• "Donald Knuth lectures" https://www.youtube.com/playlist?list=PL94E35692EB9D36F3 (111 videos)
This includes several sub-series but the playlists don't have the videos in the right order:
• “Aha sessions”: https://www.youtube.com/playlist?list=PLoROMvodv4rNbeodV7vqx... (Knuth used to run a “problem-solving seminar” at Stanford; these are videos from one such year.)
Three lecture series on TeX that are now of historical interest (e.g. the TeX program has changed considerably):
• “TeX for Beginners” https://www.youtube.com/playlist?list=PLoROMvodv4rN1PKcXvzjo...
• “Advanced TeXarcana” https://www.youtube.com/playlist?list=PLoROMvodv4rNrDaAftaqM...
• “The Internal Details of TeX82” https://www.youtube.com/playlist?list=PLoROMvodv4rM2JuHk3qBh... (I've found this invaluable as I try to read the TeX program)
The following two playlists are still unlisted and I no longer know how to get to them:
• Mathematical Writing https://www.youtube.com/playlist?list=PLoROMvodv4rOrFl78-o6m...
• Computer Musings - Donald Knuth https://www.youtube.com/playlist?list=PLoROMvodv4rNMsVRnSJ44...
(I happened to have them in my browser history… these playlists used to be linked from http://scpd.stanford.edu/knuth/ but as of yesterday they seem to have changed it up, and also made the videos public (why were they “unlisted” earlier? No idea).)
And completely unrelated, but if you happen to be interested in church organ music and the Bible's Book of Revelation, the world premiere of Knuth's Fantasia Apocalyptica (https://cs.stanford.edu/~knuth/fant.html):
Don Knuth, 1974 ACM Turing Award Recipient - Part 1 [video] https://www.youtube.com/watch?v=vUJ01nRE7r0
I think he gave this talk twice, once in 2000 and once at HERCMA 2001
Elon Musk has a similar pattern, but it's not so much a speech disorder as it is their brain is working so fast, pulling from multiple sources and considering multiple perspectives. They're auto-editing their words in real-time, revising what they're saying while considering all of the above factors and more. But sometimes they get ahead of themselves and so in an effort to be clear and precise, they backtrack a few words and rephrase, filling-in as they anticipate potential contextual gaps. This is what you're seeing.
Rather than thinking they need to see a speech therapist, view it as a mark of authentic speech by someone who strives for precision and is empathetic to their audience. When you look at it this way, you can know and appreciate that you're witnessing the genuine workings of a brilliant mind.
However, I have been thinking about the unique speech patterns of some accomplished individuals. My uninformed guess is that some people develop neural connections differently depending on what they do in their formative years. Feynman, in a video , talks about how he was able to keep accurate time while reading but not talking, whereas his friend John Tukey could keep time while talking but not reading.
If someone doesn't talk much as a kid because they spent most of their time reading or solving math problems, it might be reasonable to expect that their speech will be underdeveloped.
I have nothing but anecdotal evidence. I, for instance, cannot talk and think (perform simple arithmetic or recall something from memory or even think about the next sentence) at the same time. If I'm talking, I have to pause shortly, think and structure what I'm going to say, and then say it, and after saying it I might notice I missed something and then I rephrase it. I've recorded myself and my speech pattern is almost the same as the one in Knuth's videos. I attribute the speech pattern to not having to talk much during my formative years.
I don't know; I've listened to dozens of hours of his videos and found them all useful and rather clear. I've heard comments like yours from others though, and I guess there are two points:
* Of course a person at 80 will not speak the same way they did at 40. (I'm currently watching his lectures on Mathematical Writing, given when he was 49: https://www.youtube.com/watch?v=mert0kmZvVM&index=2&t=0s&lis... -- youtube has some even older videos on TeX etc but they're probably of less general interest.) Older people generally have more halting speech and the like, but this is perfectly natural. I suspect that if, for cultural or whatever reasons, you haven't spent a lot of time listening to old people and learning from them, you may just find it unfamiliar. Nevertheless, I was in the audience when Knuth gave his 2017 Christmas Lecture weeks before his 80th birthday, and a lot of the audience did seem to follow along and enjoyed it. (You can hear laughter in the expected places in the video: https://www.youtube.com/watch?v=BxQw4CdxLr8 -- so clearly not everyone feels the way you do.)
* Every person has their own speech style, their way of translating thought into sounds. Like an unfamiliar accent, it may take a few minutes or hours to get used to it. (If you care enough about the content you will.) What you get from speech idiosyncrasies (their pauses, backtracking, mistakes, etc.) that you don't get from the written word is a window into someone's way of thinking, and I find in Knuth's lectures it's much easier to follow along his thought process, than in speakers you may consider more "smooth". It's very natural and informal, even when he's discussing highly technical topics there's a lot of him that comes through, and that's very valuable IMO.
(And his speech seems well within the norm... I've seen comments like yours that sometimes attempt to diagnose medical conditions from afar; that can seem a bit excessive.)
He was a CWRU alum and came to rap with grad students around '89. He was wearing his trademark woven hoodie and jeans. We didn't get a room, he just plonked on the floor in a hallway somewhere and told stories and enjoyed nerding with us.