Opinions of Doron Zeilberger
Last Update: Feb. 7, 2017
"Any clod can have the facts, but having opinions is an art."
-- Charles McCabe
Read the following opinions (Listed In Reverse Chronological Order)
Opinion 157: Ninety is the New Forty for Quite a Few Mathematicians
(Written: Feb. 7, 2017)
Academic "peer-reviewed" journals Do No Longer Serve their Original Purpose of Transmitting Knowledge, But they Will Stay (Unfortunately) With Us
for a Very Long Time, since they serve an "Important" Human Need: "Inclusion-Exclusion"
(Written: Nov. 23, 2016)
Opinion 155: Scott Aaronson's "Theories" and "Theorems" are Egregiously Wrong When Taken at Face Value,
and When Interpreted Correctly are "Right" but Uninteresting
(Written: Oct. 13, 2016)
Opinion 154: HAPPY 100th Birthday, Richard Guy
(Written: Sept. 30, 2016)
Opinion 153: Editors of Math Journals (e.g.: Patrice Ossona de Mendez and Pierre Rosenstiehl, eds. of European Journal of Combinatorics)
Who Immediately Reject Submissions (without refereeing) because they decide that they are of "insufficient interest for their audience"
are ANALOGOUS to Managers of Swimming Pools Who Deny admission because of race or ethnicity
(Written: Sept. 3, 2016)
Opinion 152: The Combinatorics Giant, Major Percy Alexander MacMahon, also deserves to be the Main Character in a major movie
(Written: July 28, 2016)
Opinion 151: The True Heirs to Ramanujan's Mathematics are Concrete and Experimental Mathematicians, and not
"Fancy" ones, who "stole" him from us
(Written: May 11, 2016)
Opinion 150: President Obama's Advisory Committee on STEM Education
Should be Praised for Its Wise (and Brave!) Decision to Prohibit Fractions
from the K-16 curriculum, and only use decimals
(Written: April 1(!), 2016)
Opinion 149: Tic-Tac-Toe, Checkers, Chess, Go, and next is MATHEMATICS!
(Written: March 22, 2016)
Opinion 148: Leo Corry's Masterpiece "A Brief History of Numbers" Says as Much about the Future as About the Past of Mathematics
(Written: Nov. 25, 2015)
Opinion 147: NameRemoved, Who is Prejudiced
against Symbolic-Computational Number Theory, Should Not be Editor-In-Chief of JournalNameRemoved
(Written: Nov. 20, 2015)
Opinion 146: Why the "fact" that 0.99999999...(ad infinitum)=1 is NOT EVEN WRONG
(Written: Sept. 12, 2015)
The Tail of Statistics, Will (soon) Wag the Dog of Mathematics, and instead of
"Statistics is a Mathematical Science" we would say that "Mathematics is a Statistical Science"
(Written: Sept. 12, 2015)
"Dear Sirs: Nash is a mathematical genius": True, But even more Importantly, John Nash was a True Visionary,
who realized that using computers offers "another route to knowledge, rather than mere ideas''
(Written: May 25, 2015)
Opinion 143: Shame on you, the "Electronic Journal of Combinatorics", for rejecting a submission containing
a (correct!) proof of the Collatz 3x+1 conjecture
(Written: April 1, 2015)
Opinion 142: Why Is π So Ubiquitous?
(Written: π day, 2015 (aka 3/14/15))
Biological Evolution Did not prepare us for reasoning logically and for rigorous proofs
Mathematical Cultural Evolution Did not prepare us to Use Computers Optimally
(Written: Feb. 18, 2015)
Opinion 140: Zvi Artstein's "Mathematics and the Real World" is Destined to become a Classic
(Written: Oct. 7, 2014)
Opinion 139: Say NO to Academic Blackmail
(Written: Sept. 16, 2014)
Opinion 138: Max Tegmark got it Backwards! He claims that Physics=Math, but In fact, Math=Physics
(Written: Aug. 13, 2014)
Opinion 137: On the Changing (Alas, So Slowly!) Attitudes to Mathematics
(Written: July 15, 2014)
Opinion 136: Amir Alexander's "Infinitesimal" Should Be Read by ANYONE Interested
in Math, Regardless of whether or not they are interested in the history of math,
since it Says As Much about the Present, and more importantly, the FUTURE, of Math
(Written: April 8, 2014)
The "Mathematical Analog" of Edward Snowden,
Who is offering to reveal the identity of "anonymous" referees
of Rejected Submissions to their authors,
Should Not be Expelled from The American Mathematical Society!
(Written: April 1(!), 2014)
Opinion 134: Pure Mathematics is Forty Years Behind Chemistry
(Written: Nov. 20, 2013)
Octgogenerian-Authority-on-Social-Insects E.O. Wilson Knows Better How much Math is Needed for Science
than Quadragenarian-Authority-on-the-Langlands-Program Edward Frenkel, and Guess What?, my dear friend
Ed, You don't even need (your kind of) Math to Excel in (future) Math!
(Written: Aug. 15, 2013)
Opinion 132: Bill Duke's Brilliant ("Elementary") Proof of a Seemingly "Deep" Result
in Mainstream Number Theory is a Harbinger of Many More Elementary (Computer-Discovered) Proofs to Come
(Written: May 1, 2013)
Opinion 131: Larry Shepp (Sept. 9, 1936- April 23, 2013) A very LOUD (yet NOT Obnoxious) Mathematical Giant
(Written: May 1, 2013)
Opinion 130: Andrei Zelevinsky(Jan. 30, 1953- April 10, 2013)
(Written: April 10, 2013)
Opinion 129: The "Lost" Diary of Carl Friedrich Gauss Should Be Made Public
(Written: April 1(!), 2013)
Premature Abstraction, and Unrealistic Expectations, are the Root of All Evil:
Why are we Math Professors Doing such a TERRIBLE Job in Teaching Non-Math Majors (and Even
Math Majors) The Math That They Need
(Written: Jan. 6, 2013)
Opinion 127: The Presidents of the Professional Mathematics Societies Care About Math Education As
Much as the CEOs of Tobacco Companies care about your Health
(Written: Oct. 13, 2012)
Opinion 126: [Contemporary Pure] Math is far LESS than the Sum of
its [Too Numerous] Parts,
and Beware of Pure Mathematicians Preaching How Important Math
is for Science and Technology.
Of Course it is, but NOT their, Soon-To-Be Obsolete and PEDANTIC Style of
Doing Math, but Rather the Way
Physical Scientists Practice It:
Experimentally, Heuristically and Non-Rigorously.
(Written: July 23, 2012)
Opinion 125: Now that Alan Turing turned 100-years-old, it is time to
have a Fresh Look at His Seminal Contributions, that did lots of
Good But Also Lots of Harm
(Written: June 23, 2012)
A Database is Worth a Thousand Mathematical Articles:
An Ode to Neil Sloane's On-line Encyclopedia of Integer Sequences (OEIS)
(Written: May 22, 2012)
Shame On You, the Proceedings of the National Academy of Science (PNAS), for
Rejecting a Historic Submission of a Counterexample to Fermat's Last "Theorem"
(Written: April 1, 2012)
Shame On You, the New York Times and other "Major" Newspapers for
Not Even Mentioning That Endre Szemerédi Was Awarded
The 2012 Abel Prize (The Mathematical Analog of the Nobel Prize)
(Written: March 27, 2012)
A Case Study In Early 21st-Century Mathematical Narrow-Mindedness:
How a "Non-Rigorous", but ABSOLUTELY CERTAIN Disproof of a 45-Year Old Conjecture
Made by One of the Greatest Number Theorists of the 20th Century Got
Rejected By Three Journals
(Written: Feb. 24, 2012)
Opinion 120: Tim Gowers's Proposed Boycott on Elsevier Only Makes Sense If It is Extended To All
Subscription, Non-Free, Journals, Including those of the so-called "Non-Profit"
American Mathematical Society (That is (at least) As Greedy As Private Publishers)
(Written: Jan. 29, 2012)
Opinion 119: Farewell to "W" (Herbert Saul Wilf), a True VISIONARY for Whom EVERYTHING was INTERTWINED
(Written: Jan. 20, 2012)
Opinion 118: Even Pure Mathematics Has Its Share of Empty Suits
(Written: Oct. 21 2011)
Opinion 117: People Should Learn to Share their Ideas, and Make their Funded
Grant Proposals Public
(and an Efficient Algorithm for convincing those that refuse)
(Written: June 29, 2011)
Opinion 116: David John Wilson's Masters Essay: A Paradigm of the Future Ideal Mathematical Exposition
(Written: May 1, 2011)
Opinion 115: The Mathematical Association of America did the Right Thing When
It Recommended to the US Department of Education to Illegalize the Teaching of Calculus Except for Physics and Engineering Majors
(Written: April 1, 2011)
Philippe FLAJOLET (Dec. 1, 1948-March 22, 2011): The
SINGULAR Combinatorialist Who Made Analysis Fun!
(Written: March 29, 2011)
Opinion 113: Mathematics is Indeed a Religion, But It has
too Many Sects! Let's Unite Under the New God of Experimental Mathematics
(Written: Jan. 14, 2011)
Opinion 112: On Human Hypocrisy (and Human-Centric Bigotry): A Typical Computer-Assisted Proof is
Far More Rigorous (and Certain!, and Deeper!) than a typical Human-Generated Proof, (and
some suggestions on how to improve the reliability of published mathematics
in "peer"-reviewed journals)
(Written: Oct. 5, 2010)
Opinion 111: Congratulations Elon Lindenstrauss, Ngo Bao Chau, Stas Smirnov, and Cedric Villani
for winning a 2010 Fields Medal, but PLEASE, don't spend the next 40 years of your life
continuing to do the same old (of course very deep but SO) BORING stuff,
but instead use your great talents to do research in INTERESTING mathematics
(that not only Terry Tao can understand, but ALSO the rest of us).
(Written: Aug. 25, 2010)
Opinion 110: (Human-Made) Mathematics is Necessarily Contingent,
as I Realized on reading Amir Alexander's masterpiece "Duel at Dawn"
(Written: April 25, 2010)
[removed by the request of Gil Kalai, who believed
that it was unjust]
(Written: April 1, 2010)
...The feeling is mutual: I Feel Sorry for Infinitarian Hugh Woodin for Feeling Sorry for Finitists Like Myself!
(And the "Lowly" Finite is MUCH more Beautiful than any "Infinite")
(Written: March 16, 2010)
Opinion 107: Any Faculty Member who Votes Against Granting Tenure to a Colleague "Deserves to be Shot"
(Written: Feb. 16, 2010)
Opinion 106: How To Make the Joint Mathematical Meetings Much Better with Minimal Effort
(Written: Jan. 20, 2010)
Opinion 105: Interview with Shalosh B. Ekhad about
Mikhail Gelfand's Interview With Yuri Manin
(Interviewed by DZ)
(Written: Nov. 11, 2009)
Opinion 104: The Shocking State of Contemporary "Mathematics", and
the Meta-Shocking Fact that Very Few People Are Shocked
(Written: Oct. 28, 2009)
Opinion 103: Israel Moiseevich Gelfand (Sept. 2, 1913-Oct. 5, 2009)
(Written: Oct. 6, 2009)
Opinion 102: Some Soul Reckoning on Yom Kippur: We Are NOTHING, and we Should Not Just SAY it,
but truly BELIEVE It (and ACT accordingly)
(Written: Sept. 30, 2009)
Opinion 101: The Newly launched Journal Rejecta Mathematica IS a JOKE (but so are all math journals!)
(Written: July 31, 2009)
Opinion 100: On Human Supremacy and Why We Should Abandon It
(Written: June 14, 2009)
Opinion 99: We Need More People Like Aviezri Fraenkel, Who Taught me
that Games are Math and Math is a Game
(Written: May 22, 2009)
Opinion 98: Don't Fall In Love With Your Model: The Cautionary Tale of my Recent proof that P=NP
(Written: April 1, 2009)
Opinion 97: Towards a Gentler and Less Formal Mathematical Narrative Style
for Communicating Mathematics to Humans
(Written: March 24, 2009)
Opinion 96: I am so Sorry, my esteemed Colleagues, K. and L., for "Kicking you Out" of my Lecture,
It was my fault for not Announcing At the Very Beginning That "No Outside Work" is allowed
(Written: Feb. 22, 2009)
Opinion 95: We need both Birds and Frogs, but Most of all we need good Beavers
(Written: Feb. 15, 2009)
Opinion 94: The Human Obsession With "Formal Proofs" is a Waste of the Computer's Time, and,
Even More Regretfully, of Humans' Time (Written: Jan. 4, 2009)
Opinion 93: An ode to George Andrews on his 70th Birthday
(Written: Dec. 4, 2008)
Opinion 92: Twenty Pieces of Advice for a Young (and also not so young) Mathematician
(Written: Nov. 1, 2008)
Opinion 91: If You Want Mathematical Truth, You Better Pay For It!
(Written: July 31, 2008.)
Opinion 90: Mathematics, Religion, and Contingent Beauty
(Written: June 28, 2008.)
Opinion 89: Mental Math Whiz [And Very Good Mathematician] Art Benjamin
Should be Aware that not only his Night Job, but also some parts of
his "Day Job" should be clearly labeled "For Entertainment Only"
(Written: June 6, 2008.)
The American Mathematical Society's Ethics Committee Should Be
Praised for Its Resolution to Ban Nazi Mathematicians,
But It Went Too Far in "Disqualifying" Paul Erdös for
(Written: April 1, 2008 ).
Opinion 87: Yuri Tschinkel, the Editor-In-Chief of the Journal Experimental Mathematics, Should Be
Reminded That Proper Experimental Procedures Prohibit Faking Data in Order
to "Establish" Pre-conceived Conclusions, and that Proper Editorial Procedures
Prohibit Faking Referee Reports in Order
to "Establish" Pre-conceived Editorial Decisions
(Written: Feb. 2, 2008).
For God So Loved the World, that He gave [one of his most talented] begotten Sons,
that Whoever Masters His Art of Computer-Programming
Shall Not Perish and Crash, but have Everlastingly Bug-Free
(yet with short-lasting running times) Programs
(Written: Jan. 10, 2008).
Opinion 85: We Should Continue To Be Ambivalent Towards Ambiguity in Mathematics: It Sure Did Some Good,
But It Also Did (and Does) Lots of Harm
(Written: Dec. 11, 2007).
Opinion 84: Bye-Bye Understanding, Hello Meta-Understanding
(Written: Oct. 6, 2007).
Opinion 83: "Self-Deception" "Guru", Robert Trivers, is Deceiving Himself that
he is a Scientist
(Written: Sept. 18, 2007).
Opinion 82: A Good Lemma is Worth a Thousand Theorems
(Written: Aug. 14, 2007).
Opinion 81: Because You Snubbed Others You Were Snubbed, and Those Who Snubbed You Shall Be Snubbed
(Written: June 28, 2007).
Opinion 80: Shalosh B. Ekhad's Reply to the Math Horizons "April Fools" Spoof
Where It Was Extensively Quoted (or Rather Misquoted)
(Written: May 20, 2007).
Opinion 79: The Rutgers Mathematics Department Should Reverse
Its Unfortunate Decision To Forbid The Sale
of Mathematical Identities
(Written: April 1 (!), 2007).
Opinion 78: Music and Lyrics in Math Talks
(Written: March 8, 2007).
Opinion 77: Take This Math Journal and Shove It, Ain't
Submitting there No More
(Written: Feb. 3, 2007).
Opinion 76: Why P Does Not Equal NP and Why Humans Will
Never Prove It by Themselves
(Written: Dec. 11, 2006).
Opinion 75: James Joseph Sylvester: the GREATEST Mathematician of ALL TIMES (Written: Oct. 27, 2006).
Opinion 74: Guoce Xin's "High-School Algebra" Approach to MacMahon's Partition
Analysis: Yet Another Reason to Get Rid of Cauchy and Throw Out
all that Epsilon-Delta Nonsense
(Written: Sept. 17, 2006).
Opinion 73: My Dear Comrade Boris Mityagin,
This is [2006,USA] Not [1970,USSR], So Stop Grumbling
About Your "Lazy" Students and Try to Be the Best Possible
Teacher for THEM
(Written: Aug. 2, 2006).
Opinion 72: The Next Term in the Sequence:
[Dog, Human, Mathematician, ...] is ``Computer-Programmer for Computer-Generated Mathematics''
(Written: June 11, 2006).
Why Are There So Many Outstanding Fifty-Year-Old
Israeli Combinatorialists (and Computer Scientists, and Physicists and
...) (Written: Feb. 17, 2006).
Opinion 70: A Case Study in Math (and Logic!) Abuse by
a Social Scientist: Jon Elster's Critique of Backwards Induction
(Written: Dec. 7, 2005).
Opinion 69: Roll Over Platonism, Logicisim, Formalism,
Intuitionism, Constructivism, Naturalism and Humanism!
Here Comes Combinatorialism and Trivialism.
(Written: Dec. 7, 2005).
Opinion 68: Herren Geheimrat Hilbert und Prof. Dr. Cantor,
I'd like to be Excused from your "Paradise":
It is a Paradise of Fools, and besides feels more like Hell
(Written: Nov. 23, 2005).
Opinion 67: Why I liked Apostolos Doxiadis's Uncle Petros Ending so much better
than David Auburn's Proof Ending
(Written: Oct. 6 2005).
Opinion 66: Fine-Tuning Chaitin's Doomsday Message:
Intractability Suffices to Dump (Rigorous) Proofs
(Written Sept. 13, 2005).
Opinion 65: My Two Favorite Pedagogical Principles by Two
of my Favorite Mathematicians
(Written May 5, 2005).
Opinion 64: Make New (Kinds of) Science But Keep the Old,
One is Silver, the Other Gold [And their Fusion is
(Written April 25, 2005).
Opinion 63: A Negative Review of Negative Reviews
(Written Jan. 12, 2005).
Opinion 62: Comparative MathGeniusOlogy:
Why Grothendieck (b. 1928) "died" (in Erdos's sense)
a Long Time Ago, While Gelfand (b. 1913) is
Alive and Kicking (Mathematically!).
(Written Nov. 20, 2004).
Opinion 61: Rejected Authors of the World Unite, You have nothing to lose
but your Anger
(Written Nov. 1, 2004).
appendix (written April 15, 2006)]
Opinion 60: Still Like That Old-Time Blackboard Talk
(Written May 20, 2004).
The Rutgers Math Dept.'s Executive Committee's Decision
to Forbid Sleeping and Other Improper Behavior in Seminar
and Colloquium Talks Should be Adopted by All Math Departments.
(Written April 1 (!), 2004).
`I Saw Their Proof Now I'm a Believer': The Marcus-Tardos Proof
of the Füredi-Hajnal and Stanley-Wilf Conjectures
(Written Dec. 3, 2003).
Opinion 57:The Unbearable Non-Triviality of "Trivial" Mathematics,
and the even more Unbearable Triviality of "Non-Trivial" Mathematics.
(Written Nov. 9 2003).
Opinion 56:The DisUnity of Mathematics
(Written Nov. 7, 2003).
Apostolos Doxiadis's Narrative Approach to Mathematics Education
Should Be Embraced
(Written May 27, 2003).
Amir Alexander's Narrative Approach to the History of Mathematics
Makes Lots of Sense
(Written May 23, 2003).
Frank Quinn's Rigor is Not as Rigorous as He Thinks
(Written May 22, 2003).
The Electronic Journal of Combinatorics and arXiv.org Should
Reverse their Unfair and Bigoted Decision Not to Publish On the
So-Called Genome Code
(Written April 1 (!), 2003).
Opinion 51: It is Important to Keep Looking for
Non-Computer Proofs of the Four-Color Theorem,
BUT Not Because of the "Usual" Reasons.
(Written Feb. 25, 2003).
Opinion 50: Tim Gowers's `Mathematics-A Very Short Introduction'
Should be Recommended Reading to the General Reader and
Required Reading for Mathematicians.
(Written Oct. 25, 2002).
Opinion 49: Why is Ubiquity so Ubiquitous?
(Written Oct. 25, 2002).
Opinion 48: Some Suggestions to the IMU
(International Math Union) about future ICMs(International Congress of
(Written Oct. 11, 2002).
Opinion 47: Hello!, Sir Michael.
Have You Ever Heard of
the COMPUTER?, or of COMPUTER ALGEBRA?
(Written June 11, 2002).
Opinion 46: Mathematics is an OLD Person's GAME (Provided You Stay Away from the Mainstream)
(Written May 24, 2002).
Opinion 45: The Clay Foundation Should Pay Most
of the Million-Dollar Prize to the Anonymous Genius
Who Proved that the P vs. NP Problem is NP Hard
(Written April 1 (!), 2002).
Opinion 44: Two lessons I learned from Shalosh B. Ekhad, XIV's
webbook(Written Nov. 1, 2001).
Opinion 43: It is Time to Move On to Non-Euclidean Mathematics
(Written Nov. 1, 2001).
Opinion 42: Eric Weisstein's Math Treasure-Trove Should
Be Re-Activated As Soon As Possible
(Written Feb. 7, 2001).
Opinion 41: The British Government Should Declassify
Turing's Counterexample to the Riemann Hypothesis
(Written APRIL 1, 2000)
Opinion 40: Akalu Tefera: A Truly 3rd-Millenium
Opinion 39: Partial and Inconclusive Proofs are Welcome!
Opinion 38: Be Skeptical of Skeptics and be Optimistic
about Optimism (and Don't Tacitly Assume that
ONLY the OTHER Guy Tacitly Assumes)
Opinion 37: Guess What? Programming is
Even More Fun Than Proving, and, More Importantly
It Gives As Much, If Not More, Insight and Understanding
Opinion 36: Don't Ask: What Can The Computer do for ME?, But
Rather: What CAN I do for the COMPUTER?
Opinion 35: Mathematicians Should Pay Attention to
History and Philosophy of Math (In Particular to
Leo Corry's Fascinating Work)
Opinion 34: We Should Confess to Our Dumb Mistakes,
in Order that Our Students should not feel bad about
Opinion 33: We need a Leaner and Livelier American Math Society
Opinion 32: Neither Mathematics, nor Mathematicians, Should be Blamed
for the Hedge Funds' Debacle
Opinion 31: Dave Bayer is Right When He Said That
We Should Sometimes Forget the Sacrosanct Principle of
Opinion 30: The Math Grad Program of U-Wisc, Madison, Should Be
Opinion 29: Beware of Colloquium Wise Guys
and Smarty-Pants Referees and Grant Reviewers
Teaching Proofs to High-School Kids and Non-Math-Majors is Child-Abuse
With Opinions like Steven Krantz's It is Better To Be Unopinionated
Maple Should Be Made Upward-Compatible and Completely Source-Readable
Opinion 25: An Ode to the Los Alamos XXX Archives and
Farewell to AMS's Paper Mentality
[With a PostScript (Written 7/22/99) On How the XXX
can be still made much better.]
Opinion 24: Math Reviews Should Stop Being Humanist and Longist
Opinion 23: Immigrant Complex of a Middle-Aged in the Computer-Age
Opinion 22: Our Students, and Even Us Professors, are like
American Bar/Bat-Mitzvah Kids
The American Paradox: Why it Does Not Matter That The
Average Student is So Bad at Math
Opinion 20: Show up to the Weekly Colloquium, and Try to Behave
Opiniomn 19: SIAM Review Should Not Cancel its Problem Section
Opinion 18: Portrait of a Machino-Phobic as a Home(page)Less Mathematician
Opinion 17: One Should Always Use the Paper Medium for Publishing
Opinion 16: A propos the BIBLE CODE and its alleged Refutations:
Ramsey Theory Has Already Proven that Harmony (may I say
Opinion 15: Giving Tons of Homework and Grading Tough
Should not Conflict with Using Computers in the Classroom
Opinion 14: It Is Time to Kick Zero Out of the Elementary
Opinion 13: Beware of Gloria Olive's Math Reviews
The Genetic Mating of the `Genetic(Parallel) Approach' to Thinking
and the `Cartesian (Sequential) Approach' will Inherit the Earth
Opinion 11: Great scientists, Lousy Philosophers
Opinion 10: Gert Almkvist's One-Line Maple Proof of a Result that George
Andrews believed proved Human-Supremacy
Buy Ten Copies of John Allen Paulos's masterpiece: `A mathematician
reads a newspaper'
Opinion 8: Organized Mathematics=Organized Crime
Opinion 7: Mathematicians as Charlatans
Opinion 6: Applied Creativity is Larger or Equal Than Pure Creativity
Opinion 5: The perils of `Algebraic Combinatorics',
Let's not get too gentrified
Opinion 4: Let's Not be Religious Mathematical Fanatics
Or: Vos Savant's criticism of the proof of FLT is not so
Opinion 3: The Demise of the Paper Referee
Opinion 2: People who think that Applied Math is Bad Math
are bad mathematicians.
Topology, the slum of combinatorics , or: don't show off too much,
your specialty will soon be trivialized.
What about quarter Einsteins?,
(originally written July 25, 1967, translated and posted here July 25, 2009).
Doron Zeilberger's Home Page