Do Numbers Exist? – Marcus du Sautoy

1. 

   @markwrede8878

   August 22, 2025 at 6:59 am

   The counting of primes within the number line disrupts the distributive property as values increase when multiplication is consulted.

2. 

   @TheUSKC

   August 22, 2025 at 6:59 am

   There is no such thing as "one" and "zero cannot exist – prove me wrong – https://youtu.be/BHgLMOsVQ5M

3. 

   @jreberanlc

   August 22, 2025 at 6:59 am

   His set theory with zero being a number is unconvincing because he has essentially physicalised the set containing noting so that he is counting ‘the set’ containing zero as well as the set containing 1. But then, in that case the set containing zero is set 1. So yes, with set theory zero is counted as a number in real life it is not

4. 

   @jreberanlc

   August 22, 2025 at 6:59 am

   lol – couldn’t help notice at 42.06-08 he postulates that the Big Bang came out f nothing Ng but he can’t come out and say it – he nearly does “nnnn, nnnn …” but then he says “pure energy” and tacks onto the end a very sneaky and quick – unnoticeable “nothing”. He knows that’s nonsense.

5. 

   @raphaelreichmannrolim25

   August 22, 2025 at 6:59 am

   In my work I showed how a multidimensional view on natural numbers is allowed by Peano's axioms themselves, in what I called Spatial Arithmetics, which unify a lot of number theory and create the concept of arithmetic automorphism.

6. 

   @LikelyForgiven

   August 22, 2025 at 6:59 am

   1 exists, the rest are derived relative to that

7. 

   @KrasBadan

   August 22, 2025 at 6:59 am

   17:29 There was a great minutephysics video recently about the physics of dissonance, which I highly recommend.

   In this video it is explained that what matters the most is not pitches, but actually overtones. It just happens so that the overtones of the string overlay so nicely with each other according to their frequencies, and it is that cultures which have string as a main instrument that have this 12 note music.

   But the ones that do not have string as a main instrument often use different, often uneven, note separation, just because it is that separation needed for overtones of that particular instrument to overlap nicely.

   So the main factor in play here is that so many cultures base their music on string.

8. 

   @edwright440

   August 22, 2025 at 6:59 am

   Loving now open and enthusiastic Marcus is being to a calm and restful interviewer.

9. 

   @hrodvitnir7524

   August 22, 2025 at 6:59 am

   This has defiantly been an eye opener to mathematics

10. 

    @Truth_Tradition24

    August 22, 2025 at 6:59 am

    Hey Alex, 👋 this is Jackson from the Truth & Tradition Podcast. I am on a mission to watch every one of your videos and leave a comment on each of them.

    Do numbers exist? What a wild question! I love it! This was so fascinating, I'll have to check out his book. Thanks! 🙏

11. 

    @gratefulkm

    August 22, 2025 at 6:59 am

    0,1,2 do not exist,
    All life and experience starts at 3, So the numbers 0,1,2 have to be imagined
    I love to point out that Atheists and one god believers are part of the same delusion
    A Roman Slave mental cage , that the slaves cant "see" out of due to their belief that they are individually measurable, accountable, responsible, dependable, and trustworthy, Ps they are all words that only exist due to a Slave master and a slave relationship
    In the "Oral tradition" left echoing by the Druids ,those words don't exist

12. 

    @xhinoteque

    August 22, 2025 at 6:59 am

    After hearing this, I wanted to listen to Tool, for some reason.

13. 

    @smadaf

    August 22, 2025 at 6:59 am

    The impossibility of dividing by zero has to be universal. A problem is that too many people are taught that division by zero is 'not allowed' without being taught how it's impossible. It's easy to see if you consider how multiplication reverses a division-problem, with no changes in the numbers. Example: 14 ÷ 7 = 2 can be reversed as 2 × 7 = 14. Now consider division by zero: 14 ÷ 0 = x. What number, x, can be multiplied by 0 to give 14? There is no such number.

    You cannot chop a thing into no pieces of itself.

14. 

    @EpicMathTime

    August 22, 2025 at 6:59 am

    42:29 I want to answer this, though I'm pausing before the guests answer. This is a good question about foundational mathematics. I think this question is one of motivation.

    (I apologize for this notation, but I will refer to the empty set as {}. Therefore the set containing the empty set is {{}}, and so on.)

    So to get at the heart of what you are asking, Alex, the set {{}} is not 1 in any ontological sense.

    Rather, as set theory is foundational to mathematics, the motivation is: can we construct the natural numbers using only the axioms of set theory?

    The answer is yes, we can. We identify 0 with {}. We identify 1 with {{}}. We identify 2 with {{{}},{}}, and so on. However, this doesn't get to the important part. All I've done is identified some symbols with some other symbols.

    The important part is that this identification allows us to also turn arithmetic into operations on sets. I won't get into the details, but addition essentially becomes a type of set union. This is what gives structure to that set of symbols and allows us to identify them as the natural numbers. In other words, the axioms of set theory alone are strong enough to fully define the natural numbers as a mathematical object.

    Now, why are we using the empty set, and the set of the empty set, and all of that? The answer is simply because as our goal is to construct the natural numbers from the axioms of set theory, we must only use sets that are granted to us through the axioms of set theory alone.

    Furthermore, the set theoretic representation we are talking about (with {{}} being 1, {{{}},{}} being 2, etc) isn't unique. There are other representations, and correspondingly, the set representations of arithmetic changes. It doesn't really matter what the representation is. All we care about is that the axioms of set theory alone encodes the natural numbers.

    The key important part to realize is that to defining the natural numbers via set theory doesn't just mean we are picking sets to represent 0, 1, 2, etc. The natural numbers are ordered, we need that. They have arithmetic, we need that. The natural numbers aren't just a set, they have additional structure that we need to set theoretically formulate. The specific representations of the numbers as sets isn't the full picture. At that point, all we've done is matched some symbols together, we didn't do anything. It is the proceeding construction of arithmetic and structure through set theory axioms that actually complete the idea.

    A simpler example of this same idea is ordered pairs. The set theoretic definition of an ordered pair is (a,b) = {{a},{a,b}}. The only reason that this is so is because this definition gives us the property we want to have constructed purely in terms of sets.

    The reason that set theory / ZFC is considered foundational is because its axioms essentially encode all of modern mainstream mathematics. To see this, realize that we have constructed the natural numbers from set theory, and the rational numbers are encoded from the natural numbers, and the real numbers can be constructed from the rational numbers, and so on. Functions, calculus, vector spaces, groups, rings, topologies, functors between these objects and all morphism between them, and all of the rich and endless properties, behaviors, relationships, everything contained within all of this can all be traced back to those axioms of set theory. That is what makes set theory the foundation of mathematics.

15. 

    @JustTrustMeScience

    August 22, 2025 at 6:59 am

    The hair alex, its sticking out, hbthbrggbrtyhnnbuynybyybymu

16. 

    @Steno916

    August 22, 2025 at 6:59 am

    Should have listened to Tool Lateralus for his book. 🤘

17. 

    @heyho4488

    August 22, 2025 at 6:59 am

    Anything that's not a number is bread

18. 

    @cameronpierce9426

    August 22, 2025 at 6:59 am

    Gentlemen,

    Thanks for this interesting and genial conversation. I've long appreciated du Sautoy's public-facing mathematical work, but I must check both of you on your casual invocations of the man, Pythagoras. Unfortunately, most of the anecdotes and theories you've attributed to Pythagoras are not regarded as authentic. There's something like the 'quest of the historical Jesus' in the case of Pythagoras–except that it's even more fraught.

    The traditional literature is full of pseudepigraphy and Platonizing retrojections. I suggest beginning with Most and Laks' recent (2016) scholarly edition of Pythagoras and Pythagoreanism (Harvard University Press), to get a sense of the difficulty of ascriptions. That said, there are plenty of secondary source- and text-critical works about, including those of Burkert, for example, who rejects many of the common legends–like learning the harmonic ratios by hearing the tones of a blacksmith's hammer (it's not even clear that Pythagoras understood these ratios, let alone discovered them), or the idea that Pythagoras experimented with stringed instruments–all apparent hagiography and myth from Iamblichus many centuries later. Huffman is another knowledgeable source on Pythagoras, articulate at expounding the difficult tradition surrounding him.

    It would be better to refer to 'Pythagoreanism' or 'the Pythagorean tradition'–although, even here, one needs to specify, since this is a heterogeneous mix (e.g., early and late).

19. 

    @thesituationist

    August 22, 2025 at 6:59 am

    YESSS HE’s taLKING ABOUT TABLA .. please go into konnakol begging you

20. 

    @BadassRaiden

    August 22, 2025 at 6:59 am

    I would say, not, numbers dont exist. Values however do exist. It's doesn't matter what numbers you decide to use, the golden ratio is a value that exists in nature regardless of any degree of inquiry into its existence. All that matters is that when I define whatever numerical system I am going to use, I remain consistent in how those values relate to themselves based on their numeral position and how they relate to other values that I define. This is why I hate the question "Is math invented or discovered?" It's just a bland, uninteresting question, and frankly, not really a philosophical one either. It's invented, clearly. Math is a language and all language is invented. What's discovered is the phenomena that that language was invented to describe, and that phenomena exists out there in the world to be found regardless of whether or not we have invented a language to describe it.

21. 

    @obzerver-11

    August 22, 2025 at 6:59 am

    no, they don't… yes they do… no they don't. Sorry, what was the question?

22. 

    @Michael_X313

    August 22, 2025 at 6:59 am

    @28:18 yeah but that's because of the granting of unity. We say, "the opposite side/end of infinity " as if its supposed to mean something when it's just a semantical loop because we grant unity via language in the first place… just like the application of 0.

23. 

    @marveloussoftware1417

    August 22, 2025 at 6:59 am

    This is an easy question, just look at the universe and show me where the numbers are. You only find numbers where humans are. So we know numbers are man made. Now pick a number. Think of the definition. A number is useless without something to modify. So a number requires something else to have meaning. Now look at the something else and determine how the number modifies something else. How do you change the something else so the number doesn't modify it. When you make that change the something else is identical, there is just more or less of them.

    Numbers and math, IMHO, are just a language us insignificant humans require to explain reality. No numbers or math would exist without us.

24. 

    @chrisgreen1514

    August 22, 2025 at 6:59 am

    Excellent interview Alex ❤️
    Marcus talks about “abstract ideas”, e.g. the idea of numbers and the idea of a perfect circle. He also talks about “model structures”. Where do our ideas and math models exist if not in our minds, plus the embedded information from other minds? Perhaps mathematics and logic is just an attempt to rationally describe necessary structures that could exist? I suspect that only the math that can be applied successfully in our world is used and that plenty of models and theorems gather dust on Plato’s floor. Some solutions are just not real, but that depends on our definition of reality! 🤔

25. 

    @choppedherring7977

    August 22, 2025 at 6:59 am

    Mathematics isn't magic. It's language.

26. 

    @patchso

    August 22, 2025 at 6:59 am

    Fascinating!

27. 

    @hakighz1952

    August 22, 2025 at 6:59 am

    That was brilliant. Love it!

28. 

    @MunkyMaGik

    August 22, 2025 at 6:59 am

    I could listen to these two talk all day!! Love this. Thank You 🙂

29. 

    @user-td4do3op2d

    August 22, 2025 at 6:59 am

    31:00
    Why does he keep adding R everywhere? Indiar?

30. 

    @user-td4do3op2d

    August 22, 2025 at 6:59 am

    17:28
    This is unfortunately completely untrue. You can divide octaves in different ways. WE Divide it in different ways. A pentatonic scale sounds much more consonant than a chromatic scale. Other cultures have many scales with all sorts of different microtones, all with their own emotional connotations. Turkish music comes to mind. Remember, this man is a mathematician, not a musicologist.

    There is NO universality in the emotional understanding of major and minor scales. In the west, we didn’t even have major and minor scales until a few hundred years ago.

    27:22
    He should have said consonance as opposed to dissonance. Dissonance is a form of harmony.

31. 

    @AstaraBrightwing

    August 22, 2025 at 6:59 am

    Tywin?

32. 

    @jasft9746

    August 22, 2025 at 6:59 am

    There's nothing weird about maths ok, it's just wonderful.

33. 

    @nettiestaton2775

    August 22, 2025 at 6:59 am

    I really love listening to people this passionate about their subjects.

34. 

    @juliamccoey7496

    August 22, 2025 at 6:59 am

    Quantum physics doesn't say everything is quantised. Even quantum physicists can sometimes forget this *embarrased face*… The energy of bound states are quantised. The energy of, for example, free electrons isn't. We don't know if space is quantised (and I think we have evidence to the contrary?).

35. 

    @hillelshmuel1354

    August 22, 2025 at 6:59 am

    Fascinating! I understood almost nothing but fascinating!

Comments are closed.