# Greatest mathematician of all time | Joel David Hamkins and Lex Fridman

Source: https://www.youtube.com/watch?v=G2Ld6lp9RVY
Recap page: https://rapidrecap.app/video/G2Ld6lp9RVY
Generated: 2026-01-05T13:36:57.19+00:00

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## Quick Overview

Joel Hamkins finds ranking mathematicians by greatness incredibly difficult, but if forced to choose, he would select Archimedes for his achievements transcending his early era, while emphasizing that his personal mathematical style prioritizes simple, clear arguments proving surprising results over being the first to discover something complex.

**Key Points:**
- Hamkins considers ranking mathematicians difficult, but suggests Archimedes as a candidate because his achievements 'totally transcended the work of the other people in his era.'
- Hamkins prefers simple, clear, easy-to-understand arguments that prove a surprising result, stating the question of novelty is 'somehow less important to me' than the beauty of the proof.
- He notes that simultaneous, separate discoveries are common in mathematics because 'certain ideas are in the air and being thought about but not fully articulated.'
- Hamkins describes his personal process as playful curiosity, involving playing around with ideas, changing little things, and understanding basic cases until a path through to something interesting appears.
- Hamkins frequently uses thought experiments and anthropomorphization, such as visualizing a set-theoretic model of ZFC as a place to travel to via forcing, to understand mathematical tensions.
- Contrasting styles, Hamkins notes he could not replicate Andrew Wiles' seven-year solo grind, preferring mathematics as a social activity with nearly one hundred collaborators.
- Hamkins respects Grigori Perelman's decision to decline prizes, viewing it as a reminder that the greatest minds pursue mathematics for 'the love of it, not for the prizes or the money.'

**Context:** This is an interview between Lex Fridman and mathematician Joel David Hamkins, focusing on the philosophical aspects of mathematics, including how to define greatness among mathematicians, individual working styles, the nature of mathematical discovery, and recognition within the field. The discussion moves from naming potential candidates like Euler, Gauss, and Newton to Hamkins detailing his preference for elegant proofs and his collaborative approach to research, contrasting it with highly isolated efforts like Andrew Wiles' work on Fermat's Last Theorem.

## Detailed Analysis

The discussion centers on the subjective nature of defining the 'greatest mathematician,' with Hamkins initially listing candidates like Euler, Gauss, Newton, Ramanujan, Hilbert, Gödel, and Turing, before settling on Archimedes as his forced choice due to his era-transcending achievements. Hamkins strongly articulates his personal mathematical style: he values simple, clear arguments proving surprising results more than simply being the first to prove something, expressing skepticism toward overly complicated arguments that are hard to verify. He attributes simultaneous discoveries in science to ideas being 'in the air' and discusses his process, which involves playful curiosity, exploring basic cases, and using anthropomorphic thought experiments to visualize mathematical tension, such as imagining set theory models as physical places. Hamkins reveals his work is highly collaborative, citing nearly a hundred co-authors, and finds solo, isolated grinding on single problems, like Wiles' pursuit of Fermat's Last Theorem, terrifyingly lonely. Finally, he addresses Grigori Perelman declining accolades, agreeing that fundamental motivation in mathematics stems from the love of the art itself, not external rewards like prizes or fame.

### Defining Mathematical Greatness

- Archimedes cited for transcending his era
- Candidates include Euler, Gauss, Newton, Ramanujan, Hilbert, Gödel, and Turing
- Greatness is deemed an 'incredibly difficult question to answer.'

### Hamkins' Mathematical Style

- Preference for 'simple, clear, easy to understand arguments that prove a surprising result'
- Skepticism toward complicated arguments due to potential error
- Curiosity draws him toward simplicity.

### The Process of Discovery

- Simultaneous discoveries happen because 'certain ideas are in the air'
- Hamkins' method involves 'playful curiosity' and 'fool[ing] around with the ideas' until a path appears.

### Visualization Techniques

- Frequent use of thought experiments where ZFC models are anthropomorphized as places one can travel to via forcing
- Metaphors help understand tension in arguments, like imagining game theory players.

### Collaboration Versus Isolation

- Hamkins favors collaboration, having close to 100 co-authors
- Contrasts his style with Andrew Wiles' seven-year solo grind on Fermat's theorem
- Ideas frequently arise from social interaction on platforms like Math Overflow.

### Recognition and Motivation

- Respect for Grigori Perelman turning down the Fields Medal and Millennium Prize
- Fundamental motivation stems from the 'love of it, not for the prizes or the money'
- Joke referencing Math Overflow score as an objective criterion for greatness.