Dr. Z's Opinions

"Any clod can have the facts, but having opinions is an art."
-- Charles McCabe

• Opinion 192: For Once Our Beloved POTUS did the right thing. I Fully agree with his new Executive Order to "Make the Mile Great Again" by making it 1618.034 meters long [Written April 1, 2025]

• Opinion 191: There is Something Wrong with the Arxiv Moderation if Such an Interesting Article by Jesús Guillera got rejected because "it does not contain sufficient original or substantive scholarly research" [Written Feb. 9, 2025]

• Opinion 190: Karl Sigmund's "The Waltz of Reason": A beautiful Swan Song to the Mathematics as we know it [Written Dec. 17, 2024]

• Opinion 189: To All You Mainstreamers (e.g. Andrew Granville, Akshay Venkatesh, Michael Harris, Kevin Buzzard, ...) Waxing Eloquent about the Nature of "Proof" and the impact of Computers on Mathematics, all of it will soon be obsolete. Mathematics in Fifty Years will be so different than what it is now, and your admittedly well-written prose will be of only historical (and possibly sociological) interest. [Written June 17, 2024]

• Opinion 188: The American Mathematical Society should not prohibit its members to do TV commercials [Written April 1, 2024]

• Opinion 187: Nick Trefethen's (70-page) Book "An Applied Mathematician's Apology", is an Important Book, not Only for Working mathematicians and working philosophers of Science (as per Rob Corless), but also for Working Sociologists of Mathematics, and Especially for Young People who would really benefit from it. Hence I was very disappointed at SIAM (and the author) for not making it Open-Access [Written June 11, 2023]

• Opinion 186: The Three Mathematical Societies (AMS, MAA, SIAM) Went too far in their attempt to be PC [Written April 1, 2023]

• Opinion 185: David Jackson and Bruce Richmond Should Retract Their Erroneous Attempted Proof of the Four-Color-Theorem [Written Dec. 30, 2022]

• Opinion 184: Using Logic-Based Software like COQ and Lean in Mathematical Research is a Step in the Wrong Direction, but It is even Worse to Use it as a Teaching Tool [Written July 18, 2022]

• Opinion 183: Some Advice to the arXiv Math Advisory Committee: There should be yet-another-category, that of "Rejected Submissions" that would post Rejected Submissions (with the authors' permission, of course) along with their Rebuttals [Written May 15, 2022]

  See also appendix:Why ArXiv Moderators (including Victor Reiner) Seriously Erred in Rejecting a One Page Gem Entitled "Five More Proofs of the Cosine Addition Formula (Inspired by Mark Levi's Perpetuum Mobile Proof)"

• Opinion 182: Human-Supremacist and Pure-Math-Elitist Jeremy Avigad got it Backwards! The Same-Old (mostly boring!), currently mainstream, human-generated, and human-centrist "conceptual" pure math is DETRIMENTAL to Mathematics (broadly understood), and Experimental Mathematics is the Way To Go! [Written: Feb. 16, 2022]

• Opinion 181: Computational Complexity is Indeed Part of Current Mainstream Mathematics and is Equally Conceptually Flawed [Written: June 10, 2021]

• Opinion 180: The Ramanujan Machine is a Harbinger of Mathematics becoming a Science again (and Fun again!) [Written Feb. 16, 2021]

• Opinion 179: Some suggestions for TRULY OPEN Electronic Journals: Let's Have Full Disclosure and Full Accountability [Written Feb. 10, 2021]

• Opinion 178: Think Twice Before You Submit Your Paper to Pretentious Journals, like the "Open-Access" (but Close-Minded) Electronic Journal "ALGEBRAIC COMBINATORICS" Since the Expected Gain is Negative [Written July 30, 2020]

  Added Aug. 11, 2018: read the appendix Why co-EIC Akihiro MUNEMASA and Steering Committee Head Sara BILLEY of the Electronic Journal ALCO (Algebraic Combinatorics) Seriously Erred in Rejecting (w/o Refereeing) the Kauers-Zeilberger submission about Counting Young Tableaux".

• Opinion 177: Aviezri Fraenkel (b. June 7, 1929) is Yet Another Example of the "Exception that proves the `Rule'" [due to G. H. Hardy and, independently, to Abraham A. Fraenkel (1891-1965)] that Mathematics is a Young Person's Game [Written June 7, 2020]

• Opinion 176: The SIAM and AMS councils did the right thing when they decided that due to COVID-19, all submitted papers to their "prestigious" journals would be automatically accepted, without any "peer review" (Written: April 1, 2020.)

• Opinion 175: The Current Editors and Referees of the American Mathematical Monthly Should Realize that Sometimes More is Less (and Less is More) (Written: Jan. 29, 2020)

• Opinion 174: The "Greek" (Euclidean, Axiomatic, Deductive. ...) approach to mathematics did much more damage than just ruin mathematics, as is clear from Amir Alexander's fascinating new Book "Proof!". It is high time that we move over to the much more democratic and egalitarian (and far less boring!) "Babylonian" (Algorithmic, Inductive, Experimental,...) approach to mathematics (Written: Oct. 20, 2019)

• Opinion 173: Theoretical Physics Is Turning Into Metaphysics, and it is JUST AS WELL (Written: Aug.20, 2019)

• Opinion 172: Correlation is not Causation, Hence the Conclusive Report that Proves that Smokers are better Mathematicians (on average) than non-smokers, should not be suppressed (Written: April 1, 2019)

• Opinion 171: Be skeptical of "skeptics" like Jeffrey Shallit who do not apply their skepticism to themselves, and worse, are dismissive of people who they disagree with (Written: March 21, 2019)

• Opinion 170: If the American Mathematical Monthly wants to publish proofs of routinley-provable identities, they should at least mention that they are routinely provable (Written: March 21, 2019)

• Opinion 169: Guru Sir Timothy Gowers Has Abdicated His Moral Responsibility (Written: Oct. 7, 2018)

• Opinion 168: The Downside of Fields Medals (Written: Aug. 12, 2018)

• Opinion 167: The New Criteria for Promotion and Tenure, Based on the h-Index, Recently Adopted by the Consortium of Mathematics Departments, should be Applauded, but one should severely prosecute "h-index enhancement reciprocity agreements" (Written: April 1(!), 2018)

• Opinion 166: The Work of Aaron Robertson, William Cipolli, and Maria Dascalu introducing the "Delaporte Paradigm" is a Paradigm Shift in Ramsey Theory
  Or: Being Dismissive of Experimental Mathematics (and/or Small Universities) is Just as Bad as Being Dismissive of Women (Written: Jan. 22, 2018)

• Opinion 165: The MASTERPIECE "Ten Great Ideas about Chance" by Persi Diaconis and Brian Skyrms is Fascinating for (at least) two reasons: It tells you a lot about Probability (and Statistics) But It also tells you a lot about Humans and their "Infinitary Religion" (Written: Dec. 31, 2017)

• Opinion 164: The American Mathematical Society's Fellows Program Does More Harm than Good (But it DOES increase the AMS Dues Revenues!) (Written: Dec. 31, 2017)

• Opinion 163: Prime Numbers are Often Red Herrings (Written: Dec. 31, 2017)

• Opinion 162: Advice to a Middle-Aged Mathematician (Written: Sept. 24, 2017)

• Opinion 161: A quick rebuttal to Clifford Truesdell's 1982 Machino-Phobic Tirade: "The Computer: Ruin of Science and Threat to Mankind" (Written: Sept. 9, 2017)

• Opinion 160: Constructive (Infinitarian) Mathematics is a Step in the Right Direction, but It is Much Better to Dump Infinity Altogether (Written: July 2, 2017)

• Opinion 159: What is Mathematics and What Should it Be? (Written: April 22, 2017)

• Opinion 158: The American Mathematical Society Should not Force People to Stop using the Historical Names of Mathematical Theorems, Conjectures, Theories, Etc. and Replace Them by their AMS-ID-numbers: Galois Theory Should NOT become Theory001040 and the Riemann Hypothesis Should NOT become Conj011400 (Written: April 1, 2017)

• Opinion 157: Ninety is the New Forty for Quite a Few Mathematicians (Written: Feb. 7, 2017)

• Opinion 156: 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)

• Opinion 145: 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)

• Opinion 144: "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))

• Opinion 141: Biological Evolution Did not prepare us for reasoning logically and for rigorous proofs
  and Analogously 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)

• Opinion 135: 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)

• Opinion 133: 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)

• Opinion 128: 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)

• Opinion 124: 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)

• Opinion 123: 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)

• Opinion 122: 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)

• Opinion 121: 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)

• Opinion 114: 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)

• Opinion 109: [removed by the request of Gil Kalai, who believed that it was unjust] (Written: April 1, 2010)

• Opinion 108: ...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.)

• Opinion 88: 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 using Amphetamines (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).

• Opinion 86: 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).

• Opinion 71: 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 Platinum] (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).

• Opinion 59: 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).

• Opinion 58: `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).

• Opinion 55: Apostolos Doxiadis's Narrative Approach to Mathematics Education Should Be Embraced (Written May 27, 2003).

• Opinion 54: Amir Alexander's Narrative Approach to the History of Mathematics Makes Lots of Sense (Written May 23, 2003).

• Opinion 53: Frank Quinn's Rigor is Not as Rigorous as He Thinks (Written May 22, 2003).

• Opinion 52: 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 Mathematicians) (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 Mathematics Ph.D.

• 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 their Mistakes

• 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 Minimality

• Opinion 30: The Math Grad Program of U-Wisc, Madison, Should Be Emulated.

• Opinion 29: Beware of Colloquium Wise Guys and Smarty-Pants Referees and Grant Reviewers

• Opinion 28: Teaching Proofs to High-School Kids and Non-Math-Majors is Child-Abuse

• Opinion 27: With Opinions like Steven Krantz's It is Better To Be Unopinionated

• Opinion 26: 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

• Opinion 21: 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 God) Exists.

• 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 School Curriculum

• Opinion 13: Beware of Gloria Olive's Math Reviews

• Opinion 12: 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

• Opinion 9: 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 dumb

• Opinion 3: The Demise of the Paper Referee .

• Opinion 2: People who think that Applied Math is Bad Math are bad mathematicians.

• Opinion 1: Topology, the slum of combinatorics , or: don't show off too much, your specialty will soon be trivialized.

• Opinion 0: What about quarter Einsteins?, (originally written July 25, 1967, translated and posted here July 25, 2009).

Added Sept. 3, 2022: Many thanks are due to Eve Stone for "cleaning up" the numerous dead links from Opinions 91-184. She is currently working on cleaning up Opinions 1-90.