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

Comments · 386

• LE

  @LexClips · 3 years ago · pinned

  Full podcast episode: <a href="https://www.youtube.com/watch?v=Osh0-J3T2nY">https://www.youtube.com/watch?v=Osh0-J3T2nY</a><br>Lex Fridman podcast channel: <a href="https://www.youtube.com/lexfridman">https://www.youtube.com/lexfridman</a><br>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.

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• HE

  @heikodatchi3715 · 3 years ago

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

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• ST

  @Starday723y · 3 years ago

  Math is like fire, we didn&apos;t invent it, but we invented uses for it, how to contain it, how to create it, how to keep it going...

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• RY

  @Ryan-9000 · 3 years ago

  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.

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• JA

  @jasonhendricks4562 · 3 years ago

  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 &quot;truth&quot; to be discovered or created, but a language to explain quantity and it&apos;s applications.

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• IS

  @IsomerSoma · 3 years ago (edited)

  In some other part of this podcast Frenkel states that at the beginning of mathematics there&apos;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&apos;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&apos;t the same even in case of 100% accuracy. <br><br>The question &quot;Is math discovered or invented?&quot; 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 &quot;invented&quot;, but it is much more difficult.

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• BR

  @BRDRDRDAT · 3 years ago

  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. <br><br>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.

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• AL

  @alineharam · 3 years ago

  When I heard Frenkel say, &quot;wouldn&apos;t it be nice,&quot; I thought Beach Boys.

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• MI

  @milton7763 · 2 years ago

  I’ve never heard someone speak so passionately about their love for Mad Max

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• BE

  @beetlesstrengthandpower1890 · 2 years ago

  I always think of this thought experiment: if you&apos;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.

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• RE

  @rema_style · 3 years ago

  I think if it is invented we would have control to manipulate mathematics in many ways as we wish, but actually we don&apos;t have such a freedom , so for me is more discovered. Like lows of physics - we can discover and use them but can&apos;t change them. My humble opinion.

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• QU

  @QuitYourCryin · 3 years ago

  Makes you wonder what else we have yet to unlock.

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