At the Interface of Algebra and Statistics

[@Kimwilliams45]

This is wonderful. I watched just over half your video with Timothy Nguyen. It was enjoyable but I got lost. This video is very clear and is applicable to what I am studying now - quantum computing and machine learning. In my job, there is effort going on to automate the coding of the data collected from motor vehicle crashes.

[@tomburns5231]

One of the most beautiful and amazing thesis introductions/summaries I have ever seen - artistically, creatively, and academically! Congratulations, Doctor :)

[@tomburns5231]

P.S. I am very interested in the language modelling implications. Please keep us all posted on how that project goes.

[@hunterhatfield7157]

As a linguist, I cannot hide my excitement. I can't wait to get into your thesis.

[@grahamjoss4643]

wow. got here from grant sanderson. cant wait to start !

[@jcbahr]

it's so fun seeing the physics side of something that seems related to stuff i've been learning about lately: planar algebras and free probability also thank you so much for making this accessible to a broader audience, I wish all technical fields were taught and explained like this

[@saikat93ify]

I just came here from your website. I had seen many of your videos for PBS Infinite Series and just discovered that you have your own channel !

[@alvincepongos]

Amazing Tai-Danae! Please keep sharing your thoughts and work!! :D

[@goneyet]

Tai-Dana, you're the best. No words to describe the gratitude I have towards your work and your awesome way to artistically share it with us (I read most of your posts on mathe3ma already). Congratulations on the thesis!

[@rickjames4727]

Love the effort to make your work accessible.

[@crimson02138]

Thank you, Dr. Bradley, for a fantastic video that makes a highly complex topic much more accessible to those not in your field. I’m a cancer physician but am fascinated by your thesis and now will have to read it in its entirety.

[@sentralorigin]

sick intuitive explanation for people without a background in math

[@astrophysicalevidence]

Nicely done. Found your blog about a year ago - congrats on the thesis!

[@wuschelthepuschel]

I think to present one‘s thesis with such a video is a very orange idea!

[@nicolumi7173]

Amazing work! Looking forward to read the manuscript! Please keep on the blog and this kind of material

[@NoNTr1v1aL]

Absolutely amazing video!

[@hunan131]

Wow. A dissertation that is also a beautiful work of exposition and art. Thank you

[@russellsiegelman2537]

Thank you for sharing this. It is wonderfully illustrated and annotated. Beautifully done. Kudos.

[@TheScottforever]

Woaw !!! That seems incredibly ingenious ! Good job !

[@ottoludewig1244]

Amazing work! I'm studying my Undergraduate and pursuing a career in research akin to what I understand to be Topology, Algebra and Category Theory, lately been interested in Probability and Statistics. Thanks for facilitating your work, it's enlightening and inspiring to learn about this

[@ottoludewig1244]

There might be even a connection with structuralist linguistics (Saussure for example) on building language and such, really fascinating

[@AleifrLeifrson]

I enjoyed listening to you talk about mathematics tremendously! Subscribed in case we should be so lucky that you make more videos :)

[@the_allucinator]

Universal Construction 1. Find patterns 2. Find the ranking 3. Choose the best 'tis what I learned from Bartosz Milewski. The Section 3.4 of what you presented presents the idea of Universal Construction well.

[@valloway]

Yessss so happy you are doing videos again!

[@thelastcipher9135]

Cool! Had a similar idea regarding combining algebra and probability in the desire of studying complex systems. I only had the nebulous part of the idea though so I was wondering if such mathematical structure already exists and then BAM, your thesis!

[@kfir_krak]

Looks amazing. First thing on my summer reading list. Love your work. Thank you

[@mandos9]

This is bound to be a cornerstone for a future branch of science

[@evannesmith5120]

Great video thanks ! What latex document class do you use ? It looks so satisfying to the eye !

[@Czeckie]

this looks very interesting, Tai-Danae! I'll find a time to read it, I'm particularly stoked about the glimpses to quantum information theory without physics (I'm extremely rubbish at physics and my brain stops working if the physical examples are more involved)

[@MathPhys4U]

Congratulations on your thesis. Thanks for sharing your ideas.

[@johnsabini3218]

Your video synopsis is sharp and nicely done. It spurs me on to at least look at your thesis. Congratulations Dr. Bradley.

[@hoangvinhnguyen2461]

This really is genial. Not only the thesis, but the way you brought the story to laymen like myself. THANKS !!!!

[@papistthinker]

Promising thesis, great introduction and summarization.

[@salvaalcantara4569]

Brilliant! Thanks for democratizing math, certainly there is a need (and a lot of value) for it!

[@cyrineh5602]

Wow the initial idea is just brilliant !

[@wesleyrm]

527 likes, 0 dislikes. The most liked undisliked video I've ever seen.

[@amolvaidya8666]

Congratulations, Doctor!

[@insightfool]

This is brilliantly presented.

[@pra.]

Great thesis summary!

[@zacharysmith4508]

I've always wanted to know for interdisciplinary topics like your thesis how much depth, broadly speaking do you need to know from each area? For instance, applying commutative algebra or algebraic geometry to statistics, would a pursuing masters/Ph.D. student take an entire course on those topics?

[@LemoUtan]

Nice work. Although have curious urge to sleep off a slight fury over use of orange, not green, ideas.

[@ryancook9897]

Amazing presentation! Did you do the animation yourself?

[@faraazali9589]

Wow amazing theory. I can see applications in NLP.

[@joejoe-lb6bw]

I don't understand it all, yet it makes my brain happy. In terms of fiction: I bet all this will be part of a future SciFi work that postulates a machine that uses the "Bradley Structure" to compute what will happen in the future. Like Isaac Asimov's Foundation series.

[@nehsm30126]

I'm so inspired by your work and can't wait to apply it to the music theory 🤩

[@freefrancisco]

Hi, thank you for this very interesting video. I think what you talk about here might be an explanation as to why LLMs like ChatGPT are so good at understanding language. The idea that there is real understanding under an LLM has been criticized because LLMs are purely statistical. But if I understand this video correctly, you are making an argument based on category theory that the statistical relationship between a word and the rest of the words in language is homomorphic to meaning. I need to read your actual thesis to be sure, but if that is the case I think it could explain why LLMs work so well.

[@cheyneanderson4875]

I'm really excited to read your thesis! I don't know that I've ever said that about a thesis!

[@cheyneanderson4875]

I finally got around to reading through it! I really enjoyed it, and I definitely see myself using some of this math in a project of mine. I've had a really hard time finding good learning resources on tensors and quantum math. Your paper did more to give me a good intuition for both of those than anything else I've come across. I especially liked the tensor network diagrams, which I had never come across before. Category theory is still brand new to me, so I had a hard time following chapter 5, but it left me eager to learn more about it. Thank you for your work!

[@fadmad7257]

Nice work, understood like 1% of it, how long did it take you to finish your thesis?

[@christianfrohlich3835]

Very impressive! I could image that this framework has many useful applications. Not sure whether I'm able to understand it though :/

[@physira7551]

very happy for you

[@Jhev1000]

Congrats and subscribed!

[@kategory]

Thank you

[@DavePawson]

Written with a wider audience in mind Tai-Danae, but I can't find the paper on the net, is it locked away behind BIG paywalls, or can Joe Public access it please?

[@sylviajin6968]

It's in the arxiv link in the description - on the right you can click PDF to view it

[@robertolopezbordetas]

This is amazing!

[@AdhiNarayananYR]

I think the phrase “orange idea” is gonna catch up and it could no longer be used to describe something that occurs rarely in language

[@MateuszMalinowski]

Congrats!

[@jimmyjonestodd2556]

Epic

[@deneb6139]

This gonna change the way we look at AI.

[@AesaKamar]

Congrats!