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I am almost surely ADHD, although undiagnosed. I have colleagues in mathematics who also are, but diagnosed. I have an extremely talented and successful graduate student who is (diagnosed) ADHD.

It is almost surely the case that I would have failed to do even remotely well in mathematics if I had not been intrinsically interested in it, and willing to "superfocus" on it for long periods. I was lucky enough to have been homeschooled in order to do this. Others are not so lucky. The idea of trying to learn this subject using the suggested reward structures found online that are supposed to be effective for ADHD people sounds like the worst kind torture to me. The purpose of this question is to collect some data to clarify my thoughts on the topic, and my own experiences with it.

ADHD people have, I have read, a deficit in working memory. (This suggests that math would be a very bad thing for students with ADHD to get involved with...since problem solving relies so much on working memory.) Growing up, I found that I did have a difficulty in short-term memory of some kind, but that obsessive drilling and overlearning could move ideas effectively into permanent memory where they could be accessed and used readily. (This aspect makes it seem like an ADHD person could be successful in math, if, for example, Keith Devlin's claims that math requires overlearning of concepts and procedures.) My experience has given a handful of examples showing me that the latter situation can, in fact, occur. The need to overlearn material, and the resulting expertise gained by ADHD people (often homeschooled, since this sometimes gives these people the freedom to take the time to obsess and superfocus) can make difficult mathematical topics and the grit needed to internalize them more natural than for neurotypical people.

Question: Is there any writing about ADHD mathematicians and their experiences? Is there anything out there in the literature discussing the phenomena I observed in these few cases?

Note: I'm not interested in the dystopian approaches to bring ADHD people into tow with traditional math education. I'm interested in the experiences of mathematicians and successful math students who are on the ADHD spectrum, their coping mechanisms and experiences, and writing closely related to these.

Some mathematicians often complain of having a poor memory...maybe some of this may relate to the above phenomena? Michael Atiyah veered away from studying chemistry due to a self-reported memory deficit, for example.

Problems can serve as instruments to manage attention. I'd be interested in reading about how this affects ADHD people.

(Sorry for a completely rambling question, totally confirming my suspected condition!)

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    $\begingroup$ If doesn't seem rambling to me at all, just full of the anecdotes needed to clarify. I don't know if I'm adhd. I do have a bad memory, and I tell students that this is why I'm good at math. I never tried to memorize (unless necessary) and always looked for deep understanding. $\endgroup$
    – Sue VanHattum
    Commented Dec 6, 2023 at 22:28
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    $\begingroup$ Indeed! Many mathematicians tell students this. It's so common, I find myself wondering if some math people have some combination of autistic, ADHD and OCD tendencies and have accidentally benefitted from special educational circumstances. $\endgroup$
    – Jon Bannon
    Commented Dec 7, 2023 at 13:16
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    $\begingroup$ Your question got me to search for something I remember writing concerning memorization in math class. It turns out it was something I wrote back in November 2012 in the Math Forum discussion group math-teach. I gave a link to it in my comment "Since when was math class about memorization? Math has always involved the least amount of memorization of any subject I can think of ..." to this MSE question, but the link is now dead. However, I've managed to dredge up that Nov 2012 post, which I've now included in several follow-up comments. $\endgroup$ Commented Dec 7, 2023 at 19:17
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    $\begingroup$ I'm curious what 'overlearn' means to you, Jon. I was thinking about this in the shower this morning. I don't think I like this word. The deeper we learn something, the better, and the more it becomes a part of us. $\endgroup$
    – Sue VanHattum
    Commented Dec 12, 2023 at 20:00
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    $\begingroup$ I was referring to some of the language in Keith Devlin's "the Math Gene". He claims that math knowledge is made up of an accumulation of "overlearned" routines. I think of this as learning to linguistic fluency. @SueVanHattum $\endgroup$
    – Jon Bannon
    Commented Dec 12, 2023 at 22:43

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As often happens: not an answer to the literal question (about references), but just some (substantial?) anecdotal stuff over 50 years of observing mathematicians:

I'd agree that being able to focus for long periods is unusual, whatever label.

I'd in fact disagree with the idea that people should (obediently?) focus on whatever they're told to. As a corollary, if/when people don't necessarily focus on some random thing... well, that's probably a wise choice.

Which leads me to think about prioritization: not everything is of equal importance. Sure, sometimes prioritization is just a more marketable name for procrastination, but, really, there is a meaningful notion of prioritization (all the more in our "modern times" of over-communication).

Another point, which may muddle things in terms of labels for neurodiverse people: some people do have abnormally good memories for everything, whether they're interested or not. So, one way or another, this includes remembering garbage and dumb stuff... which may require some effort to separate from the useful things. In effect, sometimes the prioritization occurs long enough after the intake that the crap is still "in the system", taking up space, and perhaps time and energy.

Still, as I've said to my students many times, it is very convenient to be able to remember things that one does not yet understand, so as to be able to think about them... as opposed to the most common situation that people can only remember things they understand (=fit into their worldview...)

In that vein, I myself do not understand the extent to which some sort of "rigidity" is part of some definition of some neurodiversity... but, yes, one of the most inconvenient impulses that I've seen is an unwillingness/incapacity to contemplate new/unanticipated things. I've certainly observed that quite a few people "like mathematics" because (supposedly) it's all settled and perfectly whatever... So then they go to grad school, and after some time encounter what T. Tao has labelled "post-rigorous" math (wherein not all details are of interest, to say the least!), and are unhappy... because they thought that the pedantic ultra-rigorous (painfully pedantic?) undergrad upper-division math classes were what math is all about.

So, yes, "undergrad math" (as often taught) is a trap for certain people.

Oppositely, as for me, "higher-level" (a touch post-rigorous?) math can be a great relief, aesthetically, etc., for some people. Not a moral virtue, for sure! ... but convenient (in my opinion) if one wants to find out new things.

:)

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  • $\begingroup$ I love it, Paul! $\endgroup$
    – Jon Bannon
    Commented Dec 14, 2023 at 12:01
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Based on a cursory investigation of the literature, it seems like ADHD can loosely be described as providing an extreme combination of "superfocus" on things that one finds interesting, and "super-distractability" on things that one doesn't find interesting. Different people with ADHD have different focus/distractability profiles across different things, so depending on who the person is and what you're asking them to do, ADHD might help or hinder their performance.

(As Sue VanHattum points out in the comments, plenty of non-ADHD people have attention "differences" where they can focus better on things that they are interested in than things they find boring. With that in mind, an attention "disorder" like ADHD might be characterized as an attention difference that is simultaneously extreme enough and unmanageable enough to cause severe distress and impediments in one's life.)

In particular, when ADHD people have trouble with math, it the issue is mainly due to impaired central executive functioning, which would suggest the issue primarily boils down to things like getting distracted and losing focus of the goal of a problem when one does not find it super interesting.

Friedman, L. M., Rapport, M. D., Orban, S. A., Eckrich, S. J., & Calub, C. A. (2018). Applied problem solving in children with ADHD: The mediating roles of working memory and mathematical calculation. Journal of Abnormal Child Psychology, 46, 491-504.

"CE [central executive working memory processes] ability fully mediated between-group differences in applied problem solving whereas math calculation ability partially mediated the relation. Neither PH STM [phonological short-term memory] nor VS STM [visuospatial short-term memory] was a significant mediator."

"Coordination within and between the two STM subsystems is superintended by the domain general CE to (a) determine the task-relevance of the information contained in the mathematical word problem; (b) update information in PH/VS STM with newer, more relevant information; (c) connect information contained in the mathematical word problem with knowledge stored in long-term memory regarding math rules and potential mathematical algorithms to be applied in the current problem; (d) maintain the overall ‘goal’ of the applied problem; and (e) sustain attentional focus while concomitantly inhibiting irrelevant information from entering/competing with temporarily stored information"

Raciquel posted a comment to a video where an ADHD mathematician describes his experience, and it sounds just like you'd expect based on the above -- basically, he's really "spikey" as opposed to well-rounded, and whether he feels his ADHD symptoms depends on whether he's doing things that are within his "spikes" of interest/ability/motivation.

How Getting a Math PhD Cured My ADHD (NOT)

"eventually I found something I felt so passionate about, I couldn't think of doing anything else. And that was applied math for me. And that ended up masking a lot of symptoms through grad school, and it wasn't until I left grad school recently in 2018 that my ADHD symptoms came back in full force."

He (Youngmin Park) describes how he actually struggled a bit with K-12 math due to the emphasis on memorizing formulas -- he didn't find that interesting, so he just rushed through homework, putting in the bare minimum amount of work for a passing grade. But he could be incredibly hyperfocused on other things (e.g. as a toddler, he would play with Legos for hours and hours and hours, forgetting to eat and sleep).

The thing that really drew him into math later on was a professor who sparked his interest in some particular research problems. He found grad school liberating because he had tons of freedom to follow his natural motivations/interests:

"I could work or not work whenever I wanted. I could work 12-hour days one day. I could work a 6-hour day the next day. I could take a day off the third day and go back to like a 14-hour day the day after that. And that was very liberating because my motivation doesn't start in the morning and fade off at night, it actually starts at very random times throughout the day and I can't predict when it comes about."

Basically, he's just really good at doing what he wants to do, when he wants to do it, on his own schedule. When he's in an environment that allows him to funnel that kind of effort into something productive, then he does really well. His impatience, impulsiveness, and obsessiveness become a superpower because he can just floor the gas and charge full-speed ahead on the stuff that he's interested in. But whenever he's in a context where this kind of behavior isn't a superpower, it creates tons of friction and becomes a super-weakness (he mentioned some examples in the video, e.g. romantic relationships).

As far as other ADHD mathematicians and their experiences, there are a bunch of famous academics in math and adjacent fields who are known not only for their contributions, but also for amusing backstories and habits that seem strikingly aligned with what Youngmin Park describes in his video above. Erdős, Einstein, Tesla, you get the idea. They all clearly have a high degree of attention "difference", and I would venture that at least some of them would have been properly diagnosed with ADHD if tested today.

Courtesy of Dave L Renfro, there are also plenty of relevant and humorous anecdotes about mathematician Norbert Wiener:

"... the time he reported the theft of his car to the police, only to discover that he had driven it to Providence for a talk and taken the train back; the conversation in an MIT hallway that he concluded by asking his interlocutor which way he had been heading when he stopped to chat, greeting the answer with 'Good! That means I’ve already had lunch.'"

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    $\begingroup$ "so his parents never really suspected that he had an attention disorder" I would not call this an attention disorder. It makes sense to me that we can focus well on interesting things, and not on uninteresting things. It might be an attention difference. $\endgroup$
    – Sue VanHattum
    Commented Dec 7, 2023 at 19:26
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    $\begingroup$ This is great. Thank you! $\endgroup$
    – Jon Bannon
    Commented Dec 7, 2023 at 19:26
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    $\begingroup$ I loved my masters program at Eastern Michigan University. I had serious trouble focusing on the math work I was supposed to be doing at UCSD (PhD program, which I dropped out of). I thought it was because it was harder, and I couldn't wrap my head around it completely. But yeah, it felt boring to me. $\endgroup$
    – Sue VanHattum
    Commented Dec 7, 2023 at 19:28
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    $\begingroup$ Erdős, Einstein, Tesla, you get the idea. --- Norbert Wiener has to be included! From here: ... famous anecdotes about Wiener’s absentmindedness: the time he reported the theft of his car to the police, only to discover that he had driven it to Providence for a talk and taken the train back; the conversation in an MIT hallway that he concluded by asking his interlocutor which way he had been heading when he stopped to chat, greeting the answer with “Good! That means I’ve already had lunch.” $\endgroup$ Commented Dec 7, 2023 at 19:28
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    $\begingroup$ (I wasn't suggesting an edit, and my choice of edit would likely be different than yours. But it's all good.) My opinion about ADHD is that it is a difference that many find valuable, and to call it a disorder does not give proper value to the inherent diversity of human beings. $\endgroup$
    – Sue VanHattum
    Commented Dec 7, 2023 at 20:19

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