At the Interface of Algebra and Statistics

This video is a nontechnical introduction to my PhD thesis, which uses basic tools from quantum physics to investigate algebraic and statistical mathematical structure.
"At the Interface of Algebra and Statistics"
available on the arXiv at arxiv.org/pdf/2004.05631.pdf
My website, Math3ma, contains lots of friendly articles on mathematics:
www.math3ma.com
Follow on Twitter/IG/FB:
@math3ma
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This video was made on an iPad Pro using an Apple Pencil 2 in Notability and the Enlight Videoleap app.

[@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.

[@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

[@hunterhatfield7157]

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

[@sentralorigin]

sick intuitive explanation for people without a background in math

[@wuschelthepuschel]

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

[@alvincepongos]

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

[@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 !

[@rickjames4727]

Love the effort to make your work accessible.

[@valloway]

Yessss so happy you are doing videos again!

[@NoNTr1v1aL]

Absolutely amazing video!

[@AleifrLeifrson]

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

[@wesleyrm]

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

[@TheScottforever]

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

[@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!

[@kfir_krak]

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

[@MathPhys4U]

Congratulations on your thesis. Thanks for sharing your ideas.

[@astrophysicalevidence]

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

[@hunan131]

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

[@nicolumi7173]

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

[@salvaalcantara4569]

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

[@russellsiegelman2537]

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

[@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!

[@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)

[@amolvaidya8666]

Congratulations, Doctor!

[@mandosGOD]

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

[@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.

[@hoangvinhnguyen2461]

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

[@insightfool]

This is brilliantly presented.

[@cyrineh5602]

Wow the initial idea is just brilliant !

[@pra.]

Great thesis summary!

[@physira7551]

very happy for you

[@nehsm30126]

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

[@diagoemanuel4800]

Promising thesis, great introduction and summarization.

[@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.

[@AesaKamar]

Congrats!

[@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.

[@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?

[@robertolopezbordetas]

This is amazing!

[@johnsabini3218]

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

[@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

[@kategory]

Thank you

[@Jhev1000]

Congrats and subscribed!

[@LemoUtan]

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

[@christianfrohlich3835]

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

[@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!

[@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.

[@faraazali9589]

Wow amazing theory. I can see applications in NLP.

[@ryancook9897]

Amazing presentation! Did you do the animation yourself?

[@fadmad7257]

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

[@jimmyjonestodd2556]

Epic

[@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

[@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

[@deneb6139]

This gonna change the way we look at AI.

[@MateuszMalinowski]

Congrats!