{"id":246,"date":"2025-04-20T12:34:59","date_gmt":"2025-04-20T18:34:59","guid":{"rendered":"https:\/\/jewlee.com\/?p=246"},"modified":"2025-04-23T15:38:58","modified_gmt":"2025-04-23T21:38:58","slug":"the-12-most-controversial-facts-in-mathematics","status":"publish","type":"post","link":"https:\/\/jewlee.com\/?p=246","title":{"rendered":"The 12 Most Controversial Facts In Mathematics"},"content":{"rendered":"\n<p class=\"wp-block-paragraph\">Here\u2019s something I came across the other day and found super interesting, even though it broke my brain. While &#8220;controversial&#8221; in mathematics usually refers to unsolved problems or conjectures, here are 12 notable and often-debated mathematical concepts: (all links will open in a new window)<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">While some of these problems are unsolved, others are well-established results with ongoing discussions about their implications or<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>1.&nbsp;<\/strong><strong>The&nbsp;<a href=\"https:\/\/www.google.com\/search?rlz=1C9BKJA_enUS1049US1054&amp;hl=en-US&amp;cs=1&amp;sca_esv=dcef92e01162e678&amp;sxsrf=AHTn8zplz3fqh__t0GzjHQVYV69kP4TOQA%3A1745172807396&amp;q=Riemann+Hypothesis&amp;sa=X&amp;ved=2ahUKEwjGn6Cpm-eMAxWWl-4BHdkuJgcQxccNegQIBRAB&amp;mstk=AUtExfBn4EIw4EPIi99cQf251tSWdTKIz3mE55hqWVNrWL3wNGxqD0CgGY4hgcsHQjg6hBNCJacsc4Bmbv4TuPy0qf5DEmnWa8pwwbE3Zvp6HXuZlGEM6j4PMVPETgZk1oplxYIHCqHMmhWhyq8n7SeKPu4QeHjm9pmsI77eEGO0NUhTmoI&amp;csui=3\">Riemann Hypothesis<\/a>:<\/strong>This famous conjecture proposes a specific relationship between the distribution of prime numbers and the behavior of a complex function.&nbsp;It remains unsolved despite extensive research.&nbsp;<\/li>\n\n\n\n<li><strong>2.&nbsp;<\/strong><strong>The&nbsp;<a href=\"https:\/\/www.google.com\/search?rlz=1C9BKJA_enUS1049US1054&amp;hl=en-US&amp;cs=1&amp;sca_esv=dcef92e01162e678&amp;sxsrf=AHTn8zplz3fqh__t0GzjHQVYV69kP4TOQA%3A1745172807396&amp;q=Goldbach+Conjecture&amp;sa=X&amp;ved=2ahUKEwjGn6Cpm-eMAxWWl-4BHdkuJgcQxccNegQILRAB&amp;mstk=AUtExfBn4EIw4EPIi99cQf251tSWdTKIz3mE55hqWVNrWL3wNGxqD0CgGY4hgcsHQjg6hBNCJacsc4Bmbv4TuPy0qf5DEmnWa8pwwbE3Zvp6HXuZlGEM6j4PMVPETgZk1oplxYIHCqHMmhWhyq8n7SeKPu4QeHjm9pmsI77eEGO0NUhTmoI&amp;csui=3\">Goldbach Conjecture<\/a>:<\/strong>This states that every even integer greater than 2 can be expressed as the sum of two prime numbers.&nbsp;It&#8217;s been verified for large numbers, but a general proof remains elusive.&nbsp;<\/li>\n\n\n\n<li><strong>3.&nbsp;<\/strong><strong>The&nbsp;<a href=\"https:\/\/www.google.com\/search?rlz=1C9BKJA_enUS1049US1054&amp;hl=en-US&amp;cs=1&amp;sca_esv=dcef92e01162e678&amp;sxsrf=AHTn8zplz3fqh__t0GzjHQVYV69kP4TOQA%3A1745172807396&amp;q=P+vs+NP+Problem&amp;sa=X&amp;ved=2ahUKEwjGn6Cpm-eMAxWWl-4BHdkuJgcQxccNegQICBAB&amp;mstk=AUtExfBn4EIw4EPIi99cQf251tSWdTKIz3mE55hqWVNrWL3wNGxqD0CgGY4hgcsHQjg6hBNCJacsc4Bmbv4TuPy0qf5DEmnWa8pwwbE3Zvp6HXuZlGEM6j4PMVPETgZk1oplxYIHCqHMmhWhyq8n7SeKPu4QeHjm9pmsI77eEGO0NUhTmoI&amp;csui=3\">P vs NP Problem<\/a>:<\/strong>This problem asks whether every problem whose solution can be quickly verified can also be solved quickly.&nbsp;A positive answer would have significant implications for computer science and cryptography.&nbsp;<\/li>\n\n\n\n<li><strong>4.&nbsp;<\/strong><strong>The&nbsp;<a href=\"https:\/\/www.google.com\/search?rlz=1C9BKJA_enUS1049US1054&amp;hl=en-US&amp;cs=1&amp;sca_esv=dcef92e01162e678&amp;sxsrf=AHTn8zplz3fqh__t0GzjHQVYV69kP4TOQA%3A1745172807396&amp;q=Four+Color+Theorem&amp;sa=X&amp;ved=2ahUKEwjGn6Cpm-eMAxWWl-4BHdkuJgcQxccNegQICRAB&amp;mstk=AUtExfBn4EIw4EPIi99cQf251tSWdTKIz3mE55hqWVNrWL3wNGxqD0CgGY4hgcsHQjg6hBNCJacsc4Bmbv4TuPy0qf5DEmnWa8pwwbE3Zvp6HXuZlGEM6j4PMVPETgZk1oplxYIHCqHMmhWhyq8n7SeKPu4QeHjm9pmsI77eEGO0NUhTmoI&amp;csui=3\">Four Color Theorem<\/a>:<\/strong>This theorem states that any map can be colored with only four colors so that no two adjacent regions have the same color.&nbsp;It was famously proven with the aid of computer analysis.&nbsp;<\/li>\n\n\n\n<li><strong>5.&nbsp;<\/strong><strong><a href=\"https:\/\/www.google.com\/search?rlz=1C9BKJA_enUS1049US1054&amp;hl=en-US&amp;cs=1&amp;sca_esv=dcef92e01162e678&amp;sxsrf=AHTn8zplz3fqh__t0GzjHQVYV69kP4TOQA%3A1745172807396&amp;q=Fermat%27s+Last+Theorem&amp;sa=X&amp;ved=2ahUKEwjGn6Cpm-eMAxWWl-4BHdkuJgcQxccNegQILBAB&amp;mstk=AUtExfBn4EIw4EPIi99cQf251tSWdTKIz3mE55hqWVNrWL3wNGxqD0CgGY4hgcsHQjg6hBNCJacsc4Bmbv4TuPy0qf5DEmnWa8pwwbE3Zvp6HXuZlGEM6j4PMVPETgZk1oplxYIHCqHMmhWhyq8n7SeKPu4QeHjm9pmsI77eEGO0NUhTmoI&amp;csui=3\">Fermat&#8217;s Last Theorem<\/a>:<\/strong>This theorem states that no three positive integers a, b, and c can satisfy the equation a^n + b^n = c^n for any integer value of n greater than 2. It was proven centuries after its formulation by&nbsp;<a href=\"https:\/\/www.google.com\/search?rlz=1C9BKJA_enUS1049US1054&amp;hl=en-US&amp;cs=1&amp;sca_esv=dcef92e01162e678&amp;sxsrf=AHTn8zplz3fqh__t0GzjHQVYV69kP4TOQA%3A1745172807396&amp;q=Andrew+Wiles&amp;sa=X&amp;ved=2ahUKEwjGn6Cpm-eMAxWWl-4BHdkuJgcQxccNegQIMhAB&amp;mstk=AUtExfBn4EIw4EPIi99cQf251tSWdTKIz3mE55hqWVNrWL3wNGxqD0CgGY4hgcsHQjg6hBNCJacsc4Bmbv4TuPy0qf5DEmnWa8pwwbE3Zvp6HXuZlGEM6j4PMVPETgZk1oplxYIHCqHMmhWhyq8n7SeKPu4QeHjm9pmsI77eEGO0NUhTmoI&amp;csui=3\">Andrew Wiles<\/a>.&nbsp;<\/li>\n\n\n\n<li><strong>6.&nbsp;<\/strong><strong>The&nbsp;<a href=\"https:\/\/www.google.com\/search?rlz=1C9BKJA_enUS1049US1054&amp;hl=en-US&amp;cs=1&amp;sca_esv=dcef92e01162e678&amp;sxsrf=AHTn8zplz3fqh__t0GzjHQVYV69kP4TOQA%3A1745172807396&amp;q=Monty+Hall+Problem&amp;sa=X&amp;ved=2ahUKEwjGn6Cpm-eMAxWWl-4BHdkuJgcQxccNegQILhAB&amp;mstk=AUtExfBn4EIw4EPIi99cQf251tSWdTKIz3mE55hqWVNrWL3wNGxqD0CgGY4hgcsHQjg6hBNCJacsc4Bmbv4TuPy0qf5DEmnWa8pwwbE3Zvp6HXuZlGEM6j4PMVPETgZk1oplxYIHCqHMmhWhyq8n7SeKPu4QeHjm9pmsI77eEGO0NUhTmoI&amp;csui=3\">Monty Hall Problem<\/a>:<\/strong>This probability puzzle involves a contestant choosing a door with a prize behind it, and the host then revealing a door with no prize.&nbsp;Should the contestant switch their choice, or stay with their initial selection?&nbsp;The counterintuitive answer is that switching increases the odds of winning.&nbsp;<\/li>\n\n\n\n<li><strong>7.&nbsp;<\/strong><strong>The&nbsp;<a href=\"https:\/\/www.google.com\/search?rlz=1C9BKJA_enUS1049US1054&amp;hl=en-US&amp;cs=1&amp;sca_esv=dcef92e01162e678&amp;sxsrf=AHTn8zplz3fqh__t0GzjHQVYV69kP4TOQA%3A1745172807396&amp;q=Twin+Prime+Conjecture&amp;sa=X&amp;ved=2ahUKEwjGn6Cpm-eMAxWWl-4BHdkuJgcQxccNegQIChAB&amp;mstk=AUtExfBn4EIw4EPIi99cQf251tSWdTKIz3mE55hqWVNrWL3wNGxqD0CgGY4hgcsHQjg6hBNCJacsc4Bmbv4TuPy0qf5DEmnWa8pwwbE3Zvp6HXuZlGEM6j4PMVPETgZk1oplxYIHCqHMmhWhyq8n7SeKPu4QeHjm9pmsI77eEGO0NUhTmoI&amp;csui=3\">Twin Prime Conjecture<\/a>:<\/strong>This conjecture suggests that there are infinitely many pairs of prime numbers that differ by 2. While there&#8217;s no proof, extensive research suggests it&#8217;s true.&nbsp;<\/li>\n\n\n\n<li><strong>8.&nbsp;<\/strong><strong>The&nbsp;<a href=\"https:\/\/www.google.com\/search?rlz=1C9BKJA_enUS1049US1054&amp;hl=en-US&amp;cs=1&amp;sca_esv=dcef92e01162e678&amp;sxsrf=AHTn8zplz3fqh__t0GzjHQVYV69kP4TOQA%3A1745172807396&amp;q=Poincar%C3%A9+Conjecture&amp;sa=X&amp;ved=2ahUKEwjGn6Cpm-eMAxWWl-4BHdkuJgcQxccNegQICxAB&amp;mstk=AUtExfBn4EIw4EPIi99cQf251tSWdTKIz3mE55hqWVNrWL3wNGxqD0CgGY4hgcsHQjg6hBNCJacsc4Bmbv4TuPy0qf5DEmnWa8pwwbE3Zvp6HXuZlGEM6j4PMVPETgZk1oplxYIHCqHMmhWhyq8n7SeKPu4QeHjm9pmsI77eEGO0NUhTmoI&amp;csui=3\">Poincar\u00e9 Conjecture<\/a>:<\/strong>This conjecture, proven by&nbsp;<a href=\"https:\/\/www.google.com\/search?rlz=1C9BKJA_enUS1049US1054&amp;hl=en-US&amp;cs=1&amp;sca_esv=dcef92e01162e678&amp;sxsrf=AHTn8zplz3fqh__t0GzjHQVYV69kP4TOQA%3A1745172807396&amp;q=Grigoriy+Perelman&amp;sa=X&amp;ved=2ahUKEwjGn6Cpm-eMAxWWl-4BHdkuJgcQxccNegQIJxAB&amp;mstk=AUtExfBn4EIw4EPIi99cQf251tSWdTKIz3mE55hqWVNrWL3wNGxqD0CgGY4hgcsHQjg6hBNCJacsc4Bmbv4TuPy0qf5DEmnWa8pwwbE3Zvp6HXuZlGEM6j4PMVPETgZk1oplxYIHCqHMmhWhyq8n7SeKPu4QeHjm9pmsI77eEGO0NUhTmoI&amp;csui=3\">Grigoriy Perelman<\/a>,&nbsp;states that any simply-connected, closed 3-manifold is homeomorphic to the 3-sphere.&nbsp;It was one of the Millennium Prize Problems.&nbsp;<\/li>\n\n\n\n<li><strong>9.&nbsp;<\/strong><strong>The&nbsp;<a href=\"https:\/\/www.google.com\/search?rlz=1C9BKJA_enUS1049US1054&amp;hl=en-US&amp;cs=1&amp;sca_esv=dcef92e01162e678&amp;sxsrf=AHTn8zplz3fqh__t0GzjHQVYV69kP4TOQA%3A1745172807396&amp;q=Collatz+Conjecture&amp;sa=X&amp;ved=2ahUKEwjGn6Cpm-eMAxWWl-4BHdkuJgcQxccNegQIDBAB&amp;mstk=AUtExfBn4EIw4EPIi99cQf251tSWdTKIz3mE55hqWVNrWL3wNGxqD0CgGY4hgcsHQjg6hBNCJacsc4Bmbv4TuPy0qf5DEmnWa8pwwbE3Zvp6HXuZlGEM6j4PMVPETgZk1oplxYIHCqHMmhWhyq8n7SeKPu4QeHjm9pmsI77eEGO0NUhTmoI&amp;csui=3\">Collatz Conjecture<\/a>:<\/strong>This conjecture, also known as the &#8220;100 problem&#8221;, posits that starting with any positive integer and repeatedly applying the rule (n is even, n = n\/2; n is odd, n = 3n+1), you will eventually reach the number 1.&nbsp;<\/li>\n\n\n\n<li><strong>10.&nbsp;<\/strong><strong><a href=\"https:\/\/www.google.com\/search?rlz=1C9BKJA_enUS1049US1054&amp;hl=en-US&amp;cs=1&amp;sca_esv=dcef92e01162e678&amp;sxsrf=AHTn8zplz3fqh__t0GzjHQVYV69kP4TOQA%3A1745172807396&amp;q=The+Birch+and+Swinnerton-Dyer+Conjecture&amp;sa=X&amp;ved=2ahUKEwjGn6Cpm-eMAxWWl-4BHdkuJgcQxccNegQIBxAB&amp;mstk=AUtExfBn4EIw4EPIi99cQf251tSWdTKIz3mE55hqWVNrWL3wNGxqD0CgGY4hgcsHQjg6hBNCJacsc4Bmbv4TuPy0qf5DEmnWa8pwwbE3Zvp6HXuZlGEM6j4PMVPETgZk1oplxYIHCqHMmhWhyq8n7SeKPu4QeHjm9pmsI77eEGO0NUhTmoI&amp;csui=3\">The Birch and Swinnerton-Dyer Conjecture<\/a>:<\/strong>This conjecture is a deep result in number theory concerning the number of rational points on algebraic curves.&nbsp;It remains unsolved.&nbsp;<\/li>\n\n\n\n<li><strong>11.&nbsp;<\/strong><strong>The&nbsp;<a href=\"https:\/\/www.google.com\/search?rlz=1C9BKJA_enUS1049US1054&amp;hl=en-US&amp;cs=1&amp;sca_esv=dcef92e01162e678&amp;sxsrf=AHTn8zplz3fqh__t0GzjHQVYV69kP4TOQA%3A1745172807396&amp;q=Hodge+Conjecture&amp;sa=X&amp;ved=2ahUKEwjGn6Cpm-eMAxWWl-4BHdkuJgcQxccNegQIBhAB&amp;mstk=AUtExfBn4EIw4EPIi99cQf251tSWdTKIz3mE55hqWVNrWL3wNGxqD0CgGY4hgcsHQjg6hBNCJacsc4Bmbv4TuPy0qf5DEmnWa8pwwbE3Zvp6HXuZlGEM6j4PMVPETgZk1oplxYIHCqHMmhWhyq8n7SeKPu4QeHjm9pmsI77eEGO0NUhTmoI&amp;csui=3\">Hodge Conjecture<\/a>:<\/strong>This conjecture relates the algebraic structure of a complex projective variety to its topological structure.&nbsp;It&#8217;s a major unsolved problem in algebraic geometry.&nbsp;<\/li>\n\n\n\n<li><strong>12.&nbsp;<\/strong><strong>The&nbsp;<a href=\"https:\/\/www.google.com\/search?rlz=1C9BKJA_enUS1049US1054&amp;hl=en-US&amp;cs=1&amp;sca_esv=dcef92e01162e678&amp;sxsrf=AHTn8zplz3fqh__t0GzjHQVYV69kP4TOQA%3A1745172807396&amp;q=Navier-Stokes+Equations&amp;sa=X&amp;ved=2ahUKEwjGn6Cpm-eMAxWWl-4BHdkuJgcQxccNegQIBBAB&amp;mstk=AUtExfBn4EIw4EPIi99cQf251tSWdTKIz3mE55hqWVNrWL3wNGxqD0CgGY4hgcsHQjg6hBNCJacsc4Bmbv4TuPy0qf5DEmnWa8pwwbE3Zvp6HXuZlGEM6j4PMVPETgZk1oplxYIHCqHMmhWhyq8n7SeKPu4QeHjm9pmsI77eEGO0NUhTmoI&amp;csui=3\">Navier-Stokes Equations<\/a>&nbsp;and&nbsp;<a href=\"https:\/\/www.google.com\/search?rlz=1C9BKJA_enUS1049US1054&amp;hl=en-US&amp;cs=1&amp;sca_esv=dcef92e01162e678&amp;sxsrf=AHTn8zplz3fqh__t0GzjHQVYV69kP4TOQA%3A1745172807396&amp;q=Yang-Mills+Existence+and+Mass+Gap&amp;sa=X&amp;ved=2ahUKEwjGn6Cpm-eMAxWWl-4BHdkuJgcQxccNegQIBBAC&amp;mstk=AUtExfBn4EIw4EPIi99cQf251tSWdTKIz3mE55hqWVNrWL3wNGxqD0CgGY4hgcsHQjg6hBNCJacsc4Bmbv4TuPy0qf5DEmnWa8pwwbE3Zvp6HXuZlGEM6j4PMVPETgZk1oplxYIHCqHMmhWhyq8n7SeKPu4QeHjm9pmsI77eEGO0NUhTmoI&amp;csui=3\">Yang-Mills Existence and Mass Gap<\/a>:<\/strong>These two problems are fundamental in mathematical physics and fluid dynamics.&nbsp;They concern the existence and properties of solutions to certain differential equations.&nbsp;<\/li>\n<\/ul>\n","protected":false},"excerpt":{"rendered":"<p>Here\u2019s something I came across the other day and found super interesting, even though it broke my brain. While &#8220;controversial&#8221; in mathematics usually refers to unsolved problems or conjectures, here are 12 notable and often-debated mathematical concepts: (all links will open in a new window) While some of these problems are unsolved, others are well-established [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1,13],"tags":[],"class_list":["post-246","post","type-post","status-publish","format-standard","hentry","category-general","category-isnt-that-interesting"],"_links":{"self":[{"href":"https:\/\/jewlee.com\/index.php?rest_route=\/wp\/v2\/posts\/246","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/jewlee.com\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/jewlee.com\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/jewlee.com\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/jewlee.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=246"}],"version-history":[{"count":4,"href":"https:\/\/jewlee.com\/index.php?rest_route=\/wp\/v2\/posts\/246\/revisions"}],"predecessor-version":[{"id":325,"href":"https:\/\/jewlee.com\/index.php?rest_route=\/wp\/v2\/posts\/246\/revisions\/325"}],"wp:attachment":[{"href":"https:\/\/jewlee.com\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=246"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/jewlee.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=246"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/jewlee.com\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=246"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}