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Ramanujan: Making sense of 1+2+3+... = -1/12 and Co.

Mathologer · explainer · Watch on YouTube

Recreational & visual mathPure mathematics

What it is

Mathologer examines how identities like 1+2+3+... = -1/12 arise in Ramanujan's work, starting from his 1913 letter to Hardy. The video explains the rules for summing infinite series and why such results are meaningful but not naive sums.

Why Hacker News recommends it

Recommended as a careful, honest treatment of the -1/12 claim, often preferred over flashier videos.

  • 3 people recommended it
  • 6 different months
  • 1 strong recommendations
  • first 2016, last 2024

What HN commenters said

  1. “If you have half an hour to spare, I highly recommend to watch”

    Explains extended summation and why 1+2+3+... gives -1/12.

    gus_massa, 2019-08 · Strong recommendation · in “The Ramanujan Summation: 1 and 2 and 3 and ⋯ + ∞ = -1/12”

  2. “Burkard Polster's (Mathologer) videos on the subject are probably going to be more useful than Numberphile.”

    Explains why the sum is nonsense yet useful, better than Numberphile.

    stan_rogers, 2020-02 · Recommendation · in “Ramanujan Surprises Again (2015)”

  3. “is a youtube video (Mathologer) which goes over this material fairly carefully.”

    Carefully goes over the derivation of -1/12.

    thaumasiotes, 2023-12 · Recommendation · in “Code is run more than read”

Excerpts from Hacker News comments, linked to the originals. Summaries and labels were written by a language model from those comments.

Topics: ramanujan, infinite series, -1/12, zeta function, mathematics

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