The internet needed this lecture. Thank you.

This guy has a deep and powerful understanding of mathematics and physics. I am basing this not just on this lecture, but others. I am just posting it here. Thanks for making these gems available in the public domain. I usually fall half asleep when I watch other lecturers, but this guy keeps me awake because there's so much food for thought here. Philosophically as well as mathematically/physically! No wonder Perimeter Institute hired him.

I've always admired people who can explain complicated and abstract ideas with easy and great clarity of thought - and this lecturer is definitely a person to be admired for such traits.

This guy is an exceptional lecturer. The way he seamlessly goes from the technical to the context of the subject is something most lecturers can't seem to do. All the while letting the student know where he is. The start where he outlines the layers of mathematics/logic and how the physics relies on these, the Venn diagram of algebra, analysis and geometry and DG at the centre. and the bit where he talks about how it's important to know "what we are not talking about" when explaining the fundamentals of predicate logic without getting lost in the details of the example X as an element of Y since we haven't defined "element of" yet. Exceptional teaching.

Great and clear content. We need more of these guys on the web.

Ok I just want to say that I am forever indebted to the amazing Mr. Schuller, who has practically and unwittingly taught me all the basic higher mathematics that I need! 😢

This is amazing sprinkled with a great sense of humor, thanks for sharing!

Thank you Dr Schuller for uploading this lecture! Hope to see many more!

The way he writes t & f makes him always correct.

Amazing!, not just the content but the way he delivers it with such calmness and clarity, incredible!

This is the true act of love and compassion, Thank you!

This series of Lectures is pure pleasure! Sometimes I come back here just to be amazed again. Thank you!

Amazing! He explains things very well. I can understand more than 90% materials. See you guys at the final lecture.

A clean class of computer science. Logic is exactly circuit theory among many other things. The beauty of it and importance deserves a permanent place in our hearts and the internet.

Thanks for this (second-youtubed) amazing course. So much appreciated! Constructive logic allows you to assume that A exists and reach a contradiction and by this prove that A cannot exist. But, it disallows you to assume that A not exists and reach a contradiction and by this conclude that A exists.

This is pedagogy; not whatever it is my mathematics professor was attempting to do.Thank you, Prof Schuller. ❤

You are a great teacher. Thank you for sharing these lectures.

This is the best lecture on the subject that I ever watch. Amazing knowledge of math and Physics. I am very excited to see the other lectures. Thank you so much.

For clarity, between 1:07:10 and 1:12:25, the assumption (M) should be q_j can be written as the j'th step if and only if there is m,n such that for 1≤m,nq_j is true. For example, assume P and P=>Q are axioms. Then, a valid proof that Q is true is as follows: (1) P (A) (2) P=>Q (A) (3) Q (M). Remark: (P^P=>Q)=>Q is a tautology which allows us to invoke (M) at stage j=3.

Wonderfully structured. You keep the audience engaged, you go at a pace that does not tire the student but keeps them glued to the blackboard. And you go to the deepest corners and leave no aspect uncovered.

Absolutely brilliant, breath-taking and addictive!

Dr. Eastlake : Thanks a lot, for your excellent lectures!

Mr. Schuller, these lectures are just amazing. Just wow. Thank you so much for sharing it, I wish I could attend your lectures. I am especially amazed how well you have explained the role of different math branches for understanding contemporary physics. I was looking for it for quite some time now. Thank you very much.

wow...the first 2 minutes and I am completely captured. The interpretation and reflection on those two quotes by Wittgenstein

Randomly suggested by youtube and such a fantastic approach to the theme discovered .... Unbelievable!!! Thank you for upload this classes :) Great job

I'm enormously grateful. Thank you.

Hands down for this amazing introduction to everything. If I was in the class, I will applaud but I guess the students were super confused. I watched this lecture in 4 parts so I had enough time to digest it. Thank you so much. You've been an amazing teacher to me, Dr. Schuller!

sometimes a person can be an excellent professor or an excellent scientist but this guy is both. In my life I had the privilege to watch a professor like that and I thank God for this.

thank you so much professor Schuller. The lectures are very very good.

Must watch lecture if you are into any level of mathematical logic and believe me he identifies the core principals of math logic in a precise manner. I could finally know how a proof was structured and finally didn't need to memorize any way to logic, but used logic itself to identify the content itself.

One of the best first 15min I've ever watched!!

This is really fantastic. Thank you so much!

He is clear and concise which in turn enables learning. Love it

Thank you for your wonderful lectures!

This is such an incredible series

Wonderful lecture. For those wondering, he does describe a consistent axiomatic system correctly but the definition he stated was for an incomplete axiomatic system.

1:13:09 "a computer can quickly verify a proof by this definition" This is almost true, except for the fact that you can insert any tautology as a valid step in the proof. The problem of recognizing whether a given proposition is a tautology is coNP-complete, meaning we don't know how to do it in a way that scales efficiently with the number of terms in the proposition (and it's commonly believed no such way exists)

Remarkable lectures !!!I I wish we had some problem sets to solve , so that we could test our concepts.

After finishing these lectures, you can go through the freely available book "Differential Geometry Reconstructed" which I think is a good follow up and comprehensive.

I wish I discovered this series earlier, so so good!

The first time I heard of "Modus Ponens" the computer science teacher said "All men are human, Peter is a man, therefore Peter is human". Theses lectures are great, thanks for sharing !

We need more lectures. I love the way you are explain Matematics. Are you planning to do some lectures about H - Function? A huge respect for you!

Amazing first lecture! I will try to follow the next ones until my levels allows me. Greetings from Colombia.

Hello Frederic Schuller, thank you very much for making this public. This lecture series is extraordinary clear and really excellent for a self-study and an overview (personally being a computer musician who slowly is studying more and more mathematics) Is it possible to get to know which textbook you are using? And is it possible to access the problem-sets somewhere on the web? Vilbjørg Broch

Dear Dr Schuller, Brilliantly delivered lectures, great clarity of thought. Beautifully presented. I just wanted to know if there's a website for this course taught by you. It will be great to have access to the problem sets that you mention in some of the lectures. This will reinforce our understanding of the material. Also, is there a particular textbook you are following? Thanks.

What a wonderful summary.

Thank you Dr Frederic Schuller

this guy is genius

This is pure gold!

Very nice. I am working through How To Prove It by Velleman and Sets For Mathematics by Lawvere. Found my way here by way of "The Portal" Discord group. Very helpful videos to supplement that work. This is my starting point on the long road to understanding differential geometry, the mathematical language of physics.

Watching this really makes me miss in person lectures. Sitting there and watching the board slowly fill up with proofs and implications was a bit much at times, but this online learning just doesn't hold a candle to face to face.

Difficulties of proofs, with translations: 1) "Easy" = Axiom 2) "Difficult" = Unprovable 3) "Hard" = Left as an exercise for the reader

Great lecture, Thank you!

One of the few professor which remembers that his lecture is being recorded

Love your stuff.

what a gift to the world!!

I'm Physicist. Thank You For Great Lectures. Love From India 🇮🇳🇮🇳🇮🇳🇮🇳

All the lectures of you, are brilliant! It very rigorously clears ideas of mathematics and how it is used to interprete the dynamics and ontological causal-structure of our universe. I am very grateful that these lecture series are open for all in such this public platform. Please keep posted Sir. Thank You!

😭😭 i want to study this course, thank you

Thank you, Frederic, for the lectures, these and the many others. Regarding this one: I think it is better to start with sets, because {T,F} is a set, the concept of a variable needs the set, quantifiers need the set notion, and so on. So first elementary set theory, then logic, then more advanced set theory, spaces, and so on,...

There was a lot of information to process in each lecture but I haven't lost my interest neither for a second. That also holds for the lectures in Quantum Theory and the ones given in the International winter school on gravity and light. An amazing lecturer. Thank you very much for your effort. It would be very helpful if you may upload lectures also in QFT course for instance, with this kind of mathematical clarity. Is there any way that we might get the problem sheets?

I searched up a German name I made up, and not only does he exist, he teaches what I needed. Badabingbadaboom

Where he comes a bit short in mathematical rigor and clarity, he makes up in making the physics roar.

Hi Dr. Schuller, I am afraid I have to object that contraposition implies proof by contradiction at 31:00. The basis of proof by contradiction is p || ~p, i.e. the law of excluded middle, or LEM in short. So the reason is, if a statement is tautology, then it's negation is false; so proving negation being false proves the proposition itself being tautology. On the other hand, in other logic, i.e. those non-classical logic which refuse LEM, admits contraposition. Contraposition is admissible by axioms, while LEM is required to be an axiom. If it's not, or its equivalence is not, then it's simply unusable. For example, in constructive logic, the proof of contraposition goes following: (~q -> ~p) ((q -> False) -> p -> False) p -> q by discharging (q -> False) into False.

These are absolutely brilliant. Very clear exposition. Only thing...I would rather use 1 and 0 instead of t and f as they appear nearly the same on the board...

This professor is really really good. Hes a bit serious but damn he knows his stuff very well.

28:28, 35:20, 49:56, 1:07:25, 1:10:40, 1:22:00, 1:24:08, 1:28:25

glad to hear that there are professional mathematicians that dont trust the proofs by contradiction. I am no mathematician, just an enthusiast, but this kind of proof always feel sketchy to me :)

صحيح اتابع من البيت بالرغم من تخرجي من الجامعه منذ ١٠ سنوات واكتب معاه واتابع كل المحاضرات وشريت دفتر خاص للمحاضره . Thanks I watched these lecturers frome my home in Saudi arabia i graduates frome university since10 yars

I could listen to him forever

kudos. great lectures.

How are these lectures not more popular? Fantastic.

you are amazing, the videos are the better. I'm from colombia and on this subject are not videos in Spanish :'v

Is there a lecture notes or reference book to this course ? Thank you very much.

is there anybody having access to the problem sheets?

Best explanation of *_(f, t) => t_* I have heard.

Thanks very much for the lectures. Could someone provide the precise quotations of Wittgenstein about mathematics? Thanks.

Dear Fredric, can you please advise on any reading list associated with this course? Thanks

"it is always important to know what a subject is NOT talking about" very insightful.

I wish you were my mathematics teacher; 40 years back❤

Wow! I'm awed. He lectures, writes and explains everything at the same time without any notes. How does he do it?

I wish this becomes the first principles everywhere.

you know shit's gonna be fire when Wittgenstein is credibly referenced multiple times in the introduction to the lecture.

1:26:30 Another way to put it is: "An axiomatic system is consistent if from the axioms cannot be proven a formula and the negation of the formula. (Cannot be proven that )"

really nice. thanks.

This man is a genius

Does anyone know if the problem sheets are also online somewhere?

Are there problem sets to accompany this lecture series?

Excellent

39:02 That's the only part which appears to be not as concise as the rest, because you would want to be able to explain (or give an intuition for) this without using set theory (or really anything you build on top of logic). The reason why we don't say what x and y are is because we want to study very general properties that should not rely on the specific structure we will assign to them later (e.g. being a set). Not specifiying them should therefore be considered a strength of our approach (because it will work whatever they might be) and not as a weakness (implying that we don't know what we are talking about).

37:56 What is a function however? At the starting we dicussed, set theory is built upon logic, then how are we using a concept from set theory (that of functions) in logic?

Very good professor

Take note, people: this is _the. most. important. subject._ to have a grasp on as you go into higher mathematics. Spend the time.

6:17 why is Statistical Physics at the intersection of geometry and algebra? I thought statistics is more about analysis?

Finally, a mathematician who introduces the subject the correct way, via a wider philosophical picture. Excellent!

how ca I find the problem sheet for lecture 8 Tensor Theory? Anyone?

Amazing! Why is a lecture like this (and the next one) not required for all students of math or physics?

I wish I had found this 5 years ago

Schuller you are a great mathematics teacher, I think you should write a book I would think it'd have the possibility to become a classic, something that focuses on the logical, set axiomatic, and proof theory aspects of fundamental mathematics with are I think some of the hardest concepts for beginning math students, with the most room for improvement in the current literature in structural writing and exposition. Thank you for the videos, very useful and well done.

We need more videos