Why I mostly talk about topics on which I don’t know what I am talking about

Yes, I talk about the issues of the day; sometimes I am very noisy. Often the topics have a highly technical aspect of which I am ignorant. So, I tend to try to find out where “expert consensus” and go with them for my “base facts”. Often the debate is what to make of those facts. And sometimes one has to prioritize what they want (e. g. more safety for some vs. more liberty for others, etc.)

But there are a couple of items that I tend to NOT discuss in public: mathematics and mathematics education.
Yes, I have a modest publication record in mathematics (primarily in topology, though I have a couple of analysis papers too) and I’ve taught, in one form or another, since the summer of 1986. So I probably know more about teaching undergraduate mathematics (especially calculus) than anything else.

Yet, that is a topic that I tend to avoid, at least in public (social media).

The reasons are many.

Mathematics: at the research level, it is a highly technical field, and explaining research to those who don’t heave at least a master’s degree is all but pointless. Not only is the subject loaded with technical jargon (by necessity), but one needs some experience to even begin to understand why a particular question is interesting and worthy of investigation.

And, if you are not a mathematician, you’ll just have to trust me on this statement: most “popular explanations” of technical mathematics is TERRIBLE.

Mathematics education: most people have questions about grade school education, and I am not qualified to answer that. My experience has been with, say, teaching calculus to science, engineering or business students. These students have already met a qualifying process, and what works with them might not work with a less talented, less motivated bunch.

And there are the typical comments “I am smart but couldn’t learn math”, therefore “the teachers sucked” or “math is useless in real life” of “teachers need to be able to reach students who have “different ways of thinking”.
Frankly, I haven’t the patience to endure such conversations, hence i make a practice to avoid them.

I excuse myself from such conversations and let the “unappreciated smart people” talk among themselves.

I might talk to a non-specialist privately, but they have to be someone I really like and am already good friends with.

January 5, 2017 Posted by | mathematics, social/political | Leave a comment

Not so profound

Workout notes: I had bigger plans but my legs weren’t ready. So I did a 10K shuffle in 1:09:42 (the 5.1 mile course plus an out and back down the upper Bradley Park Hill).

Yes, the Marathon Route signs are up; Race day is the 16’th of October (Sunday)


Last week’s failure has me hungry for “a finish”; time goal just isn’t that important to me now. There was a time when I took a marathon finish for granted; that time was over a long time ago (2009?)

Personal: I thought that I had something profound to say about the moment generating function and the negative binomial distribution. I don’t. In any event, I can’t talk about it in class until I talk about joint density functions.

I was also pleased with myself when I worked about the old “every vector space has a basis” argument in my head (and mostly got it right) until I realized: “yes, you are SUPPOSED to know this stuff”. Oh well. (hint: Zorn’s Lemma)

Time to type a boring request.

September 29, 2016 Posted by | mathematics, running | Leave a comment

back in Peoria

Math Fest: decent conference, but too much driving. Traffic and construction added time to the normally 5:45 hour drive. But my Google maps application helped me around one traffic jam on the way home. I did get some ideas to consider though.

Workout notes: 3.12 miles on the hotel treadmill in 30 minutes; 11:10 first mile then 17:50 for 2 miles. That was enough. I don’t think that I am caught up on sleep; I should dial back expectations for tomorrow’s longish run (maybe 14?)

Math note: I did look up something that I heard about during a talk and thought: “THAT got published?” That gives me more incentive to work on my current paper, which I think is better than some of the stuff I see in print. The editors might not agree though. 🙂

August 6, 2016 Posted by | mathematics, running, travel | Leave a comment

Recovering from a stinging rebuke (resentment and whining alert)

Workout notes: easy 2 mile jog on the treadmill (22:15). I just had breakfast and am waiting for rush hour traffic to lighten up a bit before getting on the road.

Weird FANS note: I did one lap with Centurian John Greene. He is also a math professor; he was working this years event as a volunteer. We..talked math.

He told me about two of his published results. One was about unique factorization domains (UFD): his result showed that every UFD has an “almost Euclidian algorithm”. His other was about the trace of 2 x 2 matrices and how the trace behaves under matrix multiplication. It turns out that when 3 matrices are multiplied (in various orders), a certain property is obeyed with probability p = \frac{1}{\sqrt{2}} . Note: the assumptions is that the matrices have real entries and that the entries are selected via a normal probability distribution.

Now how cool is that? I had a moving mathematics seminar. 🙂

Note on yesterday’s baseball game and today’s hotel stay
Yes, I had club seats (splurge, though I paid a discount price). I was uncomfortable with all of the service (being deferred to by attendants, etc.). I ate breakfast at the hotel. I got the “full” breakfast and ate..what I normally eat. My tummy just can’t hold that much anymore. I don’t like trying to drive while stuffed.

For me, luxury (middle class luxury anyway) is a big waste of money (even when purchased at discount rates), or at least these luxuries.

I’d never cut it as a Republican. 🙂

Accepting defeat and moving on

This result stung. I won’t pretend otherwise. I was struggling 1/3 of the way into the race and that is not a good place to be, at least so early on. I’ve thought about what went wrong, and it is possibly one of two things:

1. I didn’t do enough of the “right kind” of training (e. g. monthly 6-8 hour training sessions) even if my total weekly milage was ok.

2. I just can’t do these events any longer.

And yes, there is a bit of envy when I see the successful basking in the glow of their successes …my thinking “dammit, that used to be me”. Well, it is not me any longer. When it comes to sports, you are what you do…that is, what you CURRENTLY do, not what you did 10-12-15 years ago.

But there is still plenty of time for redemption. I have some ideas for a math paper (more important than my sports), and I still am on track to attempt to run a marathon this fall, hopefully in less than 5 hours. My “long run pace” is right as is my training mileage, and this weekend’s event didn’t set me back. So I have goals to work toward, and striving for these, rather than envying others or longing for past successes, is the way to emotionally heal. Nurturing resentments doesn’t help.

And there is my home. My wife: yes, I am glad that the fitness bug bit her in a minor way. This should add some quality of life for her and I want to remain encouraging. But: last night, she listened to my whining for about a minute or two and then wanted to know if I remembered her text about what SHE did…parked 2.5 miles away from lunch, walked to lunch, and walked 2.5 miles back. Yeah, I know, my first marathon and 50K were very slow (7:12, 8:40 respectively, but remember I was going at my “I hope to go much longer than this pace”) but in my current emotional state, it is hard for me to work up much enthusiasm for my wife’s “feat”, even if she got a ton of “likes” for it on Facebook, way more “likes” than any of my marathons/50 milers get. 🙂

But that’s how it works. A “I got an A on my calculus test” gets more attention than “I published another math paper”; it is WHO you get the kudos from that counts.

June 6, 2016 Posted by | mathematics, relationships, walking, whining | , , | Leave a comment

Trouble accepting what I have not seen…

I wonder if it is a human trait to reject the experience of others if that said experience is not a part of one’s life.

For example, it has been difficult to persuade my conservative friends that darker skinned males are often seen as “suspect” by the police (example)

I had a brush with being profiled (probably many things, including having a cheap car with Texas plates) and note one of the comments that I got on that post.

It is tough to accept what we haven’t experienced, observed, or been a party to, especially when we don’t want it to be true.

In my case: I have trouble accepting that sexism within the sciences still exists. What caught my eye was this story (from outside of the United States):

In the final months of my physics degree, one of my professors asked me into his office – an exciting prospect, given that I assumed we’d be discussing subjects for my potential honours theses. He closed the door, invited me to sit, and declared he’d fallen in love. He wanted to have an affair, he said, and if I couldn’t share in that plan he couldn’t continue as my advisor – he’d find my presence ‘too distracting’. He was a senior academic, and married; but this was Australia in the late 1970s and the subject of sexual harassment wasn’t on any university radar. It seemed this was just one of life’s inequities, another hurdle facing being a woman in science. So I made the decision to leave physics – a subject I loved – and in the following academic year switched to computer science at a different university.

Now of course, the reasons I resist this claim so strongly is that:

1. I don’t want it to be true.
2. I haven’t seen this in person.
3. I haven’t ever done this to another person.

Note: the degree data I’ve seen in mathematics surprises me. I do know that we’ve had more success in hiring female math professors than we’ve had in the past; is a bad job market part of the reason? I do know that things are better than when I first got my Ph. D., but evidently the numbers have stagnated.

Anyway, I do believe in data and facts though.

Of course, part of what turns me off is the low quality of the arguments that I’ve read. For example, from the article that I quoted from::

Part of what women are up against in science is a continuing widespread attitude that, deep down, we’re not really up to it, which by extension implies that a high rate of attrition is no big loss. That view was startlingly articulated in 2005 by Lawrence Summers, then president of Harvard, when in a conference he mused that if there weren’t more women in top science positions at elite universities it might be in part because women’s mental abilities are different. The ensuing furore led Summers to resign and precipitated a great deal of hand-wringing about academic sexism. Yet here we are, a decade later, with yet more academic sexism.

What surprised me about Summers was not what he thought – in my experience, it’s not an uncommon view among elite academic men – but that he thought he could say it out loud. He didn’t seem to understand the absurdity of stating, in an intellectual forum, that half the Harvard student body might be inherently unsuited for intellectual success.

I see two big problems here. First of all, “he thought he could say it out loud”: this is a hostility to freedom of expression that I find troubling. Also: “that half the Harvard student body might be inherently unsuited for intellectual success”.

The author of this article misses the point badly. For one, Summers remarked that the demands of science at the world class level may be incompatible with family life and it “could be” that women were more interested in the latter. As far as the intellect: remember that Harvard faculty are supposed to be world class; we are talking about the extreme ends of the “bell curve” here. Might it be possible that the variation between men and women are statistically different? Again, I am talking about the “extreme ends”, which is where Harvard STEM faculty would be. That has nothing to do with, say, people like me (ordinary Ph. D. people with a modest publication record) and nothing to do with the student body at Harvard (on the whole.

And, I’ve been turned off by some of the hare brained “sexism!” complaints I’ve seen (e. g. calling an animal part a “penis”).

So yes, some of the “sexism in STEM fields” arguments are bad arguments. But that doesn’t mean that sexism doesn’t exist; I think that I am now convinced that it does.

A bad argument for a position doesn’t invalidate that position (e. g. there are bad pro-evolution arguments out there) , though it does mean that the person making the argument did not make a convincing case for it.

May 31, 2016 Posted by | mathematics, science, social/political | , | Leave a comment

My take on a professor’s lament

A college professor writes:

Salon is running a particularly poorly thought-out piece, even by Salon standards, about the inability of college students to use the English language to express themselves in writing. I’ll let the author off the hook for the stupid title (“Death to High School English”) and the tagline, as an editor probably chose those. But the argument overlooks such an obvious explanation in favor of a more complicated one that it’s difficult to take whoever she is seriously. When the tagline asks, “My college students don’t understand commas, far less how to write an essay. Is it time to rethink how we teach?” We could do that, I guess. Or we could rethink how we grade them in high school.

There is a tendency, even among educators, when outcomes are not as they should be to assume that teachers as individuals or the educational system writ large must be to blame. In this case we’re hypothetically dismantling all K-12 English education and starting over from scratch with some sort of newer, better method. What this overlooks is the reality that most students in college – the same ones the author rightly points out are terrible at writing – have no idea that they’re terrible at writing. They think they are quite good at it, in fact. They do not believe this because of simple arrogance or Those Darn Millennials or any other popular explanation. They believe they are good writers because they have been getting good grades on written assignments and in English throughout their educational careers.

The rest of the piece at Gin and Tacos is worth reading.

Now I have never tried to teach anyone how to write, aside from supervising a senior project and reading student’s mathematical proofs. I have had some conversations with English faculty and I remember one saying: “I can get most students to an A…..” at which case I wondered if was the STUDENT who was supposed to get THEMSELVES to the grade.

Here is what was going on, I think: many professors let students rewrite and rewrite their papers prior to turning in the final copy. This makes me wonder: at what point is the professor actually grading their own work rather than the work of the student? I can easily see a student learning how to game the system by, in effect, getting the professor to write their work for them. Hence, they get a good grade by producing a polished paper, and move on to the next class not having learned a thing, other than how to get someone else to fix up their writing.

At some point, someone has to kick up the training wheels!

Now, on a related note, I am not without guilt. Yes, I think that I assign grades fairly; I let the spread sheet do the calculations, and then I move the student names off of the screen and just look at the numbers. Yes, at times, I’ve used cut offs that were slightly more generous than those stated on the syllabus, though, again, I am looking at the numbers and NOT at the names.

But, that aside, even strange things can happen.

In one case, a student with a 98 average made an 86 on the final exam, which still gave the student an A. But on ONE other problems (the rest of the exam was good), I was told: \int^{\infty}_0 e^{-3x} dx = lim_{b \rightarrow \infty} \frac{e^{-3x+1}}{-3x+1}|^b_0 . Yes, the student aced the other integral problems, including the trig substitution problem as well as the substitution problem \int e^{sec(x)}sec(x)tan(x) dx . The error that the student made on that problem was just plain inexplicable.

In another case, a linear algebra student missed problem one, which was to determine the determinant of a two by two matrix of integers! But the student got enough of the other problems right to end up with a (low) C for the course, including one that involved finding eigenvalues and eigenvectors of a 2 by 2 matrix.

Anyway, I shudder to think of these students making such errors in a subsequent class the their instructors finding out that they had their previous class from me. 🙂

Go figure.

May 17, 2016 Posted by | education, mathematics, social/political | | Leave a comment

Public Perceptions of Science

Yes, the public, on the whole, doesn’t understand STEM fields. In fact, one economist was briefly detained for questioning when a fellow passenger on an airliner saw what he was writing down and thought it might be something evil (it was a differential equation).

And the results can be difficult to understand. When one attempts to explain them to a non-expert, say via a popular article or a popular book, one has to make simplifications:


Though this meme is probably unnecessarily harsh, it does get across the point that when one is trying to understand something outside of one’s specialty, one is doing a translation of sorts, and we know that information can be lost in translation.

I go through this all the time when I go to mathematics conferences and take in a talk that is outside of my narrow area. I have the advantage that I KNOW that I am missing the nuances and that if I wanted to understand the results or the conjectures, I’d have to engage in intense study in that field..and I still might not be able to understand what is going on.

Aside from that, there is how the media interacts with the science studies themselves, along with the fact that scientists like publicity too. This John Oliver segment (30 minutes) is outstanding and is making the rounds on the various science blogs.

May 13, 2016 Posted by | mathematics, science, social/political | Leave a comment

My Head Talks

The Dean opens it up (talks about 1:30 or so) and introduces me. Then I talk for about 5 minutes, and then the speaker gives an excellent talk about topology, algebra and the mathematics of financial prediction. So if you haven’t met me in person, this is what I sound like.

April 16, 2016 Posted by | mathematics | , | Leave a comment

Creature of habit (and missing workouts)

I have to cover for someone’s class, which cuts into my morning workout. Hence today I ran 5 miles over lunch (about 5.2 actually)

Good news: it was very pretty, though there was a breeze. I did 2 lower Bradley loops (1.22-1.24 miles each) in 21:39 (8:44-8:52 mpm) with the laps being 11:05/10:34. I walked the big hill coming out of the park after these two laps, and then slow jogged it home. Hey, 5 miles are better than zero. 🙂

I do have to get new shoes though as my teeth are starting to rattle as I run.

Think of this: suppose you have an ordered list of ingredients of a food stuff (say, water, salt, sugar, gelatin..), the weight of a serving, and the amount of say, protein, fats, sugar (nutritional information on the label).

You can use linear programming (and similar techniques) to determine upper and lower bounds for the various ingredients and have a phone application do this.

Why is this important? Some people have dietary restrictions (e. g. some can’t process phenylalanine) and therefore have maximum amounts of this substance they can have in their daily diet.

Who knew?

April 14, 2016 Posted by | mathematics, running | | Leave a comment

The walk of shame to the library

Workout notes: 8 mile “run” on the Rivertrail to Glenn Oak Park, up Prospect and into Springdale to the Mausoleum and around that small loop. It was windy and just under freezing; not bad running weather though. The footing was mostly good.


Not shown is the small spur I did on the trail which parallels Perry Ave.; that was iced over so I turned around but I did enough to get 8.
Then I did 10 minutes on the elliptical and a few weightless squats to loosen up.

Note: while out on the “run” I found a dollar bill.

Walk of Shame I took a whole stack of books to the library; they were mostly for a project that didn’t work out. But I did check out a new book to look at something else and what did I find in that book?


I put it on social media but that isn’t exactly “like-bait” 🙂 But seeing that did remind me that I need to get moving. It has been too long since I’ve had one of these.

I am thinking about things and I have a mystery that I don’t understand…yet. For the mathematically inclined: it has to with speeding up the convergence of an alternating series by using Cesàro summation. For the first two examples I’ve tried (one conditionally convergent, one absolutely convergent), the convergence sped up by a constant multiplicative factor. That isn’t very good for computational purposes, but why “that” factor and not some other one?

January 26, 2016 Posted by | mathematics, running | | Leave a comment