Posts

No rewriting on fiction

More on Dean Wesley Smith. I just find the story of this guy very interesting. You can read it on his blog. To sum up, he started writing and had an initial success, so he decided to go seriously into writing and started to read and learn about writing. Along this path, he took in a lot of myths about the writing process that really harmed him. The outcome: seven years of not being able to write or to write very little (like two short stories a year rather than a short story a week). He even took therapy for four years to overcome his mental obstacles. One day Smith read about Heinlein's rules on the business of writing and everything clicked. The business habits are: You must write. You must finish what you start. You must refrain from rewriting except to editorial order. You must put it on the market. You must keep it on the market until sold. Smith develops each point in his blog (and wrote a non-fiction book about it later). The habit that shocks me the most is number 3, b...

Setting up a challenge and blogging about it

I like this concept of setting a challenge to be accomplished in a given time frame and blogging about it. I have seen the examples set by Dean Wesley Smith on writing a novel in a given time frame. He wrote no-fiction books a fter these experiences. These challenges are a good idea because setting up a challenge publicly gives extra motivation to accomplish it, and blogging about it helps to keep a journal. Keeping a journal helps to keep track of what happened, see what worked and what did not. I wish to be able to set up this type of challenge, especially for students of the undergraduate in maths. It sounds like a lot of fun.  

Emotional leadership

This friend of mine told me something interesting today. He had heard a podcast where  a military leader states that a leader should bring emotional balance to their group. T his also happens when leading a group of researchers.  In leading research groups, there is an important part of the role that is not based on knowledge transfer or experience, but on being an emotional counterbalance: they are too excited, you have to calm them down to avoid over-motivation; they are too nervous, you have to downplay  and relativize; they are anxious, you have to stay calm; they are under-motivated, you have to show excitement and positivity; they think "they are shit", you have to show extra appreciation,... If emotions are too high, you have to bring them down; if they are down, you have to bring them up. The toughest part, though, is to not get infected by their emotional state. For example, it was hard for me to be with a student that showed high signs of anxiety. In the beginni...

Writing into the dark

I read recently a book about discovery writing by Dean Wesley Smith, "Writing into the dark". I am going to give it a go since plotting fiction has not really worked for me (even though I finished a first draft of a novel). In any case, it is very interesting the idea of writing without planning ahead. Scientific writing is completely the opposite. I used to do discovery writing as a child to write short stories, but high school destroyed that. At that time to pass the selection exam, we were taught to plan ahead every type of text. We were even requested to write the skeleton of the text (paragraph by paragraph) and include it as part of the evaluation. The structure of the texts that we were asked to write was very rigid. And writing maths has not helped in this aspect. When I try to write creatively I find it difficult because I feel like I have put a corset on my mind, motion is restricted, creativity is restricted. I think that my "critical voice", as Smith say...

Future trip by train

I will be going to Konstanz (Germany) by the end of this month, and I will be traveling by train. The trip is around 8 hours and a half, and it costs around 270 euros (both ways). I do hope that traveling by train around Europe becomes easier, faster, and cheaper. It would be great if I could avoid taking the plane. However, an 8-hours-and-a-half trip seems a lot to me. This is the first time I try such a long trip.  My plan is to work during the trip. Let's see if that is possible and for how long.  I will post something here when the time comes.  I used to work all the time when I was commuting to London. I was working on the train (around an hour) and on the Picadilly line (around 20 minutes). And b efore Covid times, I did travel a lot. Traveling can be very tiring, but it was very important during that time that I was also able to work during the trips, because they were very time-consuming. Recently I experienced a period when I could not work during the trips (mayb...

Job-hunting and losing well-being

Some years ago, I had a very tough period because of my career. It was the time of job-hunting, the time when I was trying to become independent in my research, and to get a job that could afford me that independence. And it was not easy, especially because I also wanted to be close to my husband. By "close" I mean to have a good connection like a direct flight to wherever my husband was (he is also an academic). The job applications and the interviews became a soul-killer. It is hard to explain how the process worked. It ended up eating me inside. This happens to many. It created wounds. At the moment I did not realize that. I thought that the instant I would get a decent job, I would just forget about all that and move on. That is what I do, leave the past in the past. But it did not happen that way.  I remember starting off in Vienna (actually, the second great job that I got, the first one was at the University of Sussex). In Vienna everything looked great - from the outs...

Working in spurs by alternating projects

I have been changing a bit my working methodology. I pick a project and I work on it intensely, and when I see that my attention or motivation goes down (which tends to happen abruptly), I switch tasks. Sometimes I keep cycling on tasks, but I always find myself doing something that I want to do. And maybe I also find that after a short time (e.g., after half an hour or an hour), I do not want to do that anymore. It is ok, I just look at my list of tasks and I pick the one that "calls" me the most. Curiously, tasks with a coming deadline tend to be on top of my "want-to-do list". I said that ironically, of course. Deadlines are powerful motivators. But I do not pick tasks based only on deadlines. For tasks that are especially energy-consuming, like refereeing a paper, I prefer to work in short bursts, of around half an hour. A bit every day towards the deadline, rather than dedicating continuous hours close to the deadline. Honestly, it makes everything much more en...

A fixed amount of intelligence?

I am not even going to try to define "intelligence". Just take the definition you like the most, and it will be good enough for this post. I want to debunk one of the most ingrained myths when studying maths (or actually, any subject): you do not have a fixed amount of intelligence. You can see that very easily on the negative side: can you think better or worse when you are tired, angry, sleepy, or drunk (or on drugs)? Can you think better or worse with a full and heavy stomach? Can you think better or worse when you are suffering from some pain, when there is some loud distracting noise, when you are anxious? I am sure that every time you where in one of those scenarios your capacity for thinking diminished. In the same way, your capacity for thinking can increase: sleeping properly, doing maths, managing your emotions, reading wholesome books, doing sports, eating healthy, having a proper place to study, having healthy self-talk, having nice people around you, speaking pol...

Beliefs... limiting life's possibility

This is a little follow-up on the previous post . I was reading today a writer talk about how some years ago editorials would not like authors that produced "too many" books. "Too many" could mean more than one novel per year. The reason behind this is the belief that prolific authors must produce low-quality novels. Again, another harmful belief. It is not true, but if you believe that, what are the consequences? This reminds me of the sage Sadhguru when he talks about "limiting life's possibility". All the beliefs that we have about the process to do or achieve something just limit life's possibilities. Sadhguru says that we should stop dictating what is possible and what is not possible. It is not possible to produce more than one high-quality novel a year? Well, if you think it is not, you will not be able to do it.

How things should be

Yesterday I watched some basketball. I realized that one of the reasons why I stopped playing basketball is because I had a very clear picture in my mind of how basketball should be played, or better said, the kind of basketball I like to play. And it is mostly team play. But to get a team to play as a team, proper training is needed, because even if individuals are very good, it does not mean that they know how to play together. It also requires that the coach has the willingness to play this way and knows how to coach this team spirit. The reality is that this rarely happens - it is difficult to achieve. The normality is to find a group of individuals that just play together where players either pass the ball, or do not pass the ball. No team plays. But this is life. I had in my picture the perfect scenario, the one I lived as a youngster and I enjoyed the most. But this picture of perfection, of how things "should be", made me stop playing because I could not meet this or ...

We are making it hard for them, and why do we need a bridge course?

When I went to university to study mathematics, the knowledge gap between high-school and university seemed insurmountable. I studied at the Universitat Politecnica of Catalunya (Barcelona) and there were only 50 spots for new students. So, the people that went there were really motivated to study maths. All of them were top of their class in maths, and probably also got top marks in math on the selection exams that we had to take to access university. So, we were supposed to be the best at maths. Yet, in our first exam, only three out of fifty passed. I was devastated. Why the hell had I worked so hard through my previous education? (yes, I was one of those that worked hard) Why couldn't have been taught an adequate level of maths?  The standards of pre-university  education had  been dropping while the university was keeping its standards. That was around 20 years ago. It seems that things have gotten worse. I did not have a "transition" course to fill up the gap - but ...

A nice morning tricked by maths

I had this question in my mind (a math question), it popped yesterday in my head and I had to wait patiently until this morning to be able to examine it. I dug into it immediately after breakfast. Since I had a list of tasks planned for this morning, I decided that I would dedicate just one hour to explore the problem. But that's the issue with curiosity: one hour does not suffice. Lunchtime came, "Already? I guess I have to stop". And I had to stop, there were other things happening after lunch: meetings and admin and stuff. The morning was over. Three hours and a half had passed flying by while thinking and jotting down some computations on a page. What a nice feeling. The initial pile of work had not been reduced. I did not stick to my original schedule. But, do not blame me, from time to time, a researcher cannot help doing research.

Be yourself, relax

  "Tension is who you think you should be, relaxation is who you are" - Chinese proverb

If my inbox gets out of control, my mind does too!

I do not know how people manage their email, but for a long time it felt like the devil itself had invented it. It felt like a source of distraction, time waste, and stress. Seeing all those messages piling up, thinking of the person behind them waiting for a response, and getting them at any time was driving me crazy. And there was the guilt. The guilt of not responding to them or if I responded to them, then the guilt of not doing something that was "more important". At times it felt that either I replied to emails or I did research, there was not enough time to do both. With emails sometimes I was frozen in the process of decision-making, "what do I do with this email?" And they would stay in my inbox and I would keep reading the subject line, again and again, every time I opened the inbox anew. What a waste of time and energy. It also hindered my capacity to take action. The solution for me came with an 'empty inbox' policy. The only thing that gives me ...

Working with experimental biologists: providing food for thought

Maths are rigorous, complete, and "correct". By "correct" I mean that we can prove that our statements are true. But when we apply maths to investigate biological systems, we cannot prove anything about these systems - actually, we cannot prove anything in applied science - we can just provide theories and evidence in support of those theories. Science is revisionistic and there is no amount of mathematics that will ever change that.  So when we apply mathematics to study biological systems, the goal is never to prove that a theory is true.  I see my research in collaboration with biologists as providing 'food for thought', for example: 1. When we collaborate, our discussions offer different points of view and ways of structuring thought and the research project. 2. While we cannot provide 'proof', modeling can offer a new interpretation of biological events. 3. The model can point to new directions to explore or spark new questions. This happens esp...

Some days just go by like that

I do not know what happened today, the day just went past me and I did not realize it. It felt as if the day was way shorter than usual. I have worked all day and my pile of work has increased rather than diminished. What has happened? How did the hours slip by so quickly? Probably it was because of the decision-making. Today I had quite a few decisions to make and difficult emails to write and those take a lot of time, but they do not make me feel productive. Tomorrow I am taking back "control" of time again. This is just a psychological trick that consists of "ticking boxes" like emptying the inbox or fulfilling a given task to the end (e.g., sending a referee report). This gives me a sense of accomplishment and I need these little things from time to time in this sea of long projects that I am navigating.

Robbing opportunities with the inner voice

On the surface it may seem that we are giving equal opportunities to everyone to study mathematics at university. Of course, we know that it is not completely true because many factors play an important role, like differences in economic and social background - being well off and having people supporting you makes opportunities seem more real. Still, the fact is that, where I am, everyone has the right to go to university and, therefore, everyone has the right to study mathematics. But even before going to university, children and youngsters may already have been robbed of the opportunity, not because of lack of financial or external support, but by lack of internal support. Robbing opportunities this way works very simply: convince children that they are inferior to others (because, e.g., they belong to a given group), convince them that they cannot do it, convince them that they do not belong somewhere. This process will create an inner voice in the child that will whisper relentless...

Do it, NOW!

This quote in Someday is today  by Matthew Dicks resonates so much with me: "One of the primary stumbling blocks for most of the creative and entrepreneurial people I meet is the inability to actually launch their endeavor. Rather than saying yes and leaping into the abyss, people wait, calculate, ponder, and prepare. There is always a better time. The right time. Conditions that must be met in order to achieve the perfect time. They also tend to cling to their original vision, unable to see divergent paths and new opportunities. They have dreamed of a single thing for a long time, and as a result, they cannot reconfigure, reimagine, or pivot to something new. They can’t say yes to a new possibility because they remain locked on their original dream. But instead of waiting, you must say yes. You must launch, regardless of your state of preparation or accumulation of resources. Perfection is insidious. The desire for perfection is nothing more than fear masquerading as something el...

Congrats, Dr Plunder!

Today Steffen Plunder defended his thesis. He is the first PhD student to graduate that I have supervised on my own. We did it! A PhD is a long project that requires a high level of motivation and self-management. It is time to look back at the path walked and all the challenges that were faced. Steffen did great and will start soon to work as a post-doc at the University of Kyoto.  It is hard to write right now. The defense finished like an hour ago and everything feels still a bit unreal. Words are not coming to me. 

Writing with purpose

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A tip from editor Harry Dewulf on how to edit novels: understand the objective of every chapter, every scene, and every paragraph (even every sentence and word), and ask yourself if they are fulfilling their purpose. This is so different from life: in life things happen that do not seem to serve any purpose (maybe we make up a purpose a posteriori), but in storytelling, every element should serve the story in some way; it is not about filling pages. I find that this is even truer in academic texts: every word should count and serve the purpose of conveying your message, because that is the fundamental goal of any text. In a novel, the first sentence, paragraph, and chapter are what need more revision. Dewulf recommends to first-time writers to erase the first chapter altogether: typically the real story starts in the second paragraph of the second chapter. Link to the interview (by The Creative Penn): 

Difficult style in other fields

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I am taking a course on scientific writing and today we analyzed a text brought by another student. Apparently, it is the standard style of how people write in her field. I found very hard to understand the abstract: Dobson, Amy Shields, and Akane Kanai. "From “can-do” girls to insecure and angry: Affective dissonances in young women’s post-recessional media."  Feminist Media Studies  19.6 (2019): 771-786. It feels that written communication has become very complex in some disciplines, but it is not only due to jargon. I feel it is over-complicated, but this over-complication is considered good writing.  It reminds me of legalistic documents (in that case texts are over-complicated on purpose so that only people in the field can understand them).  Anyway, I tried to change the text according to what I understood, just as an exercise. I tried to keep the vocabulary of the field like "feeling rules" and "affective dissonance", whatever they mean. I am still ...

Mixing discovery writing and outlining

Yesterday I was watching a video about discovery writing, i.e., writing without outlining: the writer does not know  a priori   how the story will unfold - the story is being "discovered" as it is being written.  I used this technique  at school,  without realizing it, to write short stories, and it is very satisfying. But the problem with discovery writing is that you may not get a good finalization for the story - which is highly unsatisfying. However, many writers do discovery writing because it is the one that resembles the most the process of reading. You can hear discoverer writers say, "if I know the end, why would I want to write the story?" Outliners, on the other hand, are on the other side of the spectrum: they have a clear structure of the book divided into scenes and what happens in each scene. The full plot is known before writing, so you can make sure that everything is coherent and has a satisfying ending. However, the drawback of outlining is th...

"Many" does not create dispersion, but balance

I do not know what caused it, but today I finally realized this: it does me good to have many pursuits. However, there were many periods of my life where I focused on just one thing. I did focus only on math as an undergraduate. I even dropped out from basketball. I wanted to devote myself body and soul to maths so that I could become the best I could be. I ended up burned out and "fleeing" to France for an Erasmus because I was very unhappy. Something similar happened later when I was hyper-focused on my research career. And I burned out a second time. Now I have many pursuits and interests: research, writing, coaching, doing videos, ukulele, a husband. And I give importance to all of them - I try not to be defined by just one of them. Having so many pursuits - even though it is sometimes overwhelming -   feels  good. It gives me well-being; balance - it keeps me away from obsession. This reminded me of some things that author Matthew Dicks wrote in his book "Someday is...

Ingermanson and the Snowflake method for outlining

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Randy Ingermanson came up with the "Snowflake method" for outlining novels. It is an analytical approach to plotting, based on iteratively refining ideas for the novel.  I will give this method a try. Given that I am quite analytical myself (Ingermanson is a doctor in Physics), maybe his method will suit me well. I will not explain the method here, but I give a link at the end. I was listening to an interview with Ingermanson and there are  three particular points that thought of sharing: 1. The one-sentence summary.  The first step of the snowflake method - there are ten steps in total - consists of writing down a one-sentence summary of the novel. This is actually pretty difficult to do and, therefore, easy to get stuck there. Ingermanson recommends dedicating just one hour to this process and then moving on to the next step. This is not a problem because after each step we can revise and update the previous ones, so this one sentence will evolve during the process. I l...

The goal and its process

In Zen philosophy, we are encouraged to focus more on the process needed to achieve a goal, rather than on the goal itself. Of course, goals are important - they give direction, - the point is that the process and the final product are not separated from each other - the process is part of the goal . Eckhart Tolle asks something along the lines: 'If in the end you achieve your goals, but you become depleted, was it worth it?'. That is why we are encouraged to take care of the process and live it joyfully - to avoid becoming victims of our achievements.  I was thinking about how many of our goals - when looking at them holistically - can be seen as processes. Say I write a blog post. One could think that my goal is the final product: the post. But I do not write to have a product - at least not just because of that. As a creator, I have two processes in mind: my own writing process, and the reader's reading process. My actual objective - producing a blog post - is just a mea...

You are a group leader, not a super-hero

Going from a post-doc position to a group leader position is a big jump. For me, the biggest difference is to have people under my care. And I use the expression "under my care" on purpose: I feel responsible for them - at least to an extent. This puts pressure. However, what puts more pressure on me is the mentality of "now I am a group leader", i.e., I have a new identity and I have to live up to its expectations. And what happens when group leaders feel that are not meeting their own standards? Group leaders may feel like hiding their own lack of knowledge and weaknesses. This is human, but also devastating. When leaders try to hide their vulnerabilities, they avoid situations of growth: asking questions, meeting people, starting discussions. Not only that, every situation is about " what does this say about me?" rather than being about the project, the people, the lesson. In the end, every situation becomes a potential threat - a threat to their ident...

Going line by line with a student

When a PhD student produces a new piece of maths, checking its correctness can be very daunting. Typically, there is a high communication barrier: it is simply not easy to communicate maths. In this case, I think that  going line by line through their document - having the PhD student next to you - may be the best strategy; even though it is very time-consuming.  Going line by line with them can be good because they can see at which points their explanation is not clear; at which points notation is not consistent or definitions are ambiguous; where more details are needed. In this sense, it also saves time and energy: trying to understand the text while having its writer at hand to ask questions can make the process less tedious and faster. Of course, I am talking about documents where the student wants to check out the math, not just editing a text to make it understandable.  If it is just editing, I am hoping that the text will be clear enough so that I would not need t...

A hidden perk of blogging: the revision

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After more than a week of starting this blog, I realized that there is something about it that I really like: the revision part. Normally I write quite a lot by doing journaling and putting down ideas or random thoughts. But this type of writing, even though it feels nice, it never gets a proper revision - it is never written having in mind that someone else may read it. I like the revision part: the purification of the text, the evolution of the original idea, killing the darlings, erasing unnecessary words, and reducing the text as much as possible. With a big text, revision can be tedious, but blog entries are bite size.  It is the revision process that gives me the feeling of getting a final product and the satisfaction that comes with it. There is also an inner transformation during the process - sometimes the original message can transmute. Brandon Sanderson - I already talked about this author - wrote more than ten novels before getting published, but he never got down to ac...

PhD supervision style: hands-on or hands-off?

There was a time when I doubted that meeting PhD students every week and getting involved in their projects was a good way of supervising and doing research. When I started supervising I met my PhD students once a week, but I was trying not to get too involved in their projects. Already by meeting them so often, I was  feeling a bit guilty and unsure: "Is this the right thing to do? Will this affect their independence and their development as a researcher?" A common type of supervisor that one finds in pure maths is the "hands-off" supervisor , they will typically say: "This is your project, not mine, do not come to me until you get results or get stuck; then, we discuss - and Latex everything before coming". Typically, students are a bit left on their own to struggle and try to find their way by themselves. Many times advisors give students projects and they do not work on them. T he project of the student is only theirs: it is not the project of the supe...

Doing educational videos... or trying

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 I decided to do educational videos and post them on YouTube.  Today I posted the first video. After having made it, I realized that: - I do not pronounce well some words; - my voice stills sounds funny to me; - some things are not going to be completely clear to the students (I should have defined better some notation!) - it took a lot of time to actually do it, even though each part of the process does not take so long; - I was left with the doubt "Do I want to do this again?" Everyone warns you that the first video is going to be crap. Well, they are right in my case, but I am just glad that it is out there. I hope to keep posting and improving. I heard that it takes around 20 videos to start doing something decent. Hopefully, I will not stop now.

The dangers of retirement

For Christmas, I went back home to Spain and I noticed something that I have been trying to assimilate since then: many of the people I know and love have become old.  I am not talking about the type of "old age" that we associate with physical decay. I felt that they have become old because they only seem interested in the past, or rather, they do not seem interested in their present or their future unless they have something to do with the younger generation - their kids and grandchildren. I was shocked because I need to let go of the past to focus on the present and the future. There are so many things happening now, so many things to plan, to decide, and choices to make, why would I spend so much time in the past? But I guess that when you have been a parent and you have had a career, it may be tough to think of any other project as more engaging than those. When do we stop thinking about the possibilities in life? Are they looking forward to something in the future? I kn...

Actions and choices, starting from Epictetus

I really like the Stoics and Epictetus is my favorite one. H ere are some of his quotes: "Some things are in our control and others not. Things in our control are our opinions, pursuits, desires, aversions, and, in a word, whatever are our own actions ." "There is only one way to happiness and that is to cease worrying about things which are beyond our control " The concept 'action' in the first quote is fundamental and it appears also in many other contexts, like the Zen culture. Epictetus says that under our control are our actions .  The fifth Buddhist remembrance says "My only possessions are my actions. I cannot avoid the consequences of my actions" .  Krishnamurti says " Life is action" . I find these three philosophies to be linked through the concepts of 'action' and 'choice'. If what is under our control are our actions, then we must  choose   our actions . Hence, making the right choices  is the basis of r...

Anxiety in oral presentations

I recently came across young colleagues concerned about how to manage their anxiety when giving oral presentations. I remember the first time I did a talk at a conference. It was during my Ph.D and at the Erwin Schrödinger Institute, in Vienna. Bless the organizers, they had put me on the first day - the last talk in the afternoon. I was not able to listen to any of the talks before mine. I was that nervous. The first day of the conference was lost to me. If I had talked on the last day, I would have been nervous for the whole week. To make things worse, the room was full - I had never been to a conference with so many participants - and the work I was going to present was a continuation of something initiated by two researchers that were there.  The only thing that I was capable of before my talk was to count away the time left for my onstage execution. How to deal with nerves? In the long run,  I think the best is to just keep giving talks - in different contexts, to differe...

Why I write... a blog

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“Writing apparently filled a void I was feeling in my heart, just before I turned thirty.” – Haruki Murakami

Doing what I want

There is a delicate balance between what I want to do and what I must do to "survive".  Now that I am tenured - I have a permanent job, - I have more freedom to decide what to do (how to direct my research, how to run my group, how to teach). There is a lot of freedom in the 'what to do' but also in the 'how', and both are important.  Freedom comes with a price: one must constantly apply it in a conscious way. It is too easy to get swept by inertia; by what is trendy; by what we think others expect from us. Psychologically, it is safer to follow the trend rather than to be authentic.  After all, if we fail, at least we fail "doing what was expected from us". U nder these circumstances,  failure seems more acceptable. On the other hand, succeeding in this manner may be a failure in disguise: a success by consensus may not be a real success.  I do believe that everyone is unique in terms of motivations, skills, beliefs, experiences,..., and what makes ...

More analogies: discovery writer vs researcher

Following the previous post , there are even more analogies between writers and researchers in mathematics. Typically writers are categorized into two types: the discoverers (they write without a plot in mind) or the plotters (the ones that organize all the scenes, the points of view, and the structure). Discoverers do not know what is going to happen next, plotters know everything. Typically writers are in between these two extremes. I think researchers are more the 'discovery' type. We have some kind of end goal that can be more or less vague, and some initial path to get there, but that is where our understanding of the plot ends. When walking the initial path new things are learned, new questions are asked, new curiosity is spiked and new motivation is born. So we keep changing paths, goals, and the story. As a consequence, we create a lot of work that will go to the bin: piles of written papers that will not appear in the end product, but that was necessary to reach the de...

Mathematician as an artist

Tomorrow, back to work. It has been the first long holiday (2 weeks) in a long time. Among other things, I read the book "Someday is today" by the novelist and storyteller Matthew Dicks. I found it great. It is especially useful for creative people that do not manage to find the time (and strategy) to get things going. Dicks is a brave and generous guy: he goes out there and exposes his journey and vulnerabilities. I found him a true source of inspiration. Reading "Someday is today" and "Storyworthy" (another book of his) , I found quite a few analogies between being a researcher (in mathematics) and being an artist: Despair (of not knowing if you will make it or if you will be good enough): Apparently, both Matthew Dicks and Stephen King (and others) had a moment of despair where they thought that they would never become novelists; nobody was going to buy their books. The same tends to happen in maths: PhD students (and post-docs) tend to go through a ...