I’m David Lowry-Duda. I’m a Senior Research Scientist at ICERM.

I study mathematics. More specifically, I study number theory and algebraic geometry. As an undergrad, I really enjoyed elementary and additive number theory. As a grad student studying under Dr. Jeff Hoffstein at Brown, I focused on analytic number theory, arithmetic dynamics, and $L$-functions. As a postdoc working with John Cremona at the University of Warwick, I began to work on the LMFDB and incorporate computational number theory techniques into my repertoire. At ICERM I continue my work in number theory, arithmetic statistics, computational number theory, math software, and related topics.

**What is number theory?**

I get this question a lot, but I’ve never been really good at answering it. When I took my first number theory class with Dr. Matt Baker, an excellent inspirateur likely responsible for my career path, it was apparent to me: number theory is the study of numbers. We like divisibility tests, primes, or density of special numbers in progression. This encompasses much of what I now call elementary number theory, from the prime number theorem to modern cryptography. But this does not even begin to actually answer the question (this is sort of a Dunning-Kruger classification error).

I think a better question is ‘What is Mathematics?’ Once you see that mathematics is exploratory rather than a series of trite, uninspired exercises, I think number theory arises as the study of the properties of the basic building blocks of whatever system you’re working in. (Did you know that there is a topological proof that there are infinitely many primes? Is this a statement about topology or number theory?) For more, I encourage you to read A Mathematicians Lament by Lockhart.

**Why do you blog?**

Because it helps me reduce how often I need to repeat myself, and because I was inspired by Terry Tao’s blog when I was younger. Much of the material here is for my students, and writing it down here means I’ll have to do less later. I also find that I sometimes repeat the same series or sort of calculation or computation, or get stuck in the same process in papers – so I write it here so that I can easily document it and reuse it later. Further, all articles I write here with math in the post is originally written in $\LaTeX$, and then converted with my script latex2jax. This gives me that little extra push to TeX up my notes for talks I give, some of which I’ve already reused, or to TeX up parts of my research along the way.

I also use this site as a way to distribute and communicate my math research, including the rationale behind certain approaches and some of the less successful attempts along the way.

I also spend a good part of my time programming, and trying to conjure a way to work this into my career. You see, I’m a mathematician. But I like to program too, and there are many ways to use programming to advance mathematics.

Finally, I am a big believer of the Do Things, Tell People or Do Things, Write About It philosophy. In short, do cool things. Along the way, google is your friend. If it hasn’t been done before, or hasn’t been done well, then document your own path. Write about it. Do cool things, write about it.

**Contacting me**

Should anyone want to contact me, don’t hesitate. Shoot me an email at david@lowryduda.com, davidlowryduda@brown.edu, or comment here.

I’m davidlowryduda on keybase. I’ve signed that here as well. My keybase public key is attainable on this site.

You might also run across me on the web. I’m a moderator at math.stackexchange, and exist in various other fora and sites as either mixedmath or davidlowryduda.

There’s also the original and free wordpress version of my blog at mixedmath.wordpress.com. I’m still building this site, and I’m not certain about sticking with wordpress. It’s a work in progress, certain to be changed or updated.

For those close enough for this to make sense, you can often find me in my office at ICERM (or at Brown University) or at other times in Boston, Massachusetts.

*Disclaimer: I have been off and on the gracious support of the NSF and other grant giving bodies in the past. So I note: “Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation or any other institution.”*

you are awesome.

I’m currently living in the Land of the Lowry’s. I was wondering if you lived out this way also, however I guess not (.gatech.edu). Anyway, Love your blog and your posts in the forum.

Frea.

Hi,

You recently deleted a post I made on Stack Exchange: (http://math.stackexchange.com/questions/66077/how-to-find-the-expected-number-of-boxes-with-no-balls/) and I’m not sure why. I edited it to contain more content on actually calculating a solution, but showing a counterexample to why the currently accepted solution is not right seems like reason enough for the post. I couldn’t figure out how to message you on StackExchange, so messaged you here.

Rob

Come on mr so called moderator, read it http://math.stackexchange.com/questions/1880605/elementary-ways-to-show-zeta-1-1-12/1880630 and read what I wrote on MSE the last week, and look at : who annoyed me, who insulted me, and end asking yourself : isn’t it normal after that he is upset, having helped so many people on MSE ?

I see nowhere to submit an email so I am asking my question here. On another site you answered a question about the average number of moves to solve Freecell. You gave an in-depth answer about the studies that had been done (thank you) which was 45. What I cannot comprehend is how anyone can move 52 cards, one at a time, in 45 moves? Even if they were dealt in perfect order requiring no move beyond moving them from the tableau to the foundation takes 52 moves. Clarification?

Your post

Astoundingly enough, this has already been studied. And I’m almost embarrassed to say that I’m familiar with the result. I used to freecell a lot. And FYI, 11982 is the impossible Frecell game. But I recommend entering in games -1, -2, -3, etc too.

So here are some stats from some studies of freecell. Firstly, the depth of the aces, i.e. how many cards cover the aces, is not a good measure of difficulty. On average, 11.077 cards cover the aces (counting aces). Analyzing the dozens of thousands of deals, it takes an average of somewhere between 42.12 (from a solver that ran 1.5 million deals) and 46.33 (from a solver on 32000 deals, the original 32000) moves to solve. This is a hard measure, as this is based on the quality of the solver – and it is unknown whether these solvers were optimal.

An interesting player-based study showed that about 79% of deals are solved by a person on their first try. It also turns out that some people examine how many freecells (the four in the top left) are actually necessary to solve a game. The impossible 11982 can be solved with 5 freecells. Almost every game can be solved with 3. Over half can be solved with 2. And almost 100 can be solved without any freecells at all. Take that, freecell!

One of the big problems is that freecell games are not at all randomly assorted, and so pencil and paper solutions aren’t around. But lots of people have (surprisingly) cared about these questions, and so these results are all upper bounds. In short, about 45 moves is the average minimum.

I believe you are referring to: this post on MathSE.

Yes, that’s right. In the typical language, a “move” consists of one mouse-click-and-drag action. When there are open freecells, it is possible to move multiple cards using one mouse operation (as a shortcut to doing all the card moves individually). As an example, if all 4 freecells are open, you can move a 3-4-5-6 onto a 7 (with the correct suit combinations) with one “move”. Thus the “move” count differs from the “card move” count. Historically this came about from people tracking and sharing moves on usenet groups, and a condensed move notation emerged.

Further, I note that Freecell will automatically place cards on the ace-stack when there is no obstruction. These are also not counted as “moves”, since these are not mouse operations.

For more, I recommend checking out the links I gave in my MSE answer, and perhaps looking up some of the references or ideas you find from there. There’s quite a bit out there on Freecell — it may be that solvers have improved.

I appreciate your taking the time to reply. The version of FreeCell I play online does count taking a card from the tableau (and the Freecells) as a move when adding them to the foundation. I never realized others did not.

Hi

Could you please share the python code to generating beautiful plots? I plan to use it for my son to get interested in python programming.

Son

That’s great! If there are particular plots that you’re interested in, let me know. But I (very recently) posted a library for making the plots https://davidlowryduda.com/phase_mag_plot-a-sage-package-for-plotting-complex-functions/

Alternately, I make sage/python notebooks available for many of my visualizations. These are usually linked to within the post. If you see something that you want to replicate and find the code, leave a comment on that post and I’ll get back to you.

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