mathematics, the Poincaré conjecture, formulated in 1904. For this he was offered a Fields medal in 2006, the most prestigious award in mathematics, which he refused. Later, in 2010, he was offered a one million dollar prize by the Clay Foundation, which he also refused, despite living in poverty. As I mentioned in previous posts here and here I had the privilege to hear the first lecture which Perelman gave on his proof of the Poincare conjecture and afterwards I went to a cafe with him together with colleagues, so that I was able to get a further personal impression of him. Masha Gessen was never able to talk to Perelman because by the time she was working on her book he had completely withdrawn from public contacts. She was, however, able to talk to people who had known Perelman very well. She also has special insights into the world in which Perelman grew up in the Soviet Union since she grew up in the same society.

Masha Gessen is not a mathematician although she did apparently have a good school education in mathematics. For that reason her ability to write about the Poincaré conjecture itself is limited. What she does write on that is imprecise in a way which is likely to be a little irritating for people who know the subject fairly well and could be confusing for professional mathematicians with no special knowledge of the subject. However that is only a small part of the book. The main subjects are Perelman himself, the people around him and the society around him. In the previous post where I mentioned Perelman I compared him to another famous mathematician who refused prestigious prizes, Grothendieck. Now I still see similarities between the two men but also major differences. Grothendieck was a very political person and his motivation for refusing prizes probably came mainly from politics. Perelman, as he is portrayed in the book, is very different. He sees it as a disgrace for a mathematician to pay attention to politics. For him mathematics is much more important and valuable than politics. His reasons for refusing prizes are rather personal. He is absolutely convinced of the value of his work and he is not prepared to accept that others (who understand less about the subject than himself) should judge it. The book was written before Perelman had been awarded the Clay prize but at that time it already seemed probable that he would not accept it. At that time his complaint was that it should have been given equally to him and Richard Hamilton, on whose work he had built. However other examples are given where Perelman refuses something for a certain reason, the offer is modified to remove this obstacle and he still refuses. It seems that in a way Perelman was an exceptionally honest person but that he often kept his motives hidden. I notice that I am talking about Perelman here in the past tense and the reason is that he long ago cut off all contact with the rest of the world, with the exception of his mother. It should be mentioned that his mother herself wanted to become a professional mathematician but was prevented from doing so by antisemitism and sexism.

An interesting aspect of the book for me is the picture it gives of mathematics in the Soviet Union, something which was previously just a black box for me. Another is that I know some of the people who play a role in the book personally and I also experienced some aspects of the ICM in Madrid described in the book myself, for instance the lecture of Hamilton, and it is interesting to have some of the background to what I saw revealed. I did not specially like the way the book is written but it certainly kept my attention and I did learn a lot.

The Bell Jar by Sylvia Plath

I recently bought the novel ‘The Bell Jar’ by Sylvia Plath. This came about as follows. I have now lived in Mainz for over ten years. Bookshops exert a strong attraction on me. It is therefore strange that I had never entered the shop ‘Shakespeare and so …’ which I must have passed very many times. Now I have done so. I had nothing special in mind and I had no definite plan to buy anything. I spent quite some time looking around the shelves and in the end I did buy a book, ‘The Bell Jar’ by Sylvia Plath. I knew the title of the book and the name of the author but not much more than that. So why did I feel attracted to it? I guess that it is due to the fact that forty years ago Ali Smith talked to me positively about the author. I do not know if this is really the case but it seems to me plausible. I suppose that the recommendation has slumbered in my unconscious all the time and was brought out again by the chance encounter with the book. I did once have a flat-mate who was writing a PhD on Ted Hughes, the husband of Sylvia Plath, but I do not think that the recommendation came from him. In fact I must have read at least one poem by Plath at that time since on the way home the following fragment which must have been lodged in my memory came into my mind: ‘ebon in the hedges fat’. After I got home I was able to find out that it comes from a poem called ‘Blackberrying’, which must have impressed me as a student. On the way home in the tram I read the first few pages of the novel and it became clear to me that it was a piece of luck that I had bought the book. I had the delicious experience of beginning to read a book and immediately feeling at home.

Reading the book was a positive experience for me from beginning to end, although it includes things I experienced as frightening perspectives. I had warm feelings towards both the protagonist and the author. The book has now been given a place of honour on the bookshelf containing those books I esteem most. I do not feel that I have to provide a justification for the feelings I have just expressed but I will at least mention a couple of aspects of the book which have played a role in producing these. One is the remarkable objectivity with which Plath describes all kinds of things which in principle could have a strong emotional impact. Here I think of Jünger although the authors’ subjects are so different. A second is the way I experience many of Plath’s sentences. When the sentence starts you think it is going in a certain direction and then it suddenly turns and goes in quite a different one. A third is the fact that the book presents a picture of mental illness as seen from the inside. Here I think of the shell-shocked veteran in Mrs Dalloway who I see as portraying some part of Virginia Woolf’s illness. A fourth is that I was struck by the fact that the main character assesses the attractiveness of men by the sound of their names. I never proceeded in this way when deciding how attractive I found women but in this point, where in a sense language overrules reality, and in several others in the book I felt ‘This could be me’. As a last point I simply mention the great originality of the book which is quite different from any other book I have read. This originality is not just an effect of the book as a whole but instead impregnates the whole text.

Event with Marie-Agnes Strack-Zimmermann

I have a rather poor opinion of most current politicians. An exception is Marie-Agnes Strack-Zimmermann. I have seen her from time to time in short TV appearances and I have also read about her. All this made a positive impression on me. When I saw that she was due to talk at an event at the University of Mainz on Saturday I decided to go there and Eva, who also previously had a positive impression of the speaker, accompanied me. What we experienced at the event strengthened our previous opinion. The speaker came in with a microphone in a very modest way and just started to talk, without any introduction. Strack-Zimmermann is a member of the FDP and is their leading candidate for the coming European elections. This event was certainly part of her campaign for that election and was organized by her party. At the same time it should be emphasized that she did not say ‘vote for me’ but instead ‘go out and vote for a democratic party’, with a particular recommendation not to vote for the AfD or the party of Sahra Wagenknecht who have both explicitly said that they want Germany to leave the EU. I am not a devotee of the FDP. I find some of their policies good and others bad. I went to the event not because Strack-Zimmermann is a member of the FDP but also not in spite of that fact. My motivation was independent of the party she belongs to. We both thought that she made a milder impression than on TV. Probably the reason is that she was in a relatively friendly environment. When she is forced to defend herself against political attacks she is very capable of doing so and then she is less mild. At this event one person did shout out something about peace from the back row. This might have been due to the fact that Strack-Zimmermann is a strong and outspoken supporter of military intervention in the Ukraine by Germany and other Western countries or it might have had to do with Gaza. In any case she was easily able to handle it. In particular she repeated several times, ‘We all want peace’.

Strack-Zimmermann is chair of the defence committee in the German Parliament. Correspondingly her appearances in the media are often related to military themes. She was in the news recently because of her support of providing the Ukraine with the Taurus cruise missile, thus opposing the policy of Chancellor Scholz. She voted in favour of an initiative of the opposition party CDU that Taurus should be provided to the Ukraine. She was the only member of the government to do so. In her presentation yesterday she discussed many political themes and in particular how they all relate to each other. She is qualified to talk about these things because she has been more than once in the Ukraine during the present war, because she has been in other hotspots such as Mali and Niger, because she has spoken personally with one of the Israeli women taken hostage by Hamas and meanwhile released etc. For me it was refreshing to hear a politician talking in a way which struck me as honest, well-informed, experienced, rational and courageous. One thing which surprised me was what she said about the population of Europe compared to that of the world. She gave the figure 5% and I found that very low. In the internet I found the figure 10% which would have surprised me almost as much. Perhaps the explanation for the discrepancy in the figures is that I was not paying enough attention and she mentioned the population of the EU and in that case 5% could be correct. She talked about many political themes, including the Ukraine, China and Taiwan, the US and NATO, the Red Sea and the Houthis and of course Gaza. At the end of her presentation she took questions. An interesting one came from a young woman who identified herself as being in the army. She asked why the German army was not recruiting people from other European countries. Strack-Zimmermann pointed out the following problem. Soldiers in Germany are paid significantly better than soldiers in many other European countries. Thus the danger exists that if Germany tried to recruit in this way this might seriously weaken the armies of allied countries by draining the human resources. She indicated that discussions were underway to find an alternative.

This speech was not recorded but another presentation by Strack-Zimmermann can be found here:

There is quite a lot of overlap in the topics but it was more defiant in tone that what we heard live, as befits an election speech made to politicians.

The call of the north and the voyage of the Vega

I grew up in the Orkney Islands, a place which is further north than most people live. As a schoolboy I had a map of the world on my bedroom wall and I was fascinated by faraway places and travel. A natural consequence of my place of birth is that when I heard about people I knew travelling they were almost always travelling towards the south. For this reason the north seemed to me to be the direction which was most exotic. At one time I started reading books about arctic exploration. One of the first of these, and probably the best, was the book of Fridtjof Nansen about his voyage with his ship Fram. It was a perfect book to capture my imagination about the far north. On the basis of the fact that wreckage from a ship which sank in the Bering Strait was found in Greenland Nansen was convinced that there was a flow of ice in this direction. He decided to let a ship get frozen into the ice near Siberia in the hope that this current would carry it near the North Pole. The Fram was a ship specially built so that when it was squeezed by the surrounding ice it would be lifted to the surface of the ice instead of being crushed and sunk. His plan worked and the Fram was eventually released by the ice near Spitzbergen. He himself left the ship at what he judged to be the most northerly point of its trajectory in an attempt to be the first to reach the North Pole. He did not reach the pole and turned around to reach Franz Josef Land. There he met another expedition which was able to bring him back to civilisation.

Recently a book came into my hands about another arctic explorer, Adolf Erik Nordenskiöld. It is called ‘Nordostpassage’ [northeast passage] and is by Friedrich-Franz von Nordenskjöld, a descendant of the explorer. As the title indicates, the most famous achievement of Nordenskiöld was that he led the first expedition through the northeast passage, i.e. this was the first time that someone had travelled by ship from Europe to the Bering Strait along the north coast of Siberia. This was something which was a worldwide sensation at that time. For instance at the end of his journey he was invited to visit the emperor of Japan. The success of an expedition of this kind depends a lot on luck but I think this particular expedition depended essentially on the personal qualities of its leader. At the same time I had the feeling that he was often stubborn in an unreasonable way. At least he was apparently a lot more competent than Scott on his attempt to reach the South Pole. (Of course once I had started to read about arctic explorers I also had to read about antarctic ones. Cf. my post on my trip to Ushuaia.) The Vega was the ship which successfully achieved the northeast passage. In fact almost the whole voyage was completed in one summer. Unfortunately, when already close to the Bering Strait the ship got caught in the ice and had to spend the winter a short way from its goal. It was necessary to wait until late July before further progress was possible. On the expedition nobody died and no ships sunk, which is not to be taken for granted for an expedition of this kind.

The starting point for the voyage (and for other arctic expeditions of Nordenskiöld) was Tromsø. It was interesting to read that during one visit to Tromsø Nordenskiöld saw the Admiral Tegethoff, an Austrian ship on an unknown mission. I read an account of that expedition a long time ago but I think it was more of a literary work than a documentary one. I do not remember the title. What that expedition actually did was that it discovered Franz Josef Land. I visited Tromsø myself on my first trip to the far north in 1986. In that year I attended my first international conference in Stockholm as a PhD student and the temptation was great to use the opportunity to travel to the north afterwards. I took an overnight train to Kiruna and then travelled further to Abisko. I had a tent with me and camped there, being almost eaten by mosquitoes during the night. After that I switched to youth hostels despite my limited finances. My best memories of Abisko are numerous Bluethroats (I do not think I have seen another one since) and my first Long-Tailed Skuas. I travelled on to the end of the train line in Narvik. From there I took a bus to Tromsø. At midnight I boarded the Hurtigrute and crossed to Svolvaer in the Lofotens. In 1997 I passed Tromsø again on a cruise after visiting Iceland and Spitzbergen but did not spend any time there. I previously wrote something about that cruise here. That cruise also brought me to the most northerly point I have reached up to now in my life which is the Magdalenenfjorden at the north-west corner of Spitzbergen, about 79.5 degrees north. There was a picnic there for the passengers from the ship with sausages and mulled wine. It was not exactly a sublime experience but I was excited to have set foot on Spitzbergen. Another high point of that trip was Jan Mayen. That island is notorious for being covered with fog and I did not expect to see much of it. When we arrived about midnight the fog rose and we had excellent views. The conditions were so good that the ship circled for an hour to let us enjoy it. Most of Jan Mayen is a huge volcano rising straight out of the sea, the Beerenberg which is more than 2000 metres high. It is spectacular sight. The cruise was also due to pass close to Bear Island but I did not realise that. Nordenskiöld was one of the first to make scientific observations on Bear Island. Now Bear Island is probably much less spectacular than Jan Mayen, also usually covered in fog and I would probably have had to get up some time in the middle of the night to see it. Despite that, if I had known I had a chance of that type I would have taken it. The far north exerts an irresistible attraction on me. I have been in Iceland again and spent time in Vardø in the extreme north east of Norway, where I saw a White-Billed Diver. Maybe I will return to the north this summer.

An evening with Dieter Nuhr

Yesterday Eva and I went to a performance by the comedian Dieter Nuhr in Mainz. It was in a building called Halle 45. According to the ticket it was possible to enter the building 30 minutes before the event. We arrived 40 minutes before the event and most of the people were already inside. The capacity of the building is 2000 people but the chairs are moveable and so this can be varied depending on the event. I do not think that there were so many people there yesterday but it was full and there were many hundreds. Due to the circumstances we ended up sitting quite far back, a long way from the stage. This was a bit disappointing since it meant that there was little sense of intimacy with the performer. We had better experiences with performances we have attended by Lisa Eckhart and Josef Hader (twice) in the past in other (smaller) venues.

In recent years, especially since the pandemic, our society has become more and more polarized in its opinions. It would be an oversimplifcation to think that this is only a polarization along one axis, although there are remarkable correlations between opinions on issues which at first sight are quite unrelated. In fact there are fault lines running in different directions and two people who are on opposite sides in one case may be on the same side in another case. In comedy in Germany (and Austria) there is a clear polarization in the political views expressed. This might be formulated in terms of the words ‘left’ and ‘right’ but this is too simple. Often people with extreme right wing views and those with extreme left wing views seem to agree on many subjects. It seems that the topology of the political spectrum is rather that of a circle than that of the real line. Another word which might be used to characterize one direction on this axis is ‘woke’. That direction is the one often propagated by established political parties and state media in Germany. It is fortunately the case that this bias is not complete. There are two state-run TV companies in Germany, ARD and ZDF and while the principal representative of the ‘woke’ direction among the comedians, Jan Böhmermann, has a show with ZDF Dieter Nuhr, the principal representative of the other direction, has a show on ARD. In his show he performs himself part of the time and he also invites other comedians to take the stage. Recently it was often the case that the last person to appear, and in some sense the highlight, was Lisa Eckhart who I have written about in a previous post.

In the description of the event on the web page of Halle 45 it says ‘Ein Abend mit Dieter Nuhr ist Spaß und Therapie zugleich’ [An evening with Dieter Nuhr is fun and therapy at the same time]. Interestingly, during his performance Nuhr said that he did not consider his performance as therapy, or that he did not like it to be considered in that way. Was this statement sincere or was it intended as a joke? In any case it is worth taking a moment to think about in which sense it might be considered therapy. There are some people who at least some of the time (and I consider myself one of these people) do not feel at home in the public consensus presented by politics and media, which could also be associated with the word ‘woke’. They feel themselves confined by certain barriers in an unpleasant way. The ’therapeutic’ aspect of Dieter Nuhr is that in his texts he breaks through these barriers. (The same is true of Eckhart and Hader in their own ways.) I appreciate Dieter Nuhr because I like his humour. At the same time it is not the only reason I appreciate him. I think he has an important role to play in German politics by contributing to a certain balance and helping to prevent public opinion from becoming too extreme in certain directions. For example, he stepped forward to publicly support Lisa Eckhart when she was attacked in the way I described in a previous post. He also exerts a significant influence by his regular appearances on TV.

There is one point I want to mention before ending this post. In the last post I wrote about Karl Lauterbach. In his programme yesterday Nuhr made jokes about Lauterbach in a rather insulting way. (He has also behaved similarly in other places.) For instance he refers to him as the Sensenmann (‘grim reaper’), referring to his pessimism and his appearance. Now I tend to believe that a comedian should have a lot of freedom in making jokes about public figures, even if they might be unpleasant for the people concerned. Correspondingly, Nuhr’s jokes about Lauterbach do not cross the boundary of what is acceptable for me. At the same time I wonder if Nuhr has a particular grievance against Lauterbach and if so what it is. The jokes about Lauterbach were among the few yesterday I did not laugh at.

Postpositive adjectives

As a scientist whose native language is English it often happens that I end up correcting English texts by collaborators, other colleagues or students. There is one type of correction which I often had to make where I was not able to identify what exactly was going on. Thus I had difficulties communicating this in any other way than by lists of the examples where the problem occurred. This resulted in my wasting a lot of time. I was able to identify that certain phrases were wrong and give the corresponding corrections but I did not understand, and thus could not explain, why they were wrong. Now I have got some more insight into this problem. In particular I have found a name for the construction that some people were failing to use. It is ‘postpositive adjective’ or ‘postnominal adjective’. Anyone with some knowledge of English knows that an adjective very often comes immediately before the noun it describes, for instance ‘a black cat’. This works the same way in German, ‘eine schwarze Katze’ but in a different way in French, ‘un chat noir’. The last phrase is an example of a postnominal adjective, the adjective comes immediately after the noun. The problem is that postnominal adjectives can also occur in English. An example is ‘the method used’. This is the same in French, ‘la méthode utilisée’ but different in German, ‘die verwendete Methode’. In English it occurs when the adjective is a past participle. On the other hand that does not seem to be universal, as shown by the example ‘an escaped prisoner’. Maybe the point is that while the method is the object of the verb concerned (this is also an example of a postpositive adjective which I used without thinking) the prisoner is the subject of the verb concerned. With this start I will continue to observe.

The Fountainhead

In a recent post I mentioned the novel ‘The Fountainhead’ by Ayn Rand. This motivated me to read the book and I have now done so. I found it enjoyable and compulsive reading. The plot does have something of a TV thriller and this may have to do with the fact that the author had a considerable involvement with Hollywood. This is something which leads the reader on but the book also has interesting aspects of a quite different kind. Probably the most important feature of the central character, Howard Roark, is his uncompromising nature. He is clear about his aims and does everything to achieve them. I have met a few people in real life who are extremely uncompromising and I found that an attractive quality. I will not name them here. Of course it is important to mention that these were people where their uncompromising nature was not linked to a desire to harm, or even destroy, other people. People of the latter kind are only too common and the opposite of heroes for me. The thing which is most foreign to me in ‘The Fountainhead’ is that most of the main characters seem to be sadists, masochists or both. It is not just that they behave in a way I would condemn in many cases but it is often incomprehensible to me why anyone should behave in that way.

One of the central ideas in the book is the importance for the individual of a goal which he really wants to achieve. In contrast, the behaviour of most people is controlled by their desire for recognition by others. I am reminded of the story of Grothendieck who developed integration theory on his own as a student and was not dismayed when he learned that the problem had been solved many years previously by Lebesgue. He was satisfied that he had done it and was not concerned with questions of priority. If I compare this ideal with my own life then I see a mixed picture. Of course what you can do in life, or in a particular field of endeavour, is limited by your talents. However that it not the point here. The most important thing is not the final achievement but the commitment. Howard Roark is not able to change many aspects of the world he lives in which he sees as undesirable but he is able to achieve certain specific goals (while failing to achieve others). In my case I feel that I have spent too little of my life working to achieve elevated goals. At the same time I did often go in those directions I felt to be important, while being little influenced by scientific fashions. This was probably unfavourable for my career but favourable for my happiness. It is enough to allow me to feel myself very far from Peter Keating, the negative example in the novel and the antithesis of Roark.

Another central element in the book is the role of the press in society. The poor quality popular newspaper The Banner and its founder and editor Gail Wynand are key. A question which goes through my head is what analogies exist between the popular press of that time (and its portrait in the book) and the social media of today. I cannot judge this well since I myself hardly have any contact with social media. I nevertheless do seem to detect some similarities. There are evil tendencies out there which come into existence through the collective behaviour of the masses. Often this evil is not being directly caused by some individual. What an individual does is to spread an evil influence which is then absorbed by the masses, develops autonomously and causes damage. This is the method of the journalist Toohey in the novel. He himself compares his activity to applying weedkiller, which is much more effective than tearing out individual plants. He uses this metaphor in the context of destroying the integrity of individuals.

As a last observation I note that one of the jurors in Roarke’s trial at the end of the book, largely chosen by himself, is a mathematician.

Talk on personalized tumour therapy in pediatrics

Yesterday I heard a talk at the Mainzer Medizinische Gesellschaft by Alexandra Russo from the university hospital in Mainz. She is responsible for treating children with cancer in that hospital. She talked about progress in cancer therapy for children, focussing on the situation in Germany. She did also mention international collaborations of her group in Mainz. A positive fact is that 80% of childhood cancers can be cured definitively. In other words the tumour can be eliminated in such a way that it does not return. This sounds much better than the situation for adults. A negative fact is that this percentage has not changed significantly in the last twenty years. Another negative fact is that among those people cured many have long-time side effects resulting from the chemotherapy they had. There was a group of former patients described who had had chemotherapy with a particular substance and many of these young people had hearing aids. Hearing loss is a known side effect of the drug they were treated with. The speaker is enthusiastic and optimistic about being able to change these things by applying personalized therapies. At the moment most treatments are still based on the classical methods: surgery, radiotherapy and chemotherapy. One special feature is that radiotherapy is not used in children under the age of three since the side effects would be too dramatic.

Some special features of treating children were mentioned. One is that it is often necessary to use drugs which are not approved for the treatment of children. There is a law in Germany that new drugs must be tested for their use in children as well as adults. However there are many exceptions to this based on the argument that the disease concerned does not occur in children. For instance children do not get lung cancer. The necessity of off-label use leads to problems with getting the drugs payed for and getting permission from an ethics commission. Even when these problems have been overcome in a given case there are still the problems that for children, due to lack of studies, the correct dosage and the safety profile are not known. The commercially available drugs are not suitable for use in children. For instance a single pill may contain a dose which is much too high for a small child. This means that the drugs must be specially processed by the clinic before they can be used. The speaker proudly showed a picture of a new machine they just got which is a 3-d printer for pills. It is still at the prototype stage but she expects it to bring them great benefits in the near future.

The speaker said that the amount of money spent on therapy in Germany is one of the highest in the world although not as much as in the US. In Britain only about half as much is spent. What is not so good is that much less sequencing is carried out in Germany than in many countries. So when she needs a lot of sequencing for her patients it can be difficult. A method for trying to improve the problems with the studies and approval would be to do studies linked not to a particular type of cancer cell but to a particular type of genetic defect. To make this possible sufficient genetic data about the patients must be obtained. She mentioned the example of Pembrolizumab, which was the first cancer drug to be approved for certain genetic situations rather a specific disease.

In the talk two examples of patients were discussed in some detail. The first was of a boy with a brain tumour who was six years old at diagnosis. It was first diagnosed as an astrocytome but this was later revised to glioblastome. A genetic irregularity was found which is best known from lung cancer. Then the idea was to try to use a drug which had worked in a lung cancer of this type to treat the brain tumour. An extra difficulty was to find a drug which would cross the blood-brain barrier. A drug was found and did have a positive effect. Unfortunately an infection of the patient meant that the treatment had to be discontinued for some time. This led to the tumour getting out of control and the death of the patient. Perhaps if the detailed genetic information had been available more quickly so that a good treatment could have been started more quickly the story would have had a better end. The second example was that of a nine-month baby with apparently swollen lymph nodes which turned out to have a tumour in the neck region. Despite different types of chemotherapy the tumour grew very much until it was acutely life-threatening. In looking for a targetted drug it was again important to have enough genetic information so as to see what signalling pathways were involved in the pathology. It turned out that the MAPK cascade was involved. (My attention is always drawn by the MAPK cascade since I did some work on mathematical models for it.) One way of obtaining information was to culture pieces of tumour in the presence of different drugs to see which ones might be helpful. In this case a suitable drug was found, a MEK inhibitor called cobimetinib. After three weeks treatment the size of the tumour had decreased by 94% and the child could live a relatively normal life. Unfortunately it looks as if the drug must be given indefinitely in order to control the tumour. At the moment the strategy is to try and reduce the dose so as to reduce the side effects.

I have a lot of admiration for someone doing a job like this. It involves intellectual challenges, emotional difficulties and the need for strong practical qualities. In any case, I found the talk fascinating.

The Schauder fixed point theorem and Leray-Schauder theory

The Schauder fixed point theorem is an extension of the Brouwer fixed point theorem to the infinite-dimensional case. I already discussed the former topic in a previous post on degree theory. One good source for the topics of the present post is the book ‘Nonlinear Functional Analysis and its Applications’ by Eberhard Zeidler. When I start reading this book I automatically think of its author, who I experienced as an exceptionally pleasant human being who was very kind to me on several occasions. I first met him in 1991 when I gave a talk at a conference in Leipzig. Some time later he invited me to give talks aimed at students in the DFG project he had at the University of Leipzig at that time. I remember that at one point he stood up spontaneously and talked enthusiastically about the importance of the Brouwer fixed point theorem. He seemed impressed by the fact that I used so many German words (instead of English ones) when lecturing in German. This was not due to my achievements in collecting or inventing German words for mathematical (or physical) concepts but due to the influence of Jürgen Ehlers, who was always careful about the use of language in scientific discussions. While living in East Germany Zeidler had problems with the political system. He was not free to travel and his possibilities of doing research were restricted. Thus he concentrated his efforts on writing textbooks. After German reunification he had more freedom. He was the founding director of the Max Planck Institute for Mathematics in the Sciences in Leipzig in 1996. He then vacated his professorship at the University of Leipzig and suggested to me that I should apply for the position of his successor. I did not do so since I was in a health crisis at that time and I did not dare to take such a big step. If I had decided differently and I had been succesful with that application it would have changed my life in a way which I cannot imagine but would certainly have been fundamental. In particular I would not have met my wife. Zeidler died in 2016.

After this personal excursion I now return to the mathematics. One valuable thing which Zeidler does in the discussion of degree theory in the book and which I had failed to do is to look carefully at the one-dimensional case. This gives an intuition for the meaning of the concept of degree. Consider a continuous mapping from to the real line which is non-zero at both endpoints. If its values at both endpoints have the same sign the degree is zero. If and then the degree is one. If and then it is minus one. In this situation it is clear that the degree is unchanged by continuous deformations of within the class of functions being considered. The actual definition of the degree in the generic case where the zeroes of are non-degenerate is the sum of the signs of at the zeroes of . One version of the Brouwer fixed point theorem says that any continuous mapping from the closed unit ball in to itself has a fixed point. Another replaces the ball by an arbitrary non-empty compact convex set. I will not discuss here how the second, apparently stronger, version follows from the first. It is the second version which is extended in the Schauder fixed point theorem. That theorem says that a compact mapping of a non-empty closed, bounded, convex subset of a Banach space to itself has a fixed point. Here a compact mapping is a continuous one which maps bounded sets to compact sets. In an alternative version of the theorem it is only assumed that the mapping is continuous but it is assumed that the set is compact. This fixed point theorem can be used to develop Leray-Schauder theory. One version of this, discussed in Zeidler’s book, is as follows. Let be a Banach space and a compact mapping. If all solutions of the equation with satisfy for a constant then has a fixed point. Another nice discussion of these topics can be found in the standard textbook on elliptic equations by Gilbarg and Trudinger. They also discuss a more general version of the Leray-Schauder theory where the mapping is replaced by a more general one. In other words the requirement of the linear dependence of the mapping on the parameter is dropped. Here we see the relation to degree theory. They present quite self-contained proofs of these results, modulo the Brouwer fixed point theorem. In fact they do not need that theorem for a general compact convex subset, but only the case of the convex hull of a finite set. The theory can be used to obtain existence theorems for boundary value problems for nonlinear elliptic equations (or initial boundary value problems for nonlinear parabolic equations). The necessary input is a priori estimates together with some compactness. The latter comes from the regularizing properties of solving equations of these kinds. The idea then is to deform the problem to be solved continuously to one which is easier to solve, or even trivial.

The Frankfurt book fair and Ahmad Mansour

Yesterday I went to the Frankfurt book fair. It was the first time I had been to an event of that kind. It was the last day of the fair and I only visited the stands of some of the important scientific publishers in the afternoon. A lot of the companies I am involved with in my own work were there: Springer, Wiley, Taylor and Francis, Princeton University Press, Cambridge University Press, Oxford University Press, World Scientific. Many smaller companies were also represented, including many I did not know. Most of the stands were already more or less empty. I do not know if this would have been different on Saturday, or on Sunday morning. A lot of people seemed to have packed up and gone home. This was not only true for the scientific exhibits. A visit to the part of the fair related to French literature was similarly disappointing. The only thing which appeared to me to be extremely active was the area of children’s books. The cynical idea crossed my mind that perhaps there are many parents who feel that it is their duty to try to make their children read books but that the adults are not so interested in reading books themselves. In any case, if more children read more books I am happy about that. This aspect of the fair, the exhibits, brought me no benefit.

My main motivation for going to the fair this time was to experience the live recording of a discussion by the TV channel Phoenix, where the central participant was Ahmad Mansour, someone who I have mentioned in a previous post. When he came onto the podium Mansour looked a bit nervous to me and in fact my wife made the same comment independently. However his contribution soon became not only competent but also confident. This discussion was related to a series by Diana Kinnert und Harald Welzer which is usually a podcast. This time, exceptionally, they had a guest, Mansour, and a video was produced, which can be seen here. Of course the attack on Israel by Hamas and the reactions to it in Germany were a central theme in the discussion. Welzer quoted a policeman concerning the recent demonstrations in Neukölln who said [my translation] ‘we cannot do more than to try to pick up the pieces which are the result of the failure to integrate these people’. Mansour said that he has repeatedly experienced the following scenario. In response to a certain event mainstream politicians say the right things in public but when he, Mansour, says the same things a few months later people call him a racist for doing so. Mansour said that there is antisemitism on the right, the left and in the centre of politics as well as among Muslims. It is important for him to talk about Muslim antisemitism and about that on the left. Mansour then went on to talk about matters related to cancel culture and mentioned, without naming the organizer, what happened with the workshop of Susanne Schröter, something I discussed in a previous post. Then he went on to discuss post-truth, which he said is destroying political culture, where truth is no longer important but only emotions. At this point I have to remark that scientists and especially mathematicians should have a particular duty and motivation to combat post-truth. Mansour said that he is not interested in being praised for his courage by people who talk to him or send him e-mail. He wants to see these people becoming active themselves and becoming loud. I take the point. The participants in the discussion were looking forward to a pro-Israel demonstration to take place in Berlin later in the day. It did take place. The police estimated ten thousand participants, the organizers a bit more. There were reactions in the media, which I agree with, saying that it was good that a demonstration with this many people took place but that it would have been more appropriate if ten times as many people had attended.

Another person who I had hoped to hear live was Michel Friedman. According to the online programme of the fair, even in the form it is in at present, he should have been talking immediately before Mansour, on the same stage. However that event had been replaced by a quite different one. Maybe I can see him another time. According to the programme he was to give three different presentations at the fair, two of them on Saturday. At least one of them must have taken place, since there are corresponding videos in the internet. One of the videos is here and I can strongly recommend it.