Is math discovered or invented? | Edward Frenkel and Lex Fridman

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GUEST BIO:
Edward Frenkel is a mathematician at UC Berkeley working on the interface of mathematics and quantum physics. He is the author of Love and Math: The Heart of Hidden Reality.

PODCAST INFO:

SOCIAL:

[LexClips]

Guest bio: Edward Frenkel is a mathematician at UC Berkeley working on the interface of mathematics and quantum physics. He is the author of Love and Math: The Heart of Hidden Reality.

[Ryan-]

Before I watched this video I was confident that we discovered math as it seems like a fundamental law of the universe. But after reading the comments, I am blown away by how many great discussions and explanations you have provided. I feel more confused and undecided on the question than ever lol. Thank you.

[heikodatchi]

It is discovered and the language used to describe and interpret it is invented

[IsomerSoma]

In some other part of this podcast Frenkel states that at the beginning of mathematics there's a choice and this is the set of axioms. He was very correct about that. After this choice the mathematics of this system can be discovered, but what is very important to notice is the order in which mathematics was developed and this order isn't some mathematician set up ZFC and then all the results were step by step derived. No. Often we get inspired by nature, some pattern which seem interessting, some problem we want to solve. So mathematicians formalized those and build mathematical tools to aid the solution. Building upon that the results are generalized and a theory build around it from which new results are derived. Only after that some first principle axioms are chosen to build a (hopefully) contradiction free and complete math-universe. This happened in the 20th century with ZFC and others. In general (like with learning) the mathematical development process is recursive swinging between invention and discovery. The choice of axioms was depent on the before made inventions and these inventions were often motivated by problems or patterns arising in the natural world thus indirectly discovered. Important tho is that the basis of all of this is how human brains process information. This is the basis of logic and also patterns - patterns are a part of the cognitive process. They are the interpretation of information that our brains make. This information process must be somewhat accurate as it has evolved to be, but even if it is absolutely accurate the brain process - or lets say the idealized brain process as we certainly arent perfectly logical - must not be confused with the structure of the natural world itself. World and image aren't the same even in case of 100% accuracy.

The question "Is math discovered or invented?" is interessting, but terribly misunderstood. It isnt or shouldnt be about if mathematics is literally the structure of the universe. Even if logic truly is something fundamental (impossible to proof) and not just how our neural network process information between the logic and the mathematics there still is the mathematician, whos neural network is being feed with information that is then related, recombined and conceptionalized (and what else is invention if not that?). Thus when pressed i would answer the question with "invented", but it is much more difficult.

[Stardayy]

Math is like fire, we didn't invent it, but we invented uses for it, how to contain it, how to create it, how to keep it going...

[jasonhendricks]

Math is a tool using rational principles. One of any given unit added to another of the same unit creates a sum of 2 units. This fundamental principle replicates itself in many different directions. Math is not so much a "truth" to be discovered or created, but a language to explain quantity and it's applications.

[toddjoseph]

Math is insanity. There are infinite numbers 1.2.3 etc., but there is also infinity inbetween each number also. What amazes me about it is everything is in there we just have to find it and when I say everything, I mean everything. Want a particle to be only a particle and not a wave function, its in there, but at the same time if you want a particle to be only a wave and not a particle, its in there also. Insanity at its finest.

[peakingmantis]

Isn't maths just a measurement for something that exists already? The equation doesn't really matter if the results are the same

[polymathematics]

This is one of the best conversations I've listened to in years. It was deep and profound.

[EkillOrRyan]

I’ve always thought about this in grade school but couldn’t articulate it. Are we noticing patterns and giving it meaning or are we finding meaning from patterns?

[BRDRDRDAT]

Not sure if we live in a world of paradoxes when there is no consistent semantic system of language. More like we fail to explain what appear to be paradoxes.

Wave particle duality is a misnomer since an electron can appear as a wave, a particle, both, or neither, depending on the semantic system we use to measure and describe it. The underlying info doesnt seem to be paradoxical, just our explanations of it. Not sure why anyone would be surprised that we dont understand anything at a fundamental level, but I wouldnt assume we live in a world of paradoxes, just a world where we fail to communicate perfectly.

[rema_style]

I think if it is invented we would have control to manipulate mathematics in many ways as we wish, but actually we don't have such a freedom, so for me is more discovered. Like lows of physics - we can discover and use them but can't change them. My humble opinion.

[beetlesstrengthandpower]

I always think of this thought experiment: if you'd have multiple people/machines in a isolated room for an infinite amount of time and have them discover/invent new math. Language aside (notation used etc.), they are all going to come up with the same. It just seems way more intuitive to see as a discovery because math is already always present, we just have to find a way to understand articulate it.

[zedetach]

If math was invented then it would have been impossible for Ramanujan to have mastered mathematics at the level that he did in almost total isolation.

[ImNotHereEither]

If maths is an expression of our understanding of how to describe what is not only physical, but our shared imaginations as conceptual realities, then as part of that lingual technology it is only natural it evolves into more complex forms. It feels like a space where we can both invent and discover at the same time, as the function of that lingual technology has not simply evolved to help us share ideas and concepts, thus describing the outer edges of our reality, but to provide insight into the depths of complexity and dimensionality our imaginations are able to wander confidently.

[beatboxfmj]

In a romantized sense, creation is the discovery of the unknown. Personally I think as humans, every moment is a discovery because the future is unknown.

[jarrodfodemski]

We observe nature, then invent math to describe it. Then we test that math which yields new observations. It’s a never ending feedback loop that we’re all addicted to.

[lui]

Both, it's a question of categorization or classification. It's like asking if something is a chemical or physical process. I think the question is misleading, but I would classify it as invented, because we would also say that language is invented and with language we can also describe abstract situations and stories that are not really there, although they are of course physically exist in our neurons, so it's a matter of classification.

[markattila]

In order for math to have been discovered, it had to have been there before it's discovery in some shape or form. Since we have invented it it now appears to us to be "there", and that gives us the illusion that it was always there. But it really was not until we invented it.

[timb]

The question is not if it is invented or discovered...the question is if it exists independently of us. The answer to that is an unequivocal affirmative. IOW...something exists out of which we create this thing called mathematics. That 'something' exists independently of our discovery of it. Whether mathematics exists in the exact form within which we comprehend it ...independently of us...is a different question. It almost certainly does...and as the understanding of consciousness advances this will be confirmed. The reasoning is not that complex. Mathematics is a function of advanced consciousness. As Don Hoffman says...consciousness is everywhere...and there are almost certainly varieties of it (what Don calls 'conscious agents') that are far more advanced than our own...therefore their 'experience' of math will incorporate our rudimentary comprehension of it...as well as an equivalently advanced understanding. No big deal really.