The Rest Is Science — “The Letter That Changed Mathematics”

Hosts: Professor Hannah Fry, Michael Stevens (Vsauce)
Date: December 4, 2025

Episode Overview

In this episode of The Rest Is Science, hosts Professor Hannah Fry and Michael Stevens explore the story behind a seemingly nonsensical letter that transformed the world of mathematics—Srinivasa Ramanujan’s first letter to Cambridge mathematician G.H. Hardy. Interwoven with personal anecdotes and lively banter, the discussion delves into themes of mathematical genius, unlikely discoveries, and the enduring impact of outsider thinkers. The episode also features Q&A on scientific curiosities, a celebration of favorite elements, and reflections on the culture of mathematics.

Key Discussion Points & Insights

1. The Origin Story: Ramanujan’s Letter (02:37 – 08:26)

• Ramanujan’s Background

  • Introduced as a self-taught Indian mathematician, likened to the character in Good Will Hunting ([03:12]).
  • Worked in isolation with only a high school mathematics textbook.

• Arrival of the Letter

  • Hardy, at Cambridge, regularly receives outlandish mathematical letters.
  • Finds Ramanujan’s letter filled with pages of bizarre notation and claims—no proofs, messy presentation.
  • Initially dismisses it as “a load of gibberish” ([03:38]), throws it away, then reconsiders after recalling a few intriguing formulas.

• The Turning Point

  • Hardy and Littlewood retrieve the letter from the bin to investigate further.
  • Realize that within the mess are mathematical statements known only to experts and some beyond the existing knowledge.
  • Quote ([04:49], Fry, paraphrasing Hardy):
    "Either this person is crazy, either this is a letter that has come in from a madman, or, as is more likely, this has come in from a genius."
  • Decide the only explanation is genius.

2. The Infamous Sum and Mathematical Madness (05:50 – 06:21)

• The Viral Equation:

  • Ramanujan’s claim: 1 + 2 + 3 + 4 + ... to infinity = –1/12.
  • Fry reflects:
    "Can you imagine getting a letter from someone saying if you add 1, 2, 3, 4 all the way up to infinity equals minus 1 over 12, you would just dismiss it out of hand, surely." ([05:51])

• Controversy and Utility

  • Michael points out this imagination and confidence would make him look twice ([06:21]).
  • Fry notes:
    "He knew it sounded crazy, and yet it turns out it’s not crazy. It’s absolutely correct. And not only that, but it turns out to be phenomenally useful in the field of string theory." ([09:21])

3. Ramanujan in Cambridge (06:35 – 08:26; 10:35 – 13:15)

• Extraordinary Natural Ability

  • Despite minimal training, Ramanujan advanced number theory beyond the best mathematicians in Cambridge ([06:35]–[07:40]).

• Personal Impact

  • Fry shares her awe at viewing the original letter in Cambridge’s archives ([08:26]–[08:35]).

• Tragic Personal Details

  • Difficulties adapting to Cambridge: vegetarian diet, wartime rationing, health troubles.

  • Passed away young, tuberculosis ([10:35]).

  • Hardy describes his encounter with Ramanujan as “the most romantic encounter of his life” ([11:27]).

  • Famous anecdote: Hardy visits Ramanujan in the hospital, comments on the taxi number 1729; Ramanujan instantly identifies it as uniquely interesting ([11:27]–[13:15]).

    • Quote ([12:44]):
      "1729 isn’t uninteresting at all. It’s the smallest number that can be comprised of two cube numbers added together in two different ways…” — Ramanujan

4. Genius vs. Collaboration; The Myth of the Lone Genius (13:25 – 14:43)

• Reflection:

  • Fry:
    "The idea of there being these geniuses who walk the earth is…really magnetic…Also…I think it’s sort of problematic, because almost all science and maths…is done by big teams of people who just are normal people who work really hard." ([13:25])
  • Michael:
    "The great man theory of history…it forgets the fact that…there needed to be doctors to help Ramanujan…literally the messengers who would send the correspondences..." ([13:54])

• Connection to the Everyday Pursuit

  • Not everyone is Usain Bolt—using sports as a metaphor for the value in everyday engagement ([14:18]).

5. Mathematical Prodigies and the Fields Medal (14:52 – 16:38)

• Youthfulness in Discovery
  • Noting mathematicians’ productivity often peaks in their 20s ([14:52]).
  • Brief rundown of Fields Medal eligibility (“Nobel of Mathematics,” under 40, every 4 years) ([15:31]).
  • Only one woman has ever won the Fields Medal ([15:31]).

6. Cambridge Treasures: Principia and Ramanujan’s Letters (16:38 – 18:59)

• Viewing History

  • Fry describes holding Newton’s annotated Principia Mathematica on a pillow, marveling at Newton’s messy handwriting and doodles ([16:50]–[18:04]).

• The Royal Society Quirk

  • Tradition: scientists sign a historic book; Newton’s signature is visible, but the name after his is smudged out from centuries of fingers pointing ([18:09]).

7. Outsider Geniuses: Grigori Perelman & Modern Parallels (19:06 – 21:45)

• Perelman’s Story

  • Russian mathematician Grigori Perelman solves the Poincaré Conjecture, one of the Millennium Problems, as a total outsider ([19:06]).

  • Posts proof online; initially met with skepticism, but it holds up.

  • Declines the $1 million prize and honors to avoid distraction from mathematics ([20:39]).

    • Quote ([20:40], Fry):
      "To go to Spain would mean one day traveling, one day to collect the prize, one day to return home, and that would be three days when he wouldn’t be able to do mathematics. So he turned it down. Wow."

• Reflection on Fame and Wealth

  • Perelman’s choice to remain reclusive sparks a discussion on personal values over recognition ([21:01]–[21:45]).

Listener Q&A and Memorable Dialogue

The Science of Sneezing (25:49 – 28:26)

• Question: Why do I sneeze when I first have a mint or a piece of chewing gum?
  • Fry: The trigeminal nerve, which controls facial sensation and muscle movement, can be triggered by mint (or light), sometimes causing sneezing instead of its intended response ([26:05]).
  • Michael: Some people have "leaky nerves," leading to crossed signals from bright light, etc. ([27:00]).
  • Fry jokes about the sneeze-as-pleasure Reddit subculture ([28:08]).

Favorite and Least Favorite Chemical Elements (28:34 – 33:27)

• Hosts' Favorites:
  • Michael: Sulfur (family connection and unique qualities); least favorite—hard to decide, possible nomination: dangerous elements ([28:40]).
  • Fry: At first considers argon ("the ultimate loner"), but relents after recounting seeing it used in neutrino detection at CERN; gold emerges as a second favorite for its rich history ([30:26]–[33:27]).
  • Amusing fact: Liquid argon is cheaper than Coca-Cola by the litre ([31:38]).
  • Famous gold anecdote: Nobel medal dissolved in aqua regia to hide it from Nazis during WWII ([32:36]).

Notable Quotes & Memorable Moments

• On Mathematical Madness:
  “If I tell you this, you will at once point out to me the lunatic asylum as my goal. Like, he knew it sounded crazy, and yet it turns out it’s not crazy.” — Hannah Fry on Ramanujan ([09:21])

• On Discovery and Recognition:
  “He just wants to do his own thing…hence people stalking him and putting photos of him on the Internet.” — Fry on Perelman ([21:03])

• On Elemental Preferences:
  “If you want to send in gifts to either me or Michael, I’ll take as much gold as you want to give me, and Michael will take sulfur…” — Fry ([34:17])

Timestamps for Key Segments

• Ramanujan’s Letter and Reception: 02:37 – 06:35
• Mathematical Content and Meaning: 06:35 – 10:35
• Personal Anecdotes & Cambridge Archive: 07:40 – 08:35, 16:38 – 18:59
• Mathematicians, Genius, and Collaboration: 13:25 – 14:43
• Fields Medal & Prodigy Culture: 15:31 – 16:38
• Grigori Perelman’s Story: 19:06 – 21:45
• Sneezing & Trigeminal Nerve: 25:49 – 28:26
• Favorite Elements: 28:34 – 33:27

Tone and Style Notes

Throughout, the hosts maintain their signature blend of wit, intellectual curiosity, and humility—easily shifting from the awe-inspiring (“the most romantic encounter of his life”) to self-deprecating (“I’m way too old, Michael”) to irreverent humor (on sneezing fetishes and Reddit rabbit holes). The show’s relaxed, conversational tone makes deep scientific ideas approachable, while the anecdotes ground abstract mathematical legends in relatable human drama.

Summary prepared for listeners wanting a rich, detailed overview without spoilers or distractions. Advertisements, intro/outro, and sponsor content have been excluded for clarity.