A few months ago, I gave a talk at the IMO in Bremen on “Structure and randomness in the prime numbers”. I have now converted the slides from that talk into a more traditional paper (7 pages in length), for submission to a Festschrift for the Bremen Olympiad. The content is much the same as the slides, but some references have been added.
Recent Comments
Articles by others
- Gene Weingarten – Pearls before breakfast
- Isaac Asimov – The relativity of wrong
- Jonah Lehrer – Don't! – the secret of self-control
- Julianne Dalcanton – The cult of genius
- Nassim Taleb – The fourth quadrant: a map of the limits of statistics
- Paul Graham – What You'll Wish You'd Known
- Po Bronson – How not to talk to your kids
- Scott Aaronson – Ten signs a claimed mathematical proof is wrong
- Timothy Gowers – Elsevier — my part in its downfall
- Timothy Gowers – The two cultures of mathematics
- William Thurston – On proof and progress in mathematics
Diversions
- Abstruse Goose
- Assembler
- BoxCar2D
- Factcheck.org
- FiveThirtyEight
- Gapminder
- Literally Unbelievable
- Planarity
- PolitiFact
- Quite Interesting
- snopes
- Strange maps
- Television tropes and idioms
- The Economist
- The Onion
- The Straight Dope
- This American Life on the financial crisis I
- This American Life on the financial crisis II
- What if? (xkcd)
- White whine
- xkcd
Mathematics
- 0xDE
- A Mind for Madness
- A Portion of the Book
- Absolutely useless
- Alex Sisto
- AMS blogs
- AMS Graduate Student Blog
- Analysis & PDE
- Analysis & PDE Conferences
- Annoying Precision
- Area 777
- Ars Mathematica
- ATLAS of Finite Group Representations
- Automorphic forum
- Avzel's journal
- Blog on Math Blogs
- Blog On Mathematical Journals
- blogderbeweise
- Bubbles Bad; Ripples Good
- Cédric Villani
- Climbing Mount Bourbaki
- Coloquio Oleis
- Combinatorics and more
- Compressed sensing resources
- Computational Complexity
- Concrete nonsense
- David Mumford's blog
- Delta epsilons
- DispersiveWiki
- Disquisitiones Mathematicae
- Embûches tissues
- Emmanuel Kowalski’s blog
- Encyclopedia of Mathematics
- Equatorial Mathematics
- fff
- Floer Homology
- Frank Morgan’s blog
- Gérard Besson's Blog
- Gödel’s Lost Letter and P=NP
- Geometric Group Theory
- Geometry and the imagination
- Geometry Bulletin Board
- Girl's Angle
- God Plays Dice
- Good Math, Bad Math
- Graduated Understanding
- Hydrobates
- I Woke Up In A Strange Place
- Igor Pak's blog
- Images des mathématiques
- In theory
- James Colliander's Blog
- Jérôme Buzzi’s Mathematical Ramblings
- Joel David Hamkins
- Journal of the American Mathematical Society
- Kill Math
- Le Petit Chercheur Illustré
- Lemma Meringue
- Lewko's blog
- Libres pensées d’un mathématicien ordinaire
- LMFDB – L-functions and modular forms database
- LMS blogs page
- London number theory
- Low Dimensional Topology
- M-Phi
- MAA MinuteMath
- Mark Sapir's blog
- Math Overflow
- Mathbabe
- Mathblogging
- Mathematical musings
- Mathematics Illuminated
- Mathematics in Australia
- Mathematics Jobs Wiki
- Mathematics Stack Exchange
- Mathematics under the Microscope
- Mathematics without apologies
- Mathlog
- MathOnline
- Mathtube
- Matt Baker's Math Blog
- Mixedmath
- Motivic stuff
- Much ado about nothing
- Multiple Choice Quiz Wiki
- neverendingbooks
- nLab
- Noncommutative geometry blog
- Nonlocal equations wiki
- Not "Not Even Wrong"
- Nuit-blanche
- Number theory web
- outofprintmath
- Pattern of Ideas
- PDE blog
- Pengfei Zhang's blog
- Peter Cameron's Blog
- Phillipe LeFloch's blog
- ProofWiki
- Quomodocumque
- Random Math
- Reasonable Deviations
- Regularize
- Rigorous Trivialities
- Roots of unity
- Secret Blogging Seminar
- Selected Papers Network
- Sergei Denisov's blog
- Short, Fat Matrices
- Shtetl-Optimized
- Shuanglin's Blog
- Since it is not…
- Sketches of topology
- Soft questions
- Stacks Project Blog
- SymOmega
- tcs math
- TeX, LaTeX, and friends
- The accidental mathematician
- The capacity to be alone
- The Cost of Knowledge
- The Everything Seminar
- The Geomblog
- The L-function and modular forms database
- The Mathematics Literature Project
- The n-Category Café
- The n-geometry cafe
- The On-Line Blog of Integer Sequences
- The polylogblog
- The polymath blog
- The polymath wiki
- The Tricki
- The twofold gaze
- The Unapologetic Mathematician
- The value of the variable
- The World Digital Mathematical Library
- Theoretical Computer Science – StackExchange
- Tim Gowers’ blog
- Tim Gowers’ mathematical discussions
- Todd and Vishal’s blog
- Van Vu's blog
- Vaughn Climenhaga
- Vieux Girondin
- Visual Insight
- Vivatsgasse 7
- Williams College Math/Stat Blog
- Windows on Theory
- Wiskundemeisjes
- XOR’s hammer
- Yufei Zhao's blog
- Zhenghe's Blog
Selected articles
- A cheap version of nonstandard analysis
- A review of probability theory
- American Academy of Arts and Sciences speech
- Amplification, arbitrage, and the tensor power trick
- An airport-inspired puzzle
- Benford's law, Zipf's law, and the Pareto distribution
- Compressed sensing and single-pixel cameras
- Einstein’s derivation of E=mc^2
- On multiple choice questions in mathematics
- Quantum mechanics and Tomb Raider
- Real analysis problem solving strategies
- Sailing into the wind, or faster than the wind
- Simons lectures on structure and randomness
- Small samples, and the margin of error
- Soft analysis, hard analysis, and the finite convergence principle
- The blue-eyed islanders puzzle
- The cosmic distance ladder
- The federal budget, rescaled
- Ultrafilters, non-standard analysis, and epsilon management
- What is a gauge?
- What is good mathematics?
- Why global regularity for Navier-Stokes is hard
Software
The sciences
Top Posts
- On the universality of the incompressible Euler equation on compact manifolds
- Career advice
- Maryam Mirzakhani
- On the universality of potential well dynamics
- Does one have to be a genius to do maths?
- Nonlinear dispersive equations: local and global analysis
- Books
- On writing
- Advice on mathematics competitions
- Work hard
Archives
- July 2017 (5)
- June 2017 (1)
- May 2017 (3)
- April 2017 (2)
- March 2017 (3)
- February 2017 (1)
- January 2017 (2)
- December 2016 (2)
- November 2016 (2)
- October 2016 (5)
- September 2016 (4)
- August 2016 (4)
- July 2016 (1)
- June 2016 (3)
- May 2016 (5)
- April 2016 (2)
- March 2016 (6)
- February 2016 (2)
- January 2016 (1)
- December 2015 (4)
- November 2015 (6)
- October 2015 (5)
- September 2015 (5)
- August 2015 (4)
- July 2015 (7)
- June 2015 (1)
- May 2015 (5)
- April 2015 (4)
- March 2015 (3)
- February 2015 (4)
- January 2015 (4)
- December 2014 (6)
- November 2014 (5)
- October 2014 (4)
- September 2014 (3)
- August 2014 (4)
- July 2014 (5)
- June 2014 (5)
- May 2014 (5)
- April 2014 (2)
- March 2014 (4)
- February 2014 (5)
- January 2014 (4)
- December 2013 (4)
- November 2013 (5)
- October 2013 (4)
- September 2013 (5)
- August 2013 (1)
- July 2013 (7)
- June 2013 (12)
- May 2013 (4)
- April 2013 (2)
- March 2013 (2)
- February 2013 (6)
- January 2013 (1)
- December 2012 (4)
- November 2012 (7)
- October 2012 (6)
- September 2012 (4)
- August 2012 (3)
- July 2012 (4)
- June 2012 (3)
- May 2012 (3)
- April 2012 (4)
- March 2012 (5)
- February 2012 (5)
- January 2012 (4)
- December 2011 (8)
- November 2011 (8)
- October 2011 (7)
- September 2011 (6)
- August 2011 (8)
- July 2011 (9)
- June 2011 (8)
- May 2011 (11)
- April 2011 (3)
- March 2011 (10)
- February 2011 (3)
- January 2011 (5)
- December 2010 (5)
- November 2010 (6)
- October 2010 (9)
- September 2010 (9)
- August 2010 (3)
- July 2010 (4)
- June 2010 (8)
- May 2010 (8)
- April 2010 (8)
- March 2010 (8)
- February 2010 (10)
- January 2010 (12)
- December 2009 (11)
- November 2009 (8)
- October 2009 (15)
- September 2009 (6)
- August 2009 (13)
- July 2009 (10)
- June 2009 (11)
- May 2009 (9)
- April 2009 (11)
- March 2009 (14)
- February 2009 (13)
- January 2009 (18)
- December 2008 (8)
- November 2008 (9)
- October 2008 (10)
- September 2008 (5)
- August 2008 (6)
- July 2008 (7)
- June 2008 (8)
- May 2008 (11)
- April 2008 (12)
- March 2008 (12)
- February 2008 (13)
- January 2008 (17)
- December 2007 (10)
- November 2007 (9)
- October 2007 (9)
- September 2007 (7)
- August 2007 (9)
- July 2007 (9)
- June 2007 (6)
- May 2007 (10)
- April 2007 (11)
- March 2007 (9)
- February 2007 (4)
Categories
- expository (253)
- tricks (9)
- guest blog (10)
- Mathematics (689)
- math.AC (5)
- math.AG (37)
- math.AP (92)
- math.AT (17)
- math.CA (136)
- math.CO (160)
- math.CT (6)
- math.CV (20)
- math.DG (35)
- math.DS (72)
- math.FA (23)
- math.GM (9)
- math.GN (21)
- math.GR (79)
- math.GT (15)
- math.HO (10)
- math.IT (11)
- math.LO (46)
- math.MG (36)
- math.MP (25)
- math.NA (13)
- math.NT (142)
- math.OA (17)
- math.PR (91)
- math.QA (5)
- math.RA (31)
- math.RT (21)
- math.SG (4)
- math.SP (45)
- math.ST (6)
- non-technical (136)
- admin (43)
- advertising (26)
- diversions (4)
- media (12)
- journals (3)
- obituary (10)
- opinion (29)
- paper (176)
- question (102)
- polymath (70)
- talk (64)
- DLS (19)
- teaching (159)
- 245A – Real analysis (11)
- 245B – Real analysis (21)
- 245C – Real analysis (6)
- 246A – complex analysis (9)
- 254A – analytic prime number theory (16)
- 254A – ergodic theory (18)
- 254A – Hilbert's fifth problem (12)
- 254A – random matrices (14)
- 254B – expansion in groups (8)
- 254B – Higher order Fourier analysis (9)
- 275A – probability theory (6)
- 285G – poincare conjecture (20)
- Logic reading seminar (8)
- travel (25)
additive combinatorics
approximate groups
arithmetic progressions
Ben Green
Cauchy-Schwarz
Cayley graphs
central limit theorem
Chowla conjecture
circular law
compressed sensing
concentration compactness
correspondence principle
eigenvalues
Elias Stein
Emmanuel Breuillard
entropy
equidistribution
ergodic theory
expander graphs
exponential sums
finite fields
Fourier transform
Four Moment Theorem
Freiman's theorem
Gowers uniformity norm
Gowers uniformity norms
graph theory
Gromov's theorem
GUE
Hilbert's fifth problem
hypergraphs
inverse conjecture
Kakeya conjecture
Lie algebras
Lie groups
Littlewood-Offord problem
Mobius function
moment method
multiple recurrence
Navier-Stokes equations
nilmanifolds
nilpotent groups
nilsequences
NLS
nonstandard analysis
parity problem
politics
polymath1
polymath8
polynomial method
polynomials
prime gaps
prime numbers
prime number theorem
project heatwave
pseudorandomness
random matrices
randomness
random walks
Ratner's theorem
regularity lemma
Ricci flow
Riemann zeta function
Schrodinger equation
sieve theory
spectral theorem
structure
Szemeredi's theorem
Tamar Ziegler
ultrafilters
ultraproducts
universality
Van Vu
wave maps
Yitang Zhang
The Polymath Blog
- Non-transitive Dice over Gowers’s Blog 15 May, 2017
- Rota’s Basis Conjecture: Polymath 12, post 3 5 May, 2017
- Rota’s Basis Conjecture: Polymath 12 6 March, 2017
- Blog theme changed 28 February, 2017
- Rota’s Basis Conjecture: Polymath 12? 23 February, 2017
- MO Polymath question: Summary of Proposals 13 August, 2016
- Polymath 11 is Now Open 7 February, 2016
- Polymath Proposals on Math Overflow 7 February, 2016
- Explaining Polynomials Identities – Success! 7 February, 2016
- “Crowdmath” project for high school students opens on March 1 2 January, 2016
9 comments
Comments feed for this article
14 September, 2009 at 11:26 am
Anonymous
Interesting! (There’s a typo in the third paragraph of the first section)
15 September, 2009 at 2:38 am
Manjil P. Saikia
Interesting, maybe the other talks like the one on Poincare Conjecture can also be made into such a format.
16 September, 2009 at 4:47 am
Thuris
Thank you for posting this. Although a non-mathematician, I found it very clear. (Which gives me hope to understand some of the other posts eventually!)
17 September, 2009 at 11:31 am
Hassan Mohy-ud-Din
Greetings Professor Terence Tao.
How be you? I am a PhD student at Johns Hopkins University. My request is that if you can kindly upload the videos of the talks/lectures along with the slides it will be very helpful and also make a tab of upcoming seminars/conferences/workshops. Thank You
Good Bye
17 September, 2009 at 8:09 pm
xi'an
Dear Terence, there is a typo in the references: de La Vallée Poussin’s book is “Recherches analytiques sur la théorie des nombres premiers”
Best regards,
Xi’an
30 September, 2009 at 8:27 am
zeynel
Yes, thank you for the slides. I enjoyed reading it as a non-mathematician. In your last slide you say that primes are *mostly* odd. Does this suggest that there may be even primes except 2?
30 September, 2009 at 1:47 pm
ARN
Zeynel , I think that was probably a joke. There can be no even primes > 2.
30 September, 2009 at 5:10 pm
links for 2009-09-30 « Blarney Fellow
[…] Structure and randomness in the prime numbers (IMO Festschrift submission) « What’s new (tags: random primes math complexity computation) […]
26 January, 2011 at 7:24 am
Tom Verhoeff
The grammar seems broken in the sentence containing “to not obey behave pseudorandomly”. You can delete “obey” to fix the grammar, but probably “not” should be deleted as well to fix the semantics. This is both on the slides and in the paper.
[Thanks! I think this was fixed in the published version of the text – T.]