# 2020

USELESS ADVICE ON FINDING A JOB (11/15/2020)

Last year when I started my job search, I thought it would be a good idea to collect observations regarding my experience in the form of a supplementary article for future graduates. We are now at the (traditional) peak time for the first wave of postdoctoral and tenure-track applications. Little did I know there would be an unprecedented disruption that would decimate the whole process. In an alternate universe, where there wasn’t a random mutation in some bat that would alter the course of history, I offer the following advice.

In the spring of 2019 it started becoming evident that I would be graduating in the summer of 2020 with my doctorate in mathematics. One of the first things I did was ask PhD students who were graduating in the summer of 2019 how they would advise their former selves, if they could go back in time, to better prepare for the job market. The responses I received included the following:

• Start early! There are a lot of documents to write and everything takes longer than you expect it to take, even when taking this fact into account. I have found this advice to be exceptionally sound. You should start writing your documents in early summer for applications you plan to submit in the fall.
• Late offers come. After the landscape settles, some places haven’t found a good candidate to accept the position and, possibly quite late, might offer you a good position. I have not yet reached this phase but have heard this is true.

To start, I highly recommend two references. These include the website theprofessorisin.com and the early career columns in the Notices, a monthly publication of the American Mathematical Society (AMS). If you are a math PhD student, you might be able to get a free membership with the AMS through your institution and somewhere on their website you can opt-in to receive a monthly physical copy. The early career columns are in sync with the application process and I personally have found them helpful.

The job application process bifurcates into two major categories: academia and B.I.G. jobs. B.I.G. stands for Business, Industry, Government. Furthermore, academia bifurcates into teaching positions and research positions. Many people I know jump straight for the research positions and don’t even bother with the B.I.G. or teaching positions. This brings me to my first word of advice. Be humble. A job you currently think you would never do might just be the best fit for you. Don’t rule out places or opportunities because your background doesn’t completely match the job description or because they are “beneath you”. Be humble.

Even if you are set on doing one particular thing, I encourage you to read through all of the following sections as I frequently say things in one section that are relevant to another section. And keep an open mind.

Teaching Positions

Many institutions where the primary focus is teaching will have an interview booth at the yearly Joint Math Meetings (JMM) in January. While I strongly recommend attending and presenting at this conference in your final year as a PhD student, it is not yet clear to me that it is necessary, especially if you are looking for a research position. I am not sure of a better opportunity for networking though. It wouldn’t hurt to go the year before you graduate as well. Go to Mathfest also. You don’t have to wait until your last year to do these things. I wish someone would have told me that. Math is an isolating profession the way it is, being able to connect with other people doing similar work can be very encouraging.

I had a few interviews at the JMM for such institutions and it is clear that the most common problem they face is that applicants don’t understand what they are getting themselves into. This is probably a failure on the part of the advisor to appropriately signal to the student what the expectations are for such a university (hint: good teaching skills). The one question that I was unfailingly asked at every JMM interview (remember these are for teaching institutions) is what I thought the research/teaching/service expectations were in terms of a percentage. Teaching should take the biggest slice of the pie in this case.

SLACS and Small Teaching Colleges

SLAC stands for selective liberal arts college. The central mission of these institutions is not career-focused (think business, nursing, engineering, etc.) but rather focused on the liberal arts. Many of the less prestigious small colleges frequently hire in-house meaning people who got degrees from small teaching colleges or have some strong connection. This is likely in the interest of faculty retention. If you have experience with such an institution, then you know what you are getting yourself into and won’t back out a few years down the road after realizing the small-town life isn’t for you. SLAC could also stand for small liberal arts colleges and I will use the acronym interchangeably. One thing that I wish I had known was that more prestigious SLACs aren’t likely to hire someone with a freshly minted PhD. They also usually have a higher standard for research. You have to teach well and do good research to land a position at such a place. If you really want to work at one of these places, wait until late January/February for them to post (usually) 3-year visiting positions. These are the positions geared for rookies.

Your chances of getting a tenure-track position fresh out of graduate school are realistic only if you are focused on the remaining SLACs and more teaching based state universities. For such institutions, you really ought to emphasis your teaching abilities, ideas for undergraduate research projects, and service opportunities.

Institutions of Faith

Another option, for those of Christian faith, is to apply to Christian institutions. It should go without saying, if you are going to apply to one of these, you should really be a Christian! If you’re not, it will come up sooner or later and will end up being a waste of everyone’s time. I say should because it is an unfortunate fact that there are applicants to these places that do not share the institution’s beliefs and are willing to sign a statement of faith without actually adhering to it. In addition, usually you are required to write an essay about your faith and it’s more likely than not that this isn’t going to be very well-written if you are not a person of faith. In fact, a lot of small institutions, not just faith-based ones, make you jump through inconvenient hoops and write essays in order to see if you are really committed to taking the time to apply for their job. After all, since the advent of mathjobs.org, the common applicant strategy is to flood the market and hope probability is on their side. These inconveniences can act as a deterrent for non-serious applicants or litmus tests for candidates that aren’t as dedicated to a position. This can also work to your advantage. In Thinking, Fast and Slow, Nobel Prize winner Daniel Kahneman notes that one of his strategies to see how an average person would respond to a situation is to first reflect on his own first reaction to a situation. I encourage you to do the same. The more of a hurdle you find it is to apply to a place, the less applications they probably get. For example, I viewed one application that required something like five essays to be written in addition to the usual documents. At first I thought this was crazy and that I wasn’t going to waste my time, I then realized that most other applicants are probably thinking the same thing and that if I take the time to complete these essays, I would have a better chance of getting an offer than if there were no essays to be written in the first place.

Assistant Teaching Professor/Postdoc

There is also a new category becoming increasingly more popular. The assistant teaching professorships and teaching postdocs. As far as I can tell, these are a sort of glorified lecturer positions. It is unfortunate that this trend is making less room for those who want to be teachers and engage in research. I’m not sure that you are expected to maintain any research program in such a position. I do know of one case where someone acquired a good position at a SLAC after doing one of these. It could act as the postdoc’ buffer between your freshly minted doctorate and tenure-track SLAC position, but I doubt it will do anything more.

Research Positions

These sorts of positions will have labels such as postdoctoral positions, visiting assistant professor, and research associate. Keep this in mind when combing through the opportunities on mathjobs.org. Don’t just look for positions that have the word postdoc’ in them. Just clicking the sort by postdocs’ link will cause you to miss a lot of these positions. Also don’t sort by deadline! My experience was that a third of the institutions don’t put their deadline in the right spot and thus do not show up in the appropriate place when sorting this way. On the other hand, if you are tethered geographically or just have a strong preference for a region, the sort by state (or in the case of higheredjobs.com, by region) option seems to pretty reliable.

The first and most important thing that you should know about these positions, at least as far as I have ever heard or seen, is that, with a few exceptions, they are inside jobs. If your advisor is not pulling some strings for you or the place you are applying doesn’t have a faculty member advocating for you, you chances of getting an offer aren’t so good. Here are some words of advice if you want to land one of these positions.

• Investigate what big institutions have previously accepted PhD students from your institution. Universities that have hired, and had good experiences, with students from your institution will be more likely to hire from your institution again.
• Go to the institution and invite yourself to give a talk at a seminar. This can be particularly difficult if you live far away but it is what it is. Try to organize this earlier rather than later. Making contacts early on is very important.
• Try to publish something. It seems to be the standard now that you are unlikely to get a good research position without any publications to your name. As silly as it is, rather than trying to put your results into one coherent whole that is your thesis, try to carve out a chunk prematurely and get it published before applying to research positions. In addition to your advisor, seek help and second opinions from your committee members or other professors as well.

You should also invite potential future colleagues/employers to your JMM presentation. Especially if the institution of interest is too far to drive and give a presentation. I had one professor from a place in which I applied for a research position thank me for inviting him and gave me positive feedback. This might sound crazy but another thing you ought to do is to practice your talk 15 (!) times before actually presenting. Presenting at the JMM was the first time I tried this and it worked out quite well. After such practice, you will find that you have full command of your presentation which will thread together like a beautifully knit quilt.

Another thing that’s good to know, mathjobs.org allows you to upload more than one letter per recommender. Have your recommenders (including your advisor) observe your teaching and write two letters for you, one research focused and one teaching focused. If possible, have them upload the letters at the same time. I had one reference write a teaching letter, then sometime later a research letter. The second was automatically uploaded to the teaching positions I had already applied for. I noticed this a day later and find it unlikely that anyone saw both letters before I corrected it, but it’s something to keep in mind.

I would also recommend keeping a shared Google sheets doc with each recommender to keep track of the places which you have applied and which the recommender has submitted a letter. While this will primarily matter for teaching positions, it did apply to a few research positions to which I applied, including a few domestic positions. Applying to 100 jobs is exhausting. I actually only initially applied to about 75 places but did find a second wind in late January after getting exhausted from the process in early December. Organization from the start is key. This will also minimize the number of mistakes in your applications. While I have yet to see how it will work out, I also applied to places that I thought would be an excellent fit before they posted any positions. In two cases I actually was ahead of the curve (they were preparing to submit a posting) and received positive feedback from them about my interest.

While there is a lot of information out there regarding advice about how to perform well in an interview (practice, practice, practice), I thought I’d make a comment on something that either I missed or wasn’t explicitly stated in anything that I read. My institution had no infrastructure in place for interview preparations but that shouldn’t stop you. You should get involved with (or start!) your institutions AMS student chapter and organize a practice interview session with other graduating students, if there are any. This will help you be comfortable with answering questions on the fly.

If I could go back in time to December and give myself one piece of information that was overlooked in my interview preparations, it would be this:

Prepare to carry the entire interview.

A few other items that will improve your chances for a B.I.G. position are the following:

• Do a summer internship. While many of these are restricted to U.S. citizens, there are plenty of positions that are not. It is hard to find the time for one of these if your intentions are to go into academia, but if you can find the time, it would be quite helpful.
• Study statistics! Take a few graduate courses in statistics. It’s not even necessary to have any undergraduate background in stats. I took a few graduate courses in statistics without any stats background and fared just fine. Having some applied math or statistics is really a big plus in almost every way. We live in a stochastic century and I can tell you that the lion’s share of teaching positions or industry positions will look much more kindly on your application with some stats background.

Another thing you ought to look out for is whether your work is dependent on contracts or not. I didn’t even realize there was a difference until one of the jobs with which I interviewed pointed out that if you worked for them, you’d have a steady 9-5 job that wouldn’t rely on contract work. I later was approached by a national lab looking to hire and realized that they contracted out their work. In such a case, you have to constantly vie for jobs to contract. I really don’t know how much people who do this have to stress about finding their next contract, but I can imagine that not being dependent on contract work is better.

The Two-Body Problem

The two-body problem refers to the situation where you and your spouse are trying to simultaneously land a position at nearby (or the same!) institutions at the same time. While this is a difficult task, it is not impossible. I know of one married couple that solved the problem for their postdoc and tenure-track positions. Do keep in mind that you do not need to land a position at the same institution. Often times there are clusters of universities in one spot. Otherwise, search for institutions within reasonable driving distance.

From my understanding, the word on the street is that it used to be the expectation that, in order to obtain a good permanent position, spouses would almost certainly have to live apart for a few years. From my personal experience, this is still the (off-the-record?) advice given to married couples, sometimes with small children, by advisors and committee members of students seeking a long-term productive research career. I have personally witnessed this numerous times. I disagree with this sentiment in the strongest possible sense and urge you to do the same. I’m going to go ahead and say this should be written in stone:

I wish the mathematical community would do more to combat this expectation of separation. You should negotiate hard to solve the two-body problem and let your advisor know in no uncertain terms that living apart is not an option and it is ridiculous to even entertain the thought, especially if you have children.

The Struggle is Real

And so is the competition. This competition rings true in the fight for a postdoctoral offer. Once another graduate student refused to look up a reference on a presentation I made because it required that he visit my website, thus giving another “view” to my site. Another time, after a graduate student learned that he received a good offer, the first response of a classmate was to say something negative about the place in lieu of a congratulations’. My advice to you is not to be so petty! Celebrate your classmates’ accomplishments and be humble/thankful if you receive a good offer. The difference between you and someone who did not receive a good offer is most likely due to acts of luck and not anyone’s inherent ability. It is better for everyone involved.

When should I panic?

The short answer is that you shouldn’t. It doesn’t help anything. Do recall the second word of advice I was given, that late offers come. While unlikely, I know of one case where someone was offered a desirable tenure-track position in July after the search committee failed to find strong for the position. Try to keep active, academically and physically, it will help. One of the best decisions that I made in graduate school was to pick up running as a hobby. Make a nice website and keep it up to date. If nothing comes your way now, keep persevering and keep an open mind. Be thankful that you had the opportunity to acquire a doctorate and remember that trials build character. Good things will come eventually.

THE ETERNAL ART OF MATHEMATICS (9/05/2020)

Reproduced below is an article I wrote to for the Science Café.

Religion, beauty, mathematics, and entertainment. Their intersection is not as empty as one might think. Those who have had the opportunity to play Azul, the 2018 winner of the Speil Des Jahres have, inadvertently, experienced such an intersection. This beautifully crafted game credits its inspiration to the Portuguese ceramic tiles, called azulejos,which ultimately drew their inspiration from the Alhambra palace nestled in the Andalusian city of Granada. But what was it that initially inspired the architects of the Alhambra to create patterns that would resonate with artists and game designers for centuries. And what does such an inspiration have to do with mathematics?

Andalusia is a region in southern Spain that was occupied by the Moors, or the Muslim inhabitants of the western Mediterranean, from the 8th century through the 13th century. After its capital, Córdoba, was captured by Christians, the leader of the last Muslim dynasty on the Iberian Peninsula agreed to concede tribute and even territory to the Christians on the condition that they leave his hometown of Granada alone. Construction of the Alhambra began in 1238 and was completed later in the 1300s as the Muslim dynasty exhaled its last breath on the Iberian Peninsula. Its décor is distinctly different from the Christian basilicas of the time. While the basilicas were adorned with golden statues of saints, crucifixion displays, and murals of Biblical tales, the Moors were strictly prohibited from depictions of Mohammed or Allah or any living creatures because it was seen as a form of idolatry. Without the expression of anthropomorphic representation, the Moors turned to represent the beauty of God in an abstract way.

The walls were adorned with intricate repeating patterns and tiling that held various visual symmetries. The fascinating result is that their numerous patterns and tessellations that are scaled across the walls of the palace contain rich mathematical properties, unique to the Alhambra, that have, in turn, been an inspiration to art. The ubiquitous tessellations of Dutch artist M.C. Escher were famously inspired by these wallpaper patterns.

But isn’t mathematics about numbers with operations like addition and subtraction, and not artistic patterns? Rest assured, anywhere you see patterns or structure, there is mathematics lurking. In mathematics, there is a very precise description of what a symmetry means. Loosely, given an object, say an infinite wall with repeating designs, if you can rearrange the object in some way (think translate, rotate, and reflect in the case of our infinite wall) that makes it indistinguishable from its original state, then that rearrangement constitutes a symmetry. The branch of mathematics that studies symmetry is known as group theory and the set of all operations that leave the object unchanged constitutes a group. While operations in arithmetic are things like addition and subtraction, operations in group theory are rearrangements that don’t alter the object. In our case, the three operations of translation, rotation, and reflection generate all rigid motions, that is, motions that preserve the distances between any two given points. In the plane, our infinite wall, if you have repeating patterns such as those depicted in the Alhambra or on the wallpaper in your living room, you can perform these rigid motions in certain ways such that, after performing these operations, the original state is left unaltered. With a few natural assumptions, it turns out that the mathematical structures that arise from these “wallpaper groups” can be classified into exactly 17 categories that encapsulates all possible rearrangements of the wall in terms of our rigid motions. There remains dispute as to exactly how many of these groups are present in the Alhambra, but the number ranges between 13 and 17, still a rich and unique accomplishment in architecture, especially given that it was produced well before group theory was invented.

One can play this game in higher dimensions as well. Due to the fact that they have numerous applications to crystal structures in three dimensions, these groups are often known as crystallographic groups and have significant applications in chemistry. Although we inhabit a three-dimensional world, however, our visual interests are peaked by the two-dimensional wallpaper groups. This is a result of the fact that we mentally construct our world based on a two-dimensional projection of our three-dimensional world. In three-dimensions, the number of categories jumps to 230. The number continues to balloon as the dimensions increase. Since our cognitive faculties only allow for visual representations of objects up to three dimensions, the beautiful symmetries involved in higher dimensions can only be “seen” through mathematical analysis. Given the rate of growth of the number of distinct crystallographic groups, the precise size for dimension six and up is still unknown. With recent advances in computational power and continuing mathematical research, maybe we can come to know more about these crystallographic symmetries in higher dimensions and thus, slightly enhance our view of the beauty of God.

LETTER TO THE EDITOR (8/30/2020)

Reproduced below is a letter I wrote to the editor of the AMS Notices, published in the August 2020 edition.

The arrival of COVID-19 has prompted many members of our community to reset and reflect. During this time, I would like to make the urgent request that we learn from this seismic shift and commit to implementing positive changes to our current mode of operation.

As I fall into the Early Career/Graduate Student group, I am particularly mindful of the challenges those of us in this group face and the importance of each decision we make at this fragile point of our career. A budding career, more often than not, benefits from having a mathematical community, access to the current exchange of ideas, and the resources to bring these two together. To be candid, attending conferences is expensive. For those in more demanding circumstances, such as caretaking for others or having limited financial resources, even participating in nearby workshops may prove burdensome. One often sees advice about the importance of attending conferences, networking with others in the field, and participating in the market of perspectives. These indispensable interactions should not be left to the caprice of one’s financial standing, geographical location, or as is often expected, the mercy of one’s institution or advisor to demonstrate willingness to assist or provide the necessary resources.

Secondly, the negative environmental impact of frequent academic gatherings has gained increasing attention in recent years. The term social trap refers to a situation in which, based on short-term gains, potentially lethal long-term harm is inflicted. Even if one is aware of the calamity ahead, one must participate in these events or face massive concessions to the trajectory of one’s career. There have been efforts by some, seeing which way the wind is blowing, to try their hand at implementing incremental changes. Such efforts have included eco-friendly double conferences or, with the current state of affairs, virtual meetings. But these efforts have not gained the necessary traction to address the problem in the long term.

In one fell swoop, virtual meetings offer an opportunity to level the playing field and address the social trap of environmental catastrophe. Local seminars, collegial meetings, and the like, that have continued in this crisis, have done so through the technological miracles of platforms such as Zoom and WebEx. Circumstances, bleak as they are, have forced our hand. We have been required to adapt to these technologies. Upon exiting this chapter of history, why not perpetuate this adaptation and, as far as is conceivably possible, convert all future conferences and gatherings to such virtual formats?

Whether we implement these changes now or in the future, the arc of time will mandate that we update the way we operate.

TAKING DOWN STATUES AND RENAMING THEOREMS (07/2020)

In the end, we will remember not the words of our enemies, but the silence of our friends” Martin Luther King Jr.

Quite a few years ago I had visited New Orleans, LA where I happened upon a rather large and imposing statue of the American Confederate general Robert E. Lee. I specifically recall my middle school textbooks telling me that, although he was a general for the confederates, General Lee was an honorable and respectable man, even though he fought for the South. I was taught that the American Civil War was fought for an array of nuanced reasons, one of many being slavery. General Lee, said to be a good man, just happened to be on the losing side. In fact, many people are named after him. There is a mathematical teaching method of Socratic inquiry known as the Moore Method, named after Robert Lee Moore who, in turn, was named after General Robert E. Lee.

As I stood in New Orleans, next to this statue of Robert E. Lee, I noticed the majority of people around me were African American. I wondered what they thought about that statue and this strange juxtaposition they had to live with each day. After all, the true history of Robert E. Lee is not so kind to his beliefs. The American Civil War was about slavery and Lee was firmly on the front lines of the wrong side of history. Yet his legacy seems to live on, in part through the naming of children in a way that generals of the North, such as Ulysses S. Grant, do not. I’m sure it, in part, has to do with the aesthetics of the name Robert Lee relative to Ulysses. Even conceding this point, it doesn’t detract from the discomfort of being named after someone with a legacy such as Lee.

These issues still resound today. The recent protests in reaction to the murder of George Floyd has prompted the downfall of many confederate statues. This momentum has even led to the renaming of an American football team (formerly known as the Washington Redskins). In the mathematical community, we give honor by naming theorems, conjectures, and so forth after mathematicians of history. We saw that there is a popular pedagogical strategy known as the Moore method. It is an shameful reality that Robert Moore refused to teach African American students. Even in my narrow field of study, the study of complex maps of the unit disk into itself, the problem is pervasive. One important topic of study is known as the Nevanlinna-Pick interpolation problem which asks the following question: for a set of $n$ initial points in the disk given by $\{z_i\}^n_1$ and $n$ target points in the disk given by $\{w_i\}_1^n$, when is there a holomorphic function $\phi$ from the disk into itself such that $\phi(z_i)=w_i$ for all $1 \leq i \leq n$?

This problem is named after Rolf Nevanlinna and Georg Pick. Nevanlinna was a documented Nazi sympathizer while Pick, a Jew, died in a concentration camp. At the time Pick died in 1942, Nevanlinna, a Finnish citizen, was chair of a committee to improve relations with Nazi commanders and Finnish volunteers fighting for Germany (see, e.g., The Scholar and the State by A. Soifer). Turning to another example, there is an important and interesting class of these self maps of the disk, called inner functions, which can be thought of as maps that send the boundary of the disk onto the boundary. The reason for the name “inner” is unclear but everyone has gotten used to calling them by this name. There is an important subset of inner functions, called Blaschke products, that are named after Wilhelm Blaschke, an Austrian mathematician who described himself as “a Nazi at heart” and signed a vow of allegiance to Hitler. It’s not clear to me why we can’t just call them something like “boundary products” instead. After all, it makes more sense than inner functions. There is also the famous Bieberbach conjecture (After being proven by de Branges, it is now called the de Branges theorem), named after Ludwig Bieberbach, an enthusiastic Nazi who held firm the view that the German race was superior. All of these reside in my narrow field of study.

I have heard the argument that the political opinions of these mathematicians are irrelevant to the mathematics they did. And this is true enough. Our books should continue to acknowledge the scientific contributions of historical figures, independent of their beliefs. We should not rewrite history. Nevanlinna should be credited with his work on the problem. Blaschke should be credited with introducing the class of functions currently known as Blaschke products. But this does not mean we should do the honor of naming these things after them, so that we as mathematicians must repeat their names every time we refer to the problem.

One rather common response is that fault can be found with any historical figure and renaming one theorem, taking down one statue, will bring the whole lot down. Anyone who has taken any sort of critical thinking class will immediately identify this line of reasoning as a prime example of the logical fallacy known as the slippery slope argument. After all, this could be applied to anything. Freedom of speech is important but you cannot run into a theater and shout “fire!”. Like everything else, we should start with the cases that are clear, those who, in great excess to their peers, were racist, sexist, and so forth. We then proceed to debate the intermediate cases just like we do in every other outlet of human discourse.

We ought to take down racist statues and rename the things that are named after people who went out their way to support ideologies that were actively oppressive to different demographics, even by the standards of their peers. The sooner this step is taken, the sooner we put an end to an erroneous practice. Some steps have been taken. The statue of Robert E. Lee was taken down in 2017. The prestigious Nevanlinna prize was renamed as the IMU Abacus Medal in 2018, although the IMU failed to specify why the change was made. We are moving in the right direction, but we can move faster. As part of the mathematical community, I do not want us to be seen as a community that dragged our feet on progress or took our time to remove barriers that are insulting to so many, including members of our own community.