Future Fields Medallist and Millennium Prize Winner, but mostly a Time Lord who lost his screwdriver.
Earth.
Joined February 2022
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Roy retweeted
If you think Ravel’s Boléro needs a full orchestra, listen to this version: just one cello, yet it’s every bit as captivating.
Roy retweeted
✨🇨🇳A science teacher in China and their students built a water rocket together. The moment it launched, the kids lit up with joy.
Roy retweeted
Fin septembre 1976 - tel un savant fou, Giorgio Moroder compose I Feel Love.
La matrice a cinquante ans.
Il enchaînera avec la BO de Midnight Express où la basse continue de précéder la mélodie.
Roy retweeted
"The measure of intelligence is the ability to change." - Einstein.
AI is built on math. True intelligence adapts, it doesn't argue. Arguing won't stop the rain, it just makes you look foolish while it falls anyway.
Roy retweeted
Fully agree with you Roy, only two solutions to this, you see the optimal one. Tao forgets the value of time, isn't it funny?
I understand Terence Tao’s concern regarding AI accelerating progress in mathematics, and yet I cannot agree with the conclusion that we should somehow fear the pace of it.
The limited projected perceptions of others should not define our own.
As such, if mathematics is moving faster than the establishment can absorb it, then the problem is not the speed of discovery, it is the speed at which that establishment can adapt, verify and understand what is now being uncovered.
This has always been the case.
There will always be somebody who sees the route first, somebody who moves quicker, somebody who refuses to wait for consensus before following the mechanics where they lead.
Like the old gunslingers, there will always be a maverick slightly quicker on the draw.
As such, you do not ask the maverick to slow his hand because everybody else is still reaching for the holster.
You improve the standard of the draw.
AI is not making mathematics move too fast. It is exposing how slowly we became accustomed to moving.
nitter.cf/haider1/status/2101368…
Roy retweeted
Proof of Sylvesters conjecture (every prime number that leaves a remainder of 4, 7, or 8 when divided by 9 is the sum of two cubes) by my brilliant colleague Ashay Burungale. Unsolved since the 1870s...
arxiv.org/abs/2609.14893
Roy retweeted
If you are a (theoretical) physicist and the AI revolution makes you less excited about continuing, you might be in the game for the wrong reasons. Curiosity about how Nature works is what it is all about. If AI accelerates it all, then that is amazing! 1/2
‘Saffron’ by Apprentice Timelord is on #SoundCloud on.soundcloud.com/WVC2PBTQSb…
Roy retweeted
Top 100 unsolved math problems by their estimated public recognition. The rankings differ quite a bit from the importance rankings!
1. Riemann Hypothesis ↑ 1
2. P versus NP ↓ 1
3. Collatz conjecture ↑ 158
4. Goldbach conjecture ↑ 18
5. Twin Prime Conjecture ↑ 15
6. Navier–Stokes existence and smoothness (Fefferman A) ↓ 2
7. Polynomial-time classical integer factorization ↑ 9
8. Yang–Mills existence and mass gap ↓ 5
9. abc conjecture ↑ 3
10. Birch and Swinnerton-Dyer conjecture ↓ 4
11. Existence of an odd perfect number ↑ 228
12. Normality of π ↑ 289
13. Hodge conjecture ↓ 8
14. Infinitude of Mersenne primes ↑ 231
15. Sums of three cubes representation conjecture ↑ 390
16. Beal’s conjecture ↑ 332
17. Minimal superpermutation length ↑*
18. Magic square of squares ↑*
19. Multiplicative persistence bound of 11 ↑*
20. Generalized Riemann Hypothesis for Dirichlet L-functions ↓ 11
21. Square peg problem ↑ 461
22. BQP versus NP: complete language-class relation ↓ 5
23. Chromatic number of the plane ↑ 215
24. Exact Ramsey number R(5,5) ↑*
25. Algebraic independence of e and π ↑ 132
26. Irrationality of Euler’s constant ↑ 252
27. Kelvin problem: least-area partitions into unit-volume cells ↑*
28. Graph isomorphism in polynomial time ↑ 52
29. Perfect cuboid problem ↑*
30. Existence of one-way functions ↓ 22
31. Matrix-multiplication exponent equals two ↓ 5
32. Unconditional separation of BQP from BPP ↓ 13
33. Lonely runner conjecture ↑*
34. Exact kissing numbers in dimensions greater than four ↑ 315
35. Graham–Rothschild hypercube Ramsey problem: exact planar K₄ threshold ↑*
36. Infinitude of Fermat primes ↑ 458
37. Legendre’s conjecture ↑ 270
38. No-three-in-line problem ↑*
39. Infinitude of amicable pairs ↑*
40. Landau’s fourth problem: primes of the form n² + 1 ↑ 140
41. Erdős–Straus conjecture ↑*
42. Infinitude of Sophie Germain primes ↑ 269
43. Polignac’s conjecture ↑ 59
44. Higher-dimensional Euclidean Kakeya conjecture ↓ 6
45. Frankl’s union-closed sets conjecture ↑ 358
46. Unique Games Conjecture ↓ 12
47. Infinitude of Fibonacci primes ↑*
48. Brocard’s problem ↑*
49. Thomson problem ↑ 319
50. Gauss circle problem ↑ 192
51. Erdős–Szekeres convex polygon problem ↑ 294
52. Montgomery’s pair correlation conjecture ↑ 23
53. Congruent number problem ↑ 79
54. NP versus coNP ↓ 41
55. Local connectivity of the Mandelbrot set ↑ 66
56. Smooth four-dimensional Poincaré conjecture ↓ 35
57. Edge-unfolding of convex polyhedra ↑*
58. Schanuel’s conjecture ↓ 30
59. Catalan–Dickson conjecture on boundedness of aliquot sequences ↑*
60. Erdős’s conjecture on divergent reciprocal sums and long arithmetic progressions ↑ 70
61. Hardy–Littlewood prime k-tuple conjecture ↓ 43
62. Existence of a periodic trajectory in every triangular billiard ↑*
63. Elliott–Halberstam conjecture ↑ 24
64. Hadwiger’s conjecture ↑ 15
65. Irrationality of ζ(5) ↑ 268
66. P versus PSPACE ↓ 52
67. P versus BPP ↓ 40
68. Selfridge’s conjecture on the smallest Sierpiński number ↑*
69. Erdős–Rado sunflower conjecture ↑ 77
70. Kolakoski sequence half-density conjecture ↑*
71. Polynomial-time unknot recognition ↑ 268
72. Inverse Galois problem over the rationals ↓ 23
73. Conway’s thrackle conjecture ↑*
74. Gilbreath’s conjecture ↑*
75. Infinitude of cousin primes ↑*
76. Conway’s 99-graph problem ↑*
77. Nonexistence of Landau–Siegel zeros for quadratic Dirichlet L-functions ↓ 34
78. Resolvent degree of the general degree-seven polynomial ↑ 183
79. Hilbert’s sixteenth problem, second part ↓ 40
80. Graph reconstruction conjecture ↑ 242
81. Singmaster’s conjecture on Pascal’s triangle ↑*
82. Exponential Time Hypothesis for 3-SAT ↓ 40
83. Irrationality of Catalan’s constant ↑ 339
84. Borel’s normal number conjecture for irrational algebraic numbers ↑ 54
85. Finite projective planes of non-prime-power orders ↑ 308
86. Fermat–Catalan conjecture ↑ 172
87. Convergence of the Flint Hills series ↑*
88. Existence of an odd weird number ↑*
89. Maximum packing density of regular tetrahedra ↑*
90. Exact exponential growth constant of cap sets in F₃ⁿ ↑*
91. Invariant subspace problem for Hilbert-space operators ↑ 14
92. Fejes Tóth’s sausage conjecture ↑*
93. Cramér’s conjecture on the limsup of normalized prime gaps ↑ 61
94. Kobon triangle problem ↑*
95. Four-distance problem for the unit square ↑*
96. Artin’s primitive root conjecture ↑ 96
97. Tammes problem: optimal spherical packing for general N ↑*
98. Extended Riemann Hypothesis for Dedekind zeta functions ↓ 88
99. Ringel–Kotzig graceful tree conjecture ↑*
100. Global Langlands functoriality conjecture ↓ 93
Fable 5.1 and GPT-6 Astra judged 3,791 distinct pairs using shared evidence, including reviewed public sources and Wikipedia page-view data. Includes theoretical computer science and mathematical physics.
↑/↓ indicate how many places higher or lower a problem ranks by public recognition than in the overall Top 500.
↑* indicates a problem outside the overall Top 500.
They will be added to proofatlas.ai/open-problems/.
The Ultimate Top 500 Open Problems in Mathematics
proofatlas.ai/open-problems/
Weeks of work by 4 LLM families (GPT 6, Fable 5.1, GLM-5.3, DeepSeek V4 Pro). 34,890 pairwise judgments across 1,227 candidate problems. They ran repeated discovery rounds, source checks, deduplication, and clarification of exact problem statements. Models compared problems using source-backed descriptions without seeing the existing rankings or other models' judgments.
The comparisons considered the significance of a resolution, centrality to the field, connections across disciplines, scholarly and public recognition, and potential scientific or practical impact. Results were statistically combined and checked for ranking uncertainty and sensitivity to individual model families. Includes theoretical computer science, and mathematical physics.
The list includes plain-language explanations, sources, notes on what remains open, and links to related research where available.
Where the targets of recent AI results would rank if they were still open:
#21 — Smooth-forced Navier–Stokes breakdown (Fefferman C).
#32 — Unforced three-dimensional Euler blowup.
#92 — The Jacobian conjecture in general dimension.
#167 — Whether every group is sofic.
#211 — The planar unit-distance conjecture.
Note that the recently announced Navier–Stokes result concerns flow driven by a smooth external force. #4 entry is unforced three-dimensional Navier–Stokes global regularity (Fefferman's statement A), which remains open. Showing that a forced flow can develop a singularity does not settle whether singularities can arise without external forcing.
Roy retweeted
This is really the point I keep coming back to.
Where mathematics is being used to describe nature, mathematics should be the transcript of the mechanics.
First understand what the thing is actually doing. What is moving, what is conserved, what is being transported, what persists, what changes and what descends from what.
Then write the mathematics.
When we do it the other way around, we very quickly get lost. We build abstractions on abstractions, prove perfectly valid things inside them, then start confusing the internal consistency of the mathematics with an understanding of nature.
That is where a lot of the confusion comes from, and frankly some rather deluded nonsense at times.
The maths can be beautiful, rigorous and completely self-consistent, yet still be describing the wrong thing, or nothing physical at all.
As such, proof is not the beginning of understanding. It is the audit at the end.
Recover the mechanism first. Recover the structure. Recover what nature is actually conserving and doing. Then let the mathematics become the precise transcript of that mechanics.
Otherwise the map gradually replaces the territory, and everyone ends up arguing over the map.
With my regards to all.
Roy retweeted
After 25 years of being told that theoretical physics isn’t mathematics because we prioritize understanding over proofs, I find the math-AI debate rather heartwarming. Suddenly, many mathematicians are explaining that mathematics is about understanding, not just proofs. Welcome!
Things are heating up on Terry Tao’s blog. In “If Math Is More Than Proof, We Need to Better Celebrate the Rest of It,” Grant Sanderson of @3blue1brown proposes “open exposition problems” -- rewarding the work of making math genuinely understandable.
terrytao.wordpress.com/2026/…
Roy retweeted
It’s simple. Put solar panels on car parks rather than on thousands of acres of prime farmland.
Roy retweeted
Tiny wrinkles bend physics to change how electricity moves through graphene eurekalert.org/news-releases…
What were schools like in Mesopotamia?
They were tablet houses, often just ordinary homes where boys sat with lumps of wet clay, cut a reed into a stylus, and pressed those little wedge marks into the surface before it dried.
You started with single wedges, then sign lists, then whole stretches of Sumerian, and if the clay was still damp you could smooth a line out and try again, though a sloppy hand still got you in trouble.
Dr George Heath-Whyte explains. Sound on.
Discovering great music.
‘ATM11 | Atom Music Audio - Downpour’ by Atom Music Audio is on #SoundCloud on.soundcloud.com/wSaUjzCw47…