Mathematical events  

(In reverse chronological order)

Page maintained by Jean-Claude Evard. Last update: June 9, 2003.

May 13, 2003: The Strong Perfect Graph Conjecture: 
Update by Gérard Cornuéjols:  Link .

April 23, 2003: The breakthrough in the direction of the twin prime conjecture 
announced on March 13, 2003, does not hold. Andrew Granville of the Universite de 
Montreal and K. Soundararajan of the University of Michigan have found an error in 
the preprint Small gaps between primes of Daniel Goldston and Cem Yildirim.
Additional information:
1. See announcement of the error on the Web site 
    of the American Institute of Mathematics  Link .
2. See description of the error  on the Web site 
    of the American Institute of Mathematics  Link .
3. Article by Glennda Chui published in the Mercury News of May 7, 2003  Link .
4. See Current Research on the Web site of Daniel Goldston  Link . 

April 16, 2003: The Poincare Conjecture seems to be on the edge to be 
solved: In an article published in the Moscow Time, Sara Robinson reports that 
Grigory Perelman, from the Steklov Institute of Mathematics in St. Petersburg, 
has announced that he has proved the Poincare Conjecture.  
See page 23:  Link .

April 3, 2003: The first Abel Prize is awarded to Jean-Pierre Serre:
Jean-Pierre Serre was already awarded the highest mathematical prize, the Fields Medal, in 1954.
Additional information:
1. Announcement by the Abel Prize Committee  Link .
2. Information about the Abel Prize: See page 20:  Link .
3. Biography of Jean-Pierre Serre on the Web site of the College de France:  Link .
4. Biography of Jean-Pierre Serre  Link  by John O'Connor and E. F. Robertson 
    at the School of Mathematics of the University of St. Andrews in Scotland.

March 31, 2003: Death of Harold Coxeter:
Additional information:
1. Obituary  Link  on MathWorld Headline News, 
    by Eric Weisstein at Wolfram Research.
2. Biography of Harold Coxeter  Link  by John O'Connor and E. F. Robertson 
    at the School of Mathematics of the University of St. Andrews in Scotland.

 March 13, 2003: Hope of an important breakthrough in prime number 
theory: Daniel Goldston  at San Jose State University and Cem Yildirim have
submitted a paper entitled Small gaps between primes with the hope of an 
important breakthrough in the direction of the solution of the twin prime 
conjecture, more precisely, in the direction of the existence of infinitely many 
"small gaps" between primes, but an error in their paper was announced
on April 23, 2003 (See above).
Additional information:
1. Announcement by the American Institute of Mathematics  Link .
2. Comments by the American Institute of Mathematics  Link .
3. Copy of an e-mail from Hugh Montgomery  Link ,
    posted on the Web site of Number Theory  Link   
    maintained by Keith Matthews  Link ,
    at the University of Queensland in Australia.
4. Web site of Daniel Goldston  Link  at San Jose State University.

February 21, 2003: John Cosgrave found a new largest composite 
Fermat number, and in addition, the factorization of this number gave 
a new largest non-Mersenne prime.
See page 25:  Link .

January 16, 2003: Awards of the Birkhoff Prizes, Cole Prize, Conant Prize, 
Joint Policy Board for Mathematics (JPBM) Communications Award,
Morgan Prize, Satter Prize, and Steele Prizes, at the Joint Mathematics 
Meeting in Baltimore.
Additional information:
1. Information about these awards  Link , provided by 
    the American Mathematical Society.
2. Information about the joint Mathematics Meeting  Link .
    provided by the American Mathematical Society:

December 10, 2002: Poincare conjecture: A revised version 
of a submitted proof of the Poincare conjecture has been posted 
by Sergey Nikitin at Arizona State University. See page 23:  Link .
 See April 2002 below for a reduction of the problem by Martin Dunwoody. 

December 6, 2002: Pi calculated to 1.24 trillion digits by Yasumasa Kanada  Link .
and his team at the Information Technology Center at Tokyo University.
Additional information:
1. Comments from Cable News Network (CNN)  Link .
2. Comments from MSNBC News  Link .
3. Report  Link  of Audrey MCAvoy in the Seattle Post Intelligencer 
    of Saturday, December 7, 2002.

November 6, 2002: Submitted paper on the proof of the Riemann 
hypothethis: Carlos Castro and Jorge Mahecha have submitted a paper
to the Journal Annals of Mathematics for a proof of the Riemann hypothesis.
See page 23:  Link . 

October 25, 2002: Death of René Thom, creator of Catastrophe Theory. 
Additional information:
1. Obituary in the Washington Post  Link .
2. Obituary in the Atlanta Journal-Constitution  Link .
3. Obituary in the French newspaper Le Monde  Link .
4. Biography of René Thom  Link  
    by John O'Connor and E. F. Robertson in the School of Mathematics 
    of the University of St. Andrews in Scotland.
5. Description of Catastrophe Theory  Link  on MathWorld,  
    by Eric Weisstein at Wolfram Research.
6. René Thom was awarded the Fields medal (See page 20:  Link )  in 1958  
    for his work on cobordism.
7. The two main books published by René Thom:
    [1] René Thom, 
         Structural stability and morphogenesis, 
         An outline of a general theory of models,
         Translated from the French by D. H. Fowler. 
         With a foreword by C. H. Waddington. 
         Addison-Wesley Publishing Company, 1989, xxxvi+348 pp.
    [2] René Thom,
          Mathematical models of morphogenesis,
          Translated from the French by W. M. Brookes and D. Rand, 
          Ellis Horwood Ltd., Chichester; Halsted Press, 
          [John Wiley & Sons, Inc.], 1983. 305 pp. 

October 22, 2002: A second submitted paper on the proof of the 
Poincare Conjecture: Sergey Nikitin  Link  at Arizona State University has 
submitted, and also posted on the internet  Link , a paper for a proof of the 
Poincare conjecture.
 See April 2002 below for a reduction of the problem by Martin Dunwoody. 
 See December 10, 2002, for the most recent version.  

August 20--28, 2002: The International Congress of Mathematicians 
(ICM), organized by the International Mathematical Union, was held in Beijing 
from August 20 to August 28, 2002. The Fields Medals and the Nevanlinna 
Prize were awarded (see below) during the opening ceremony on the first day 
Congress. This congress is held every four years.
Additional information:
1. Welcome to the ICM:  Link  and  Link .
2. Welcome to the IMU:  Link .

August 20, 2002: The 2002 Fields medals and Nevanlinna Prize were 
awarded by the International Mathematical Union at the International Congress 
of Mathematicians in Beijing (See above). It had been decided to award only 
two instead of four Fields Medals. The two Fields medals were awarded to 
Laurent Lafforgue and Vladamir Voevodsky. The Nevanlinna prize was 
awarded to Madhu Sudan.
Additional information.
1. Comments  Link  by Eric Weisstein at Wolfram Research.
2. Description of the work of the awardees  Link  and  Link   
    provided by the American Mathematical Society.
3. Description of the work of the awardees  Link  and  Link   
    provided by the Mathematical Association of America..
4. Fields medals: See page 20:  Link . 

August 6, 2002: Polynomial time for primality testing: Manindra Agrawal, 
and two of his Ph. D. students, Neeraj Kayal and Nitin Saxena, have established 
an algorithm for testing whether a positive integer is prime or composite. As 
outlined by Chris Caldwell (See 4 below), what is new is that this algorithm 
does not rely on any unproved conjecture, and it is deterministic (that is 
non-probabilistic). The time taken to test an integer n is of the order 
O((ln(n))^12), and it is likely to be even better.
Additional information:
1. Announcement  Link  of this discovery on the Web site  Link   
    of the Department of Computer Science and Engineering, 
    of the Indian Institute of Technology at Kanpur.
2. Online publication  Link  (pdf file, very slow, wait for one minute): 
    Manindra Agrawal, Neeraj Kayal, and Nitin Saxena, 
    Primes is in P
    Department of Computer Science and Engineering 
    Indian Institute of Technology at Kanpur 
    Kanpur-208016, India 
    August 6, 2002.
3. Comments from Eric Weisstein  Link  at Wolfram Research.
4. Comments and presentation  Link  of the new algorithm by Chris Caldwell 
     at the University of Tennessee at St. Martin.
5. Announcement of the new algorithm  Link  
    on the "Time of India" of August 9, 2002.
6. Web site of Manindra Agrawal  Link . 

July 4, 2002: Laurent Schwartz died.  Additional information:
1. Copy from Alain Juhel posted on Math Forum of an e-mail of July 5, 2002 
    from  Michel Waldschmidt, President of the Société Mathématique de France 
    (SMF)  Link .
2. Comments published on July 9, 2002 in the French newspaper Le Monde  Link .
3. Comments published on July 10, 2002 by the historian Madeleine Rebérioux 
     in the daily newspaper l'Humanité:  Link .
4. Comments published on July 10, 2002 by Jean-Paul Monferran 
    in the daily newspaper l'Humanité:  Link .
5. Laurent Schwartz was awarded the Fields Medal in 1950 for his work on the 
    theory of distributions, also called generalized functions.
6. Biography of Laurent Schwartz  Link  and list  Link  of the winners 
      of the Fields Medal on the Web site of John O'Connor and E. F. Robertson 
      in the School of Mathematics of the University of St. Andrews in Scotland.
7. Web page  Link  on the theory of distributions, also called generalized 
     functions on the Web site MathWorld, maintained by Eric Weisstein 
    at Wolfram Research.

July 2, 2002: Three new Mathematical Institutes.  The National Science 
Foundation (NSF) has decided  Link  to fund three new mathematical research 
institutes for 24 million dollars over the next five years:
1. A Mathematical Biosciences Institute at Ohio State University in Columbus.
2. The Statistical and Applied Mathematical Sciences Institute in Research 
Triangle Park, in North Carolina.
3. The Research Conference Center at the American Institute of Mathematics 
(AIM) in Palo Alto, California. 

June 30, 2002: Claude Berge died. Additional information:
1. Biography  Link  by Vašek Chvátal  Link , 
    in the Department of Computer Science of Rutgers University.
2. Biography  Link  on the Web site of the Institut National de Recherche en 
    Informatique et Automatique (INRIA) at Rocquencourt, France.
3. Abstract  Link  of a colloquium presented by Claude Berge at the Institut 
    National de Recherche en Informatique et Automatique (INRIA) at 
    Rocquencourt, France, on October 19, 1999.
4. Pictures  Link  on WebShots.

June 6, 2002: Creation of the Abel prize: See page 20:  Link . 

May 2002: The strong perfect graph conjecture: 
In May 2002, Maria Chudnovsky and Paul Seymour announced that, they had 
completed the proof of the Strong Perfect Graph Conjecture, with a proof 
build on earlier joint work with Neil Robertson and Robin Thomas.
Additional information:
1. The Strong Perfect Graph Theorem  Link , 
    page maintained by Vašek Chvátal  Link , 
    in the Department of Computer Science of Rutgers University.

May 1, 2002: The planar triple bubble conjecture  Link  and  Link  
is proved by Wacharin Wichiramala  Link  in his Ph.D. thesis  Link  (wait 
for a long time, the connection is very slow; then go to page 2, because 
page is blank), with advisor John Sullivan  Link , at the University of Illinois 
at Urbana-Champaign.
 See March 2001 and July 2000 for more about bubble conjectures.

May 2, 2002: William Tutte died. Additional information:
1. List  Link  of related Web pages provided 
    by the Department of Combinatorics and Optimization  Link  
    of the Faculty of Mathematics of the University of Waterloo in Canada.
2. Memorial service  Link  posted by the Faculty of Mathematics  Link   
    of the University of Waterloo in Canada. 

April 18, 2002: The Catalan Conjecture: Preda Mihailescu has submitted 
a manuscript for a proof of the Catalan conjecture: See page 23:  Link . 

April 2002: Advance toward the proof of the Poincare Conjecture: 
A reduction of the problem of proving the Poincare conjecture has been posted 
by Martin Dunwoody at the University of Southampton in the United Kingdom. 
See page 34  Link . 

March 20, 2002: End of the Faber and Faber Challenge organized by the 
publishing company Faber and Faber  Link . They offered a million dollar prize 
to anyone who could determine whether the Golbach's conjecture  Link  is true 
or false, and submit the solution between March 20, 2000 and March 20, 2002. 
As expected, that problem was not solved during this period, and it is not 
expected to be solved any time soon.

December 5, 2001: The discovery of a new largest known prime 
is officially established. This new largest known prime was found 
by Michael Cameron on November 14, 2001. See page 25:  Link . 

May 17, 2001: A new largest largest known pair of twin primes is found 
    by David Underbakke and Phil Carmody. 
    See  Link  on the Web site of Chris Caldwell, 
    and  Link  on the Web page of Lucile and Yves Gallot.

March 2001: The Double Bubble Conjecture is a true statement in 
dimension 4: This was proved by the undergraduate students Ben Reichardt, 
Cory Heilmann, Yvonne Lai, Anita Spielman in the "SMALL" program  Link   
at Williams College. 
References:
[1] Proof of the Double bubble conjecture in R4 and certain higher dimensional cases, 
       Ben Reichardt, Cory Heilmann, Yvonne Lai, Anita Spielman (1999 Geometry Group), 
       Pac. J. Math., to appear  Link .
[2] Proof of the Double Bubble Conjecture, Frank Morgan, 
       The American Mathematical Monthly, Volume 108, Number 3, March 2001, pages 193--205. 
 See July 2000 and May 1, 2002 for more about bubble conjectures.

July 2000: The Double Bubble Conjecture is a true statement in 
dimension 3: This was proved by Michael Hutchings, 
Frank Morgan  Link ,  Manuel Ritore  Link , and Antonio Ros  Link . 
References:
[1] Michael Hutchings, Frank Morgan, Manuel Ritore, , and Antonio Ros, Proof 
      of the Double Bubble Conjecture, Annals of Mathematics, Vol. 155, No. 2,  
      pp. 459-489, March 2002.
[2] Michael Hutchings, Frank Morgan, Manuel Ritore, , and Antonio Ros, 
      Electronic Research Announcements of the American Mathematical Society, 
       6: 45--49, July 17, 2000  Link .
[3] Preprint of May 30, 2001 on the Web site of Manuel Ritore:  Link .
 See March 2001 and May 1, 2002 for more about bubble conjectures.

June 21, 1999: The Shimura-Taniyama conjecture is proved: 
                         See page 22:  Link .

1999: A second step in the direction of the complex Fermat's Last Theorem:
John Zuehlke proves in the following paper that the equation xⁿ+ yⁿ = zⁿ has no 
solution in positive integers x, y, and z when n is a non-real Gaussian integer:
John A. Zuehlke, Fermat's last theorem for Gaussian integer exponents, 
Amer. Math. Monthly 106 (1999), no. 1, 49. Review by F. Beukers
(Can be seen only on networks of subscribers to MathSciNet)  Link .
 For the first step, see 1993. 

1999: The Honeycomb conjecture: 

             Currently under construction             

1998: August 9, 1998, Kepler's conjecture (Problem # 18, Part C, on 
Hilbert's famous list): On August 9, 1998, Thomas Hales announced the 
completion of a proof of the Kepler's conjecture on sphere packing. The 
fifth part of the proof is the thesis of Samuel P. Ferguson, finished in 1997 
at the University of Michigan at Ann Arbor under the direction of Thomas 
Hales.
Additional information:
1. Announcement of August 9, 1998 by Thomas Hales  Link .
2. Thomas Hales has moved from the University of Michigan at Ann Arbor 
    to the University of Pittsburgh in summer 2001. His new web site is  Link .
3. Cannonballs and honeycomb, article published in the issue of fall 2001 of the 
    magazine Pitt Math Zine of the  Department of mathematics of the 
    University of Pittsburgh  Link .

             Currently under construction             

1995: Fermat's Last Theorem is proved: See page 22:  Link . 

1993: A first step in the direction of the complex Fermat's Last Theorem:
James Cross proves in the following paper that the equation  x⁴+ y⁴ = z⁴ has no
solutions with x, y, z different from zero in the ring of Gaussian integers:  
James T. Cross, In the Gaussian integers, $\alpha\sp 4+\beta\sp 4
\not=\gamma\sp 4$,. Math. Mag. 66 (1993), no. 2, 105--108.
 For the second step, see 1999. 

1984: The truth of Bieberbach's Conjecture  
              was established by Louis de Brange.

1983: Mordell's conjecture. The truth of Mordell's conjecture was 
    established by Gerd Faltings, who received the Fields Medal in 1986.  
Additional information: 
1.   Gerd Faltings published his proof in the following paper: 
      Gerd Faltings, Endlichkeitssätze für abelsche Varietäten über Zahlkörpern. 
      (German) [Finiteness theorems for abelian varieties over number fields]
      Invent. Math. 73 (1983), no. 3, 349--366. 
      Gerd Faltings, Erratum: "Finiteness theorems for abelian varieties over 
      number fields" (German), Invent. Math. 75 (1984), no. 2, 381.
      Review by James Milne(Can be seen only on networks of subscribers to 
      MathSciNet)  Link .
2.   Statement  Link  of Mordell's conjecture on MathWorld, 
      maintained by Eric Weisstein at Wolfram Research.
3.   See current biography of Gerd Faltings  Link  and list  Link  of the winners 
      of the Fields Medal on the Web site of John O'Connor  and E. F. Robertson 
      in the School of Mathematics  of the University of St. Andrews in Scotland.

1980: The classification of finite simple groups is completed.

1976: The truth of the Four Color Conjecture is established.

1973: Chen's theorem is proved by Jing Run Chen.

1955: Roth's Theorem was published in the following paper:
    Klaus Friedrich Roth, Rational approximations to algebraic numbers, 
    Mathematika 2 (1955), 1--20; corrigendum, 168.
    Review by E. R. Kolchin (Can be seen only on networks of subscribers to 
    MathSciNet)  Link .
1.  See statement of Roth Theorem  Link  on MathWorld,  
      by Eric Weissteinat Wolfram Research.
2.  Klaus Friedrich Roth received the Fields Medal in 1958. See current 
      biography of Klaus Friedrich Roth  Link  and list  Link  of the winners 
      of the Fields Medal on the Web site of John O'Connor and E. F. Robertson 
      in the School of Mathematics of the University of St. Andrews in Scotland.

1850: Bertrand's conjecture is proved by Pafnuty Lvovich Chebyshev.
This conjecture says that for every integer n greater than 3, 
there exists a prime between n and 2n-2.
1. Bertrand's conjecture  Link , on the Web site of Eric Weisstein 
    at Wolfram Research.
2. Bertrand's conjecture  Link , on the Web site of Chris Caldwell 
    at the University of Tennessee at St. Martin.
3. Biographies of Joseph Louis François Bertrand  Link ,  
    and Pafnuty Lvovich Chebyshev  Link ,   
    on the Web site of John O'Connor  and E. F. Robertson 
    in the School of Mathematics  of the University of St. Andrews in Scotland.

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Calendar  Link  and abstracts  Link  of upcoming mathematical conferences      
provided by Atlas Conferences Inc.  Link . 

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