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Category: Mathematics, Philosophy, Video


26 Responses to “Does Math Exist or Is It a Human Creation?”

  1. LiberTea says:

    If it doesn’t exist, can you fail it?

  2. harrad says:

    I think the question on “Does Math Actually Exist” is probably not the right one. It is analogous to asking if “Does English Actually Exist”. Perhaps the right way to see math is to look at it as a tool for analysis and no more just like English is a tool for communication. Any attempt to attach more importance to Math is probably a meaningless, futile exercise. If my memory serves right Courant’s “What is Mathematics” should address this question in a more elegant fashion.

    • winstongator says:

      As you say, Math as a tool is the right way to look at it. However, its power as a tool should not be underestimated, just as language is powerful too.

  3. Hutch says:

    Cool Idea. I vote for Human Creation. Computers don’t use it, just binary, on/off.

  4. seneca says:

    Does Don Quixote exist? As a real person, no. As a fictional character, yes. The right answer depends on what form of existence the questioner is looking for. He needs to spell that out when asking whether something exists or the question becomes meaningless.

  5. leopardtrader says:

    Mathematics is the basis of life. It exists as mountains do. Newtonian 3 laws of motion that drove immense scientific progress was captioned as “Mathematical basis of natural philosophy” !


    As a mathematical scientist by training sometimes I wonder how disorderly life would be without it!

    • TerryC says:

      Leopard, did your math professors tell you they were scientists? Tsk Tsk. Mathematics is merely a tool of the mind that we use to create models to help us explain the natural universe around us. All these models are wrong, of course. That is why we must constantly create new models when we learn more about nature. These new models are also wrong, and always will be. Hopefully, over centuries we get a little better at explaining nature. But, of course we never really will, no matter how smart the species gets.

      As a geologist, I can explain crystallography, radioactive dating, chemical reactions in magma melts, and just about everything else with mathematics added in to the model/explanation. But I doubt if you could show me a 2 pi r squared goat or river or star out there anywhere. Be content with being a handyman of mathematics. After all, tools of the mind are certainly more powerful than a hammer.

      • MikeNY says:

        Well said, TerryC. Math is a tool that has proven very useful at helping mankind not just to understand but to *control* the universe (Heidegger said this I believe). It does not tell us anything about Absolute Truth, it tells us a particular, perspectival truth, a partial approximation to Truth. Calculus itself is a fiction, but a very useful fiction in approximating continuity — which escapes human intelligibility.

        The answers the universe gives us are in large part determined by the questions we pose.


  6. Petey Wheatstraw says:

    At any given moment, anything outside one’s sphere of perception might not exist.

    • Petey,

      w/ seneca, above..

      “Context is crucial…”

      or, IOW, YFB!~

      as an aside, do you think this dude gets paid by the stroke (chinstroke, that is..), or, by the Pound, of Wool, he gathers?

  7. patfla says:

    I know that complex manifolds

    exist because I have several stacked in my closet.

  8. CB says:

    If human reality is collectively agreed-upon pattern recognition of sensory perceptions then math may be an elegant human construct to compare, measure and organize those perceived patterns?

  9. Winston says:

    Ah the navel gazing…

    But if math has “no empirical component,” as the host says, then how can empiricism apply to physics which requires math for its basis of measurement?

    Some aspects of pure mathematics are useless, and might as well not exist, except when a clever bit of mathematical wizardry proves itself useful when theoretical physics requires a new form of mathematics to describe heretofore undiscovered concepts.

    For me, personally, natural mathematics does exist. It exists in the peculiarly uniform Fibonacci sequence that expresses a linear measurement between the swirls of a nautilus shell. Which is like the swirling bands of a hurricane. Which is like the spirals in a pine cone.

  10. Lord says:

    Mathematics may be human, but arithmetic is more widely disseminated, with some birds able to count the eggs in their nest and bees able to provide measures of direction and distance. Evolution can solve many problems unconsciously, but sometimes the solution brings consciousness to bear.

  11. namara says:

    Rodger Penrose’s work “The Emperor’s New Mind” is probably the most comprehensive analysis of this question – is maths a product of the brain or is something separate – just out there in the Universe. Plato and Einstein certainly believe maths existed as an entity. Penrose concludes that we need to know more about the brain and how quantum mechanics operates before we can answer this question with any “certainty”. Until then I accept it as axiomatic that Maths exists beyond our brains.

  12. montaur says:

    Math, for the most part, appears to exist. When we see other organisms using division in an effective manner, does that count as observing math in action?

  13. zell says:

    Math is a quantitative language.

    • denim says:

      Exactly. And useful to communicate information to oneself and maybe a few others.

    • TerryC says:

      Succinct and correct. It is a human construct. Natural science (and natural scientists) deal with the interactions of matter, energy, time and space. I have yet to hear any mathematician, or anyone else, explain to me where in matter, energy, time and space their “math” is. Important-extremely so. Natural-no.

  14. jbb says:

    We are all given the math we deserve.

  15. FlyBoyMcCall says:

    I thoroughly enjoy reading Mr. Ritholtz’s comments on economics and finance. He, like all of us, needs to recognize when he has wandered so far beyond his own comprehension as to appear foolish. The question he poses here is meaningless, not entirely unlike asking if colorless green ideas snore when they sleep. If Mr. Ritholtz is interested in understanding why this is so, he might spend a few dozen hours beginning with Wittgenstein ff.

    • I am familiar with Wittgenstein’s work and his importance to philosophy.

      Regardless of HIS views, it does not mean that I will not share what I thought of as an interesting discussion of the question of subjectivity versus objectivity in regards to mathematics. If you wish to submit your PhD. thesis on Tractatus Logico-Philosophicus or Philosophical Investigations, by all means lets have it.

      But why should I allow your views of a dead philosopher prevent me from sharing something interesting? ESPECIALLY out of my expertise? It is only in reaching beyond our comfort areas that we grow. Its a shame you are not capable of understanding such a positive outlook.


  16. Non Sequor says:

    I thought math was man made until I studied algebraic topology (and dabbling in category theory cemented the conclusion

  17. bigsteve says:

    I finally registered to comment on this topic. This is an ancient question, boiling down to what came first the mind or matter. Did a mind or minds create matter and the rest of reality or did the mind spring forth from matter and energy? If the mind was first then of course math a creation of the mind is part of reality. If not then even our perception of conscience is an illusion. Same for love, freedom and other such ethereal things.

  18. Non Sequor says:

    I thought math was man made until I studied algebraic topology (and dabbling in category theory cemented the conclusion).

    Algebraic topology shows that there are algebraic concepts embedded in the topological structure of spaces. That is, it reveals that the “creators” of topology created rules to define the things they wanted to study, and contained within those rules are structures equivalent to the rules used to study completely unrelated things.

    No one “made” that relationship between abstract algebra and topology. That connection. Was already there, deeper than we can directly reach.

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