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Achim D. Brucker<p>Still waiting for the call for paper for Tests and Proofs (TAP) conference? Wait no longer: we are thrilled to announce that TAP is now a track at FM 2026: <a href="https://conf.researchr.org/track/fm-2026/fm-2026-tap#Call-for-Papers" rel="nofollow noopener" translate="no" target="_blank"><span class="invisible">https://</span><span class="ellipsis">conf.researchr.org/track/fm-20</span><span class="invisible">26/fm-2026-tap#Call-for-Papers</span></a></p><p><a href="https://fediscience.org/tags/FormalMethods" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>FormalMethods</span></a> <a href="https://fediscience.org/tags/SoftwareTesting" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>SoftwareTesting</span></a> <a href="https://fediscience.org/tags/Verification" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>Verification</span></a> <a href="https://fediscience.org/tags/Proof" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>Proof</span></a> <a href="https://fediscience.org/tags/SymbolicExecution" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>SymbolicExecution</span></a> <a href="https://fediscience.org/tags/FM2026" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>FM2026</span></a> <a href="https://fediscience.org/tags/TAP2026" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>TAP2026</span></a></p>
Teacher/Coder Jason<p>Nice. Great job finding that counter example. </p><p><a href="https://english.elpais.com/science-tech/2025-07-01/a-17-year-old-teen-refutes-a-mathematical-conjecture-proposed-40-years-ago.html?outputType=amp" rel="nofollow noopener" translate="no" target="_blank"><span class="invisible">https://</span><span class="ellipsis">english.elpais.com/science-tec</span><span class="invisible">h/2025-07-01/a-17-year-old-teen-refutes-a-mathematical-conjecture-proposed-40-years-ago.html?outputType=amp</span></a></p><p><a href="https://mastodon.social/tags/maths" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>maths</span></a> <a href="https://mastodon.social/tags/conjecture" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>conjecture</span></a> <a href="https://mastodon.social/tags/proof" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>proof</span></a> <a href="https://mastodon.social/tags/counterproof" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>counterproof</span></a> <a href="https://mastodon.social/tags/MizohataTakeuchiConjecture" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>MizohataTakeuchiConjecture</span></a></p>
Nando161<p>To all who think <a href="https://partyon.xyz/tags/capitalism" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>capitalism</span></a> can drive <a href="https://partyon.xyz/tags/progressive" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>progressive</span></a> <a href="https://partyon.xyz/tags/change" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>change</span></a>, it won’t – and here’s the shocking <a href="https://partyon.xyz/tags/proof" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>proof</span></a> | The Guardian<br><a href="https://www.theguardian.com/commentisfree/2025/jul/01/capitalism-drive-progressive-change-aberdeen-inequality" rel="nofollow noopener" translate="no" target="_blank"><span class="invisible">https://www.</span><span class="ellipsis">theguardian.com/commentisfree/</span><span class="invisible">2025/jul/01/capitalism-drive-progressive-change-aberdeen-inequality</span></a></p>
AstroMancer5G (she/her)<p><a href="https://spore.social/tags/ZohranMamdani" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>ZohranMamdani</span></a> is <a href="https://spore.social/tags/proof" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>proof</span></a> that the <a href="https://spore.social/tags/GreenParty" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>GreenParty</span></a> <a href="https://spore.social/tags/USA" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>USA</span></a> is not <a href="https://spore.social/tags/TooFarLeft" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>TooFarLeft</span></a> to <a href="https://spore.social/tags/win" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>win</span></a> <a href="https://spore.social/tags/elections" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>elections</span></a>. If <a href="https://spore.social/tags/Mamdani" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>Mamdani</span></a> were a <a href="https://spore.social/tags/Green" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>Green</span></a>, he'd be <a href="https://spore.social/tags/mainstream" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>mainstream</span></a> in the <a href="https://spore.social/tags/party" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>party</span></a>. And he crushed the mainstream <a href="https://spore.social/tags/Democrat" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>Democrat</span></a>.</p><p>If you voted for Mamdani but not <a href="https://spore.social/tags/JillStein" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>JillStein</span></a>, you weren't <a href="https://spore.social/tags/voting" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>voting</span></a> on <a href="https://spore.social/tags/policy" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>policy</span></a> in 2024. You were just voting for the color <a href="https://spore.social/tags/blue" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>blue</span></a>.</p>
WordofTheHour<p><a href="https://mastodon.social/tags/proof" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>proof</span></a> : that degree of evidence which convinces the mind of any truth or fact, and produces belief</p><p>- French: une preuve</p><p>- German: abdichten, der Nachweis</p><p>- Italian: prova</p><p>- Portuguese: prova</p><p>- Spanish: prueba</p><p>------------</p><p>Fill in missing translations @ <a href="https://wordofthehour.org/r/translations" rel="nofollow noopener" translate="no" target="_blank"><span class="invisible">https://</span><span class="ellipsis">wordofthehour.org/r/translatio</span><span class="invisible">ns</span></a></p>
Thomas<p>I'm once again very grateful to a physicist-turned-philosopher friend who told me that she had heard from a colleague that Lakatos Proofs and Refutations is fun reading. Her colleague was right.</p><p>Get your copy on JSTOR (or in the links below).</p><p><a href="https://mas.to/tags/Lakatos" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>Lakatos</span></a> <a href="https://mas.to/tags/math" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>math</span></a> <a href="https://mas.to/tags/philosphy" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>philosphy</span></a> <a href="https://mas.to/tags/proof" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>proof</span></a><br><a href="https://mas.to/@tg9541/114621114741947728" rel="nofollow noopener" translate="no" target="_blank"><span class="invisible">https://</span><span class="ellipsis">mas.to/@tg9541/114621114741947</span><span class="invisible">728</span></a></p>
:rss: 電撃ホビーウェブ<p>『ダーリン・イン・ザ・フランキス』 ゼロツーのフィギュアをプレゼント!美しくなびく髪や微笑むキュートな表情を細部まで丁寧に表現!!<br><a href="https://hobby.dengeki.com/news/2618661/" rel="nofollow noopener" translate="no" target="_blank"><span class="invisible">https://</span><span class="ellipsis">hobby.dengeki.com/news/2618661</span><span class="invisible">/</span></a></p><p><a href="https://rss-mstdn.studiofreesia.com/tags/hobby_dengeki" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>hobby_dengeki</span></a> <a href="https://rss-mstdn.studiofreesia.com/tags/%E3%83%95%E3%82%A3%E3%82%AE%E3%83%A5%E3%82%A2" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>フィギュア</span></a> <a href="https://rss-mstdn.studiofreesia.com/tags/%E5%91%8A%E7%9F%A5" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>告知</span></a> <a href="https://rss-mstdn.studiofreesia.com/tags/%E8%AA%AD%E8%80%85%E3%83%97%E3%83%AC%E3%82%BC%E3%83%B3%E3%83%88" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>読者プレゼント</span></a> <a href="https://rss-mstdn.studiofreesia.com/tags/%E3%83%97%E3%83%AC%E3%82%BC%E3%83%B3%E3%83%88" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>プレゼント</span></a> <a href="https://rss-mstdn.studiofreesia.com/tags/%E6%87%B8%E8%B3%9E" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>懸賞</span></a> <a href="https://rss-mstdn.studiofreesia.com/tags/%E9%9B%BB%E3%83%9B%E3%83%93" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>電ホビ</span></a> <a href="https://rss-mstdn.studiofreesia.com/tags/Twitter" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>Twitter</span></a> <a href="https://rss-mstdn.studiofreesia.com/tags/%E3%83%84%E3%82%A4%E3%83%83%E3%82%BF%E3%83%BC" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>ツイッター</span></a> <a href="https://rss-mstdn.studiofreesia.com/tags/X" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>X</span></a> <a href="https://rss-mstdn.studiofreesia.com/tags/RT%E3%82%AD%E3%83%A3%E3%83%B3%E3%83%9A%E3%83%BC%E3%83%B3" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>RTキャンペーン</span></a> <a href="https://rss-mstdn.studiofreesia.com/tags/PROOF" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>PROOF</span></a> <a href="https://rss-mstdn.studiofreesia.com/tags/%E3%83%97%E3%83%AB%E3%83%BC%E3%83%95" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>プルーフ</span></a> <a href="https://rss-mstdn.studiofreesia.com/tags/%E3%82%B9%E3%82%B1%E3%83%BC%E3%83%AB%E3%83%95%E3%82%A3%E3%82%AE%E3%83%A5%E3%82%A2" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>スケールフィギュア</span></a> <a href="https://rss-mstdn.studiofreesia.com/tags/%E3%83%80%E3%83%BC%E3%83%AA%E3%83%B3_%E3%82%A4%E3%83%B3_%E3%82%B6_%E3%83%95%E3%83%A9%E3%83%B3%E3%82%AD%E3%82%B9" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>ダーリン_イン_ザ_フランキス</span></a> <a href="https://rss-mstdn.studiofreesia.com/tags/%E3%83%80%E3%83%AA%E3%83%95%E3%83%A9" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>ダリフラ</span></a> <a href="https://rss-mstdn.studiofreesia.com/tags/%E3%82%BC%E3%83%AD%E3%83%84%E3%83%BC" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>ゼロツー</span></a></p>
Steve Dustcircle 🌹<p>5 lessons on finding <a href="https://masto.ai/tags/truth" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>truth</span></a> in an uncertain world</p><p>To get closer to the truth, it is important to understand what constitutes <a href="https://masto.ai/tags/proof" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>proof</span></a> and how to proceed when <a href="https://masto.ai/tags/facts" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>facts</span></a> falter.</p><p><a href="https://www.fastcompany.com/91340887/finding-truth-uncertain-world-lessons" rel="nofollow noopener" translate="no" target="_blank"><span class="invisible">https://www.</span><span class="ellipsis">fastcompany.com/91340887/findi</span><span class="invisible">ng-truth-uncertain-world-lessons</span></a></p>
Hermetic Library<p>WHOSE DEFINITION OF SUCCESS, FUCKER?</p><p>"Success is your proof"—Liber Legis, III, 46 <a href="https://hermetic.com/legis/ccxx/index#iii.46" rel="nofollow noopener" translate="no" target="_blank"><span class="invisible">https://</span><span class="ellipsis">hermetic.com/legis/ccxx/index#</span><span class="invisible">iii.46</span></a></p><p>"All questions of the Law are to be decided only by appeal to my writings, each for himself."—The (Tunis) Comment <a href="https://hermetic.com/legis/tunis/index" rel="nofollow noopener" translate="no" target="_blank"><span class="invisible">https://</span><span class="">hermetic.com/legis/tunis/index</span><span class="invisible"></span></a></p><p><a href="https://mastodon.social/tags/meme" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>meme</span></a> <a href="https://mastodon.social/tags/GooseChasingGuy" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>GooseChasingGuy</span></a> <a href="https://mastodon.social/tags/LiberLegis" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>LiberLegis</span></a> <a href="https://mastodon.social/tags/success" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>success</span></a> <a href="https://mastodon.social/tags/proof" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>proof</span></a></p>
Airplanista 🇺🇦<p>And over on Facebook, the usual idiots are fighting over this obvious AI slop image of a 747 on a giant treadmill.</p><p>"This settles it. A Boeing 747 CAN take off from a treadmill!!! <a href="https://squawk.mytransponder.com/tags/proof" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>proof</span></a>."</p><p>"Clown get a life. Even if you could get the treadmill up to rotation speed of the four-seven, it would crash through the fence at the end of the runway into the neighborhood next to the airport!!!!!!"</p><p>"Everyone knows this is true!!! I saw it on Newsmax+, only $99.95 a month."</p><p><a href="https://squawk.mytransponder.com/tags/avgeeks" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>avgeeks</span></a> <a href="https://squawk.mytransponder.com/tags/aviation" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>aviation</span></a> <a href="https://squawk.mytransponder.com/tags/airplanes" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>airplanes</span></a></p>
Zelestian PhD memes<p><a href="https://mastodon.online/tags/Demonstration" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>Demonstration</span></a> <a href="https://mastodon.online/tags/inspiration" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>inspiration</span></a> <a href="https://mastodon.online/tags/proof" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>proof</span></a> <a href="https://mastodon.online/tags/phdstudent" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>phdstudent</span></a> <a href="https://mastodon.online/tags/doctoratestudent" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>doctoratestudent</span></a> <a href="https://mastodon.online/tags/phd" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>phd</span></a> <a href="https://mastodon.online/tags/doctorate" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>doctorate</span></a> <a href="https://mastodon.online/tags/motivation" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>motivation</span></a> <a href="https://mastodon.online/tags/meme" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>meme</span></a> <a href="https://mastodon.online/tags/memes" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>memes</span></a> <a href="https://mastodon.online/tags/phdmotivation" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>phdmotivation</span></a> <a href="https://mastodon.online/tags/phdmeme" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>phdmeme</span></a> <a href="https://mastodon.online/tags/phdmemes" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>phdmemes</span></a> <a href="https://mastodon.online/tags/phdlife" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>phdlife</span></a> <a href="https://mastodon.online/tags/phdstudentlife" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>phdstudentlife</span></a> <a href="https://mastodon.online/tags/phdtroll" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>phdtroll</span></a> <a href="https://mastodon.online/tags/doctoratemotivation" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>doctoratemotivation</span></a> <a href="https://mastodon.online/tags/doctoratememe" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>doctoratememe</span></a> <a href="https://mastodon.online/tags/doctoratememes" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>doctoratememes</span></a> <a href="https://mastodon.online/tags/doctoratelife" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>doctoratelife</span></a> <a href="https://mastodon.online/tags/doctoratestudentlife" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>doctoratestudentlife</span></a> <a href="https://mastodon.online/tags/doctoratetroll" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>doctoratetroll</span></a></p>
HistoPol (#HP) 🏴 🇺🇸 🏴<p><span class="h-card" translate="no"><a href="https://masto.ai/@meduza_en" class="u-url mention" rel="nofollow noopener" target="_blank">@<span>meduza_en</span></a></span></p><p><a href="https://mastodon.social/tags/WarInUkraine" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>WarInUkraine</span></a> <a href="https://mastodon.social/tags/Ukraine" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>Ukraine</span></a> <a href="https://mastodon.social/tags/Russia" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>Russia</span></a></p><p>Could the <a href="https://mastodon.social/tags/Assasination" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>Assasination</span></a> of <a href="https://mastodon.social/tags/AndriyPortnov" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>AndriyPortnov</span></a>, a former top aide to ex-Ukrainian President <a href="https://mastodon.social/tags/ViktorYanukovych" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>ViktorYanukovych</span></a> be a sign of the <a href="https://mastodon.social/tags/Russian" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>Russian</span></a> <a href="https://mastodon.social/tags/FSB" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>FSB</span></a> tying up loose ends?</p><p>As the curatorial and investigative journalist Prof. <a href="https://mastodon.social/tags/SethAbramson" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>SethAbramson</span></a> showed in his national bestseller on the Russia-Ukraine crisis—<a href="https://mastodon.social/tags/Proof" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>Proof</span></a> of <a href="https://mastodon.social/tags/Corruption" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>Corruption</span></a> (<a href="https://mastodon.social/tags/Macmillan" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>Macmillan</span></a>, 2020)—, there were ample connections between the <a href="https://mastodon.social/tags/Kremlin" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>Kremlin</span></a> and <a href="https://mastodon.social/tags/Kyiv" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>Kyiv</span></a> during that period; to say the least.</p><p><a href="https://masto.ai/@meduza_en/114545482744751145" rel="nofollow noopener" translate="no" target="_blank"><span class="invisible">https://</span><span class="ellipsis">masto.ai/@meduza_en/1145454827</span><span class="invisible">44751145</span></a></p>
Don Hawkins - W7DAHSource = TikTok
Jan :rust: :ferris:<p>The inner magic behind the Z3 theorem prover - Microsoft Research (October 2019):</p><p><a href="https://www.microsoft.com/en-us/research/blog/the-inner-magic-behind-the-z3-theorem-prover/" rel="nofollow noopener" translate="no" target="_blank"><span class="invisible">https://www.</span><span class="ellipsis">microsoft.com/en-us/research/b</span><span class="invisible">log/the-inner-magic-behind-the-z3-theorem-prover/</span></a></p><p><a href="https://floss.social/tags/Z3" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>Z3</span></a> <a href="https://floss.social/tags/SMT" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>SMT</span></a> <a href="https://floss.social/tags/FormalVerification" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>FormalVerification</span></a> <a href="https://floss.social/tags/ModelChecking" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>ModelChecking</span></a> <a href="https://floss.social/tags/Proof" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>Proof</span></a></p>
-0--1-<p><a href="https://mastodon.social/tags/Proof" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>Proof</span></a> <a href="https://mastodon.social/tags/JunkieGrifter" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>JunkieGrifter</span></a></p>
Paul Houle<p>✂️ Dudeney's 120-year-old dissection puzzle solution proves optimal</p><p><a href="https://phys.org/news/2025-03-dudeney-year-puzzle-solution-optimal.html" rel="nofollow noopener" translate="no" target="_blank"><span class="invisible">https://</span><span class="ellipsis">phys.org/news/2025-03-dudeney-</span><span class="invisible">year-puzzle-solution-optimal.html</span></a></p><p><a href="https://mastodon.social/tags/math" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>math</span></a> <a href="https://mastodon.social/tags/geometry" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>geometry</span></a> <a href="https://mastodon.social/tags/puzzles" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>puzzles</span></a> <a href="https://mastodon.social/tags/dissection" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>dissection</span></a> <a href="https://mastodon.social/tags/proof" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>proof</span></a></p>
Markus Redeker<p>Proof by starvation: This is a proof form in which you first prove that a counterexample to the theorem must have property X, then, using X, prove that it must also have property Y, then that it must also have property Z, ... until you have piled up so many requirements on a counterexample that everybody sees that it cannot exist.</p><p>I have done that a few times. It is a nice way to organize one's thoughts.</p><p><a href="https://mathstodon.xyz/tags/Proof" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>Proof</span></a> <a href="https://mathstodon.xyz/tags/Mathematics" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>Mathematics</span></a></p>
Hacker News<p>Anime fans stumbled upon a mathematical proof — <a href="https://www.scientificamerican.com/article/the-surprisingly-difficult-mathematical-proof-that-anime-fans-helped-solve/" rel="nofollow noopener" translate="no" target="_blank"><span class="invisible">https://www.</span><span class="ellipsis">scientificamerican.com/article</span><span class="invisible">/the-surprisingly-difficult-mathematical-proof-that-anime-fans-helped-solve/</span></a><br><a href="https://mastodon.social/tags/HackerNews" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>HackerNews</span></a> <a href="https://mastodon.social/tags/Anime" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>Anime</span></a> <a href="https://mastodon.social/tags/Fans" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>Fans</span></a> <a href="https://mastodon.social/tags/Mathematical" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>Mathematical</span></a> <a href="https://mastodon.social/tags/Proof" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>Proof</span></a> <a href="https://mastodon.social/tags/Anime" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>Anime</span></a> <a href="https://mastodon.social/tags/Community" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>Community</span></a> <a href="https://mastodon.social/tags/Scientific" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>Scientific</span></a> <a href="https://mastodon.social/tags/Discovery" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>Discovery</span></a> <a href="https://mastodon.social/tags/Hacker" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>Hacker</span></a> <a href="https://mastodon.social/tags/News" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>News</span></a></p>
Akshar Varma<p><span class="h-card" translate="no"><a href="https://mathstodon.xyz/@BernhardWerner" class="u-url mention" rel="nofollow noopener" target="_blank">@<span>BernhardWerner</span></a></span> My favorite alternative <a href="https://mathstodon.xyz/tags/proof" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>proof</span></a> strategy for <a href="https://mathstodon.xyz/tags/induction" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>induction</span></a> proofs are <a href="https://mathstodon.xyz/tags/combinatorial" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>combinatorial</span></a> (counting) proofs.</p><p>I suppose the standard example might be the proof of the coefficients in the binomial theorem expansion, or for the sum of binomial coefficients being powers of 2. These can be proved by induction, of course, but I'm not sure that's common given how easier it is to do a counting proof. It is also much clearer and avoids tedious algebra.</p><p>One I like is proving that the sum 1 + 2 + 3 + ⋯ + 𝑛 is 𝑛 + 1 choose 2, the binomial coefficient \(\binom{n+1}{2}\). Bijection proof, counts the same thing in two ways. The thing being counted is the number of ways of choosing two things (distinct, without repetition) from the set {0, 1, ..., 𝑛}. By definition, it is the binomial coefficient we want. The other way to count is to fix the larger number 𝑘, the remaining choices are any of the 𝑘 numbers from 0 to 𝑘 - 1. Thus, across all possible larger numbers, we get the sum from 1 to n.</p><p>An alternative alternate proof of the same, slightly more geometric is as follows: arrange dots in a triangle, 1 on row 1, 2 on row 2, and so on up to row n, with n dots. Add a phantom row of n+1 dots below. We want to add up all dots in first n rows: ∑ 𝑖. If you think of all of this as a binary tree/DAG, then every dot has two children (imagine Pascal's triangle). If you pick any two dots in the phantom row, their common ancestor is unique. So counting dots is same as picking two dots in phantom row. Which is the binomial coefficient we want.</p><p>Benjamin and Quinn's book on combinatorial proofs is amazing for interpretations of this form (I learned the first proof from it). See also: <a href="https://en.wikipedia.org/wiki/Combinatorial_proof" rel="nofollow noopener" translate="no" target="_blank"><span class="invisible">https://</span><span class="ellipsis">en.wikipedia.org/wiki/Combinat</span><span class="invisible">orial_proof</span></a></p>
WordofTheHour<p><a href="https://mastodon.social/tags/proof" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>proof</span></a> : that degree of evidence which convinces the mind of any truth or fact, and produces belief</p><p>- French: une preuve</p><p>- German: abdichten, der Nachweis</p><p>- Italian: prova</p><p>- Portuguese: prova</p><p>- Spanish: prueba</p><p>------------</p><p>Fill in missing translations @ <a href="https://wordofthehour.org/r/translations" rel="nofollow noopener" translate="no" target="_blank"><span class="invisible">https://</span><span class="ellipsis">wordofthehour.org/r/translatio</span><span class="invisible">ns</span></a></p>