{"id":4102,"date":"2025-12-12T08:00:12","date_gmt":"2025-12-12T13:00:12","guid":{"rendered":"https:\/\/mathvoices.ams.org\/mathmedia\/?p=4102"},"modified":"2025-12-12T12:51:27","modified_gmt":"2025-12-12T17:51:27","slug":"math-digests-november-2025","status":"publish","type":"post","link":"https:\/\/mathvoices.ams.org\/mathmedia\/math-digests-november-2025\/","title":{"rendered":"Math Digests November 2025"},"content":{"rendered":"<h2 style=\"text-align: left\">November digests:<\/h2>\n<ul>\n<li style=\"list-style-type: none\">\n<ul>\n<li><a href=\"#1\">Gerrymandering, &#8220;the problem of democracy,&#8221; in <i>The New York Times<\/i><\/a><\/li>\n<li><a href=\"#2\">The &#8220;unimaginably smooth&#8221; world, from <i>The Rest is Science<\/i><\/a><\/li>\n<li><a href=\"#3\">When turn-taking isn&#8217;t fair enough, in <i>New Scientist<\/i><\/a><\/li>\n<li><a href=\"#4\">How to find prime numbers, in <i>Scientific American<\/i><\/a><\/li>\n<li><a href=\"#5\">The math of tariffs, in the <i>Associated Press<\/i><\/a><\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<hr \/>\n<h3><a id=\"1\" href=\"https:\/\/www.nytimes.com\/2025\/11\/03\/science\/duchin-math-elections-gerrymandering.html\">Moon Duchin on the Math of Gerrymandering<\/a><\/h3>\n<p><em>The New York Times<\/em>, November 3, 2025<\/p>\n<p>American democracy depends on the geometry of local maps. The boundaries of congressional districts are redrawn every decade, often by politicians whose reelection hinges on running in a favorable district. This encourages politicians to draw maps that benefit their political party, a practice called <strong>gerrymandering<\/strong>. In 2023, the Supreme Court found that Republicans illegally gerrymandered in North Carolina, eroding the voting power of Black communities. In this <em>New York Times<\/em> article, mathematician Moon Duchin speaks about how math can demonstrate more fair redistricting and alternative voting systems. \u201cThe whole world should be paying particular attention to this class of problem, which I\u2019ll call the problem of democracy,\u201d Duchin said.<\/p>\n<p><strong>Classroom Activities:<\/strong><em> graph theory, algebra<\/em><\/p>\n<ul>\n<li>(Mid-level) In the article, Duchin explains an approach to redistricting with an analogy about shuffling cards. Explain in your own words why Duchin prefers the spanning-tree method to randomization.<\/li>\n<li>(High level) Read <a href=\"https:\/\/mathvoices.ams.org\/mathmedia\/tonys-take-august-2025\/\">this AMS article <\/a>for more information about the mathematics of gerrymandering. The math depends on calculating the distances between points in a space, which represents how far voters in the same district live from one another. We can measure this by summing the distance between each pair of points (or voters). Below are voter locations for two congressional districts, one in state A and the other in state B.\n<figure id=\"attachment_4105\" aria-describedby=\"caption-attachment-4105\" style=\"width: 618px\" class=\"wp-caption aligncenter\"><img data-recalc-dims=\"1\" loading=\"lazy\" decoding=\"async\" class=\"wp-image-4105 size-full\" src=\"https:\/\/i0.wp.com\/mathvoices.ams.org\/mathmedia\/wp-content\/uploads\/sites\/3\/2025\/12\/District-Maps-Nov-2025.png?resize=618%2C319&#038;ssl=1\" alt=\"District A has voters with xy-coordinates: (2,3), (3,2), (4,3), (2,5), (3,4), (5,4), (4,5), (3,6), (5,6), (6,5). District B has voters at (1,1), (2,1), (3,1), (4,2), (5,2), (6,3), (7,3), (8,4), (9,4), (10,5).\" width=\"618\" height=\"319\" srcset=\"https:\/\/i0.wp.com\/mathvoices.ams.org\/mathmedia\/wp-content\/uploads\/sites\/3\/2025\/12\/District-Maps-Nov-2025.png?w=618&amp;ssl=1 618w, https:\/\/i0.wp.com\/mathvoices.ams.org\/mathmedia\/wp-content\/uploads\/sites\/3\/2025\/12\/District-Maps-Nov-2025.png?resize=300%2C155&amp;ssl=1 300w, https:\/\/i0.wp.com\/mathvoices.ams.org\/mathmedia\/wp-content\/uploads\/sites\/3\/2025\/12\/District-Maps-Nov-2025.png?resize=465%2C240&amp;ssl=1 465w\" sizes=\"auto, (max-width: 618px) 100vw, 618px\" \/><figcaption id=\"caption-attachment-4105\" class=\"wp-caption-text\">Voter locations for two districts.<\/figcaption><\/figure>\n<ul>\n<li>What is the cumulative distance between voters in each of these imaginary districts?<\/li>\n<li>What is the average distance between voters in each?<\/li>\n<li>Plot the points on the same graph, using one color for voters from District A and another for voters from District B.<\/li>\n<li>Which district do you believe may have resulted from gerrymandering? Why?<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<p style=\"text-align: right\"><em>\u2014Max Levy<\/em><\/p>\n<hr \/>\n<h3><a id=\"2\" href=\"https:\/\/www.tiktok.com\/@therestisscience\/video\/7574855023817968918?_r=1&amp;_t=ZP-91b4WwqMDhn\">Smooth Earth<\/a><\/h3>\n<p><em>The Rest is Science (TikTok)<\/em>, November 20, 2025<\/p>\n<p>How deep would the oceans be if you shrunk Earth down to the size of a classroom globe? Earth\u2019s radius is 4,000 miles but the highest mountain peak is only 12 miles above the deepest undersea trench. This means Earth is actually \u201cunimaginably smooth,\u201d as mathematician Hannah Fry noted in this video. If you shrink our planet\u2019s 42 million foot diameter to 12 inches, you could fill all the Earth&#8217;s oceans with less than one tablespoon of water.<\/p>\n<p><strong>Classroom Activities:<\/strong><em> ratios, unit conversion, geography<\/em><\/p>\n<ul>\n<li>(Mid-level) Using the data in the table below, calculate the following and show your work. (Sources: <a href=\"https:\/\/www.usgs.gov\/water-science-school\/science\/how-much-water-there-earth\">USGS Water Science School<\/a>; <a href=\"https:\/\/www.ngdc.noaa.gov\/mgg\/image\/marianas.html\">NOAA<\/a>; <a href=\"https:\/\/geo.libretexts.org\/Bookshelves\/Geography_(Physical)\/The_Physical_Environment_(Ritter)\/02%3A_The_Earth_System\/2.01%3A_The_Earth_System\/2.1.04%3A_Size_and_Shape\">&#8220;The Physical Environment: The Earth System&#8221; by Michael Ritter<\/a>; <a href=\"https:\/\/www.npr.org\/2020\/11\/24\/938736955\/how-tall-is-mount-everest-hint-its-changing\">NPR <em>Short Wave<\/em><\/a>.)<img data-recalc-dims=\"1\" loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-4106 size-full\" src=\"https:\/\/i0.wp.com\/mathvoices.ams.org\/mathmedia\/wp-content\/uploads\/sites\/3\/2025\/12\/Geological-Data-Nov-2025.png?resize=576%2C127&#038;ssl=1\" alt=\"Diameter of Earth: 42 million feet. Height of Mount Everest: 29 thousand feet. Depth of Mariana trench: 36 thousand feet. Volume of all water on Earth: 49 times 10 to the 18 cubic feet.\" width=\"576\" height=\"127\" srcset=\"https:\/\/i0.wp.com\/mathvoices.ams.org\/mathmedia\/wp-content\/uploads\/sites\/3\/2025\/12\/Geological-Data-Nov-2025.png?w=576&amp;ssl=1 576w, https:\/\/i0.wp.com\/mathvoices.ams.org\/mathmedia\/wp-content\/uploads\/sites\/3\/2025\/12\/Geological-Data-Nov-2025.png?resize=300%2C66&amp;ssl=1 300w, https:\/\/i0.wp.com\/mathvoices.ams.org\/mathmedia\/wp-content\/uploads\/sites\/3\/2025\/12\/Geological-Data-Nov-2025.png?resize=465%2C103&amp;ssl=1 465w\" sizes=\"auto, (max-width: 576px) 100vw, 576px\" \/>\n<ul>\n<li>If Earth measured only 1 foot across, how high would Mount Everest\u2019s peak reach above sea level?<\/li>\n<li>How far would the Mariana Trench reach below sea level?<\/li>\n<li>What volume of liquid water would Earth contain?<\/li>\n<li>How tall would your school be on this shrunken surface <strong>in inches<\/strong>?<\/li>\n<li>Convert the height of your shrunken school into meters and millimeters and write the measurements in scientific notation.<\/li>\n<li>What metric system unit best matches that order of magnitude? (e.g. 10<sup>-3<\/sup> = millimeters)<\/li>\n<\/ul>\n<\/li>\n<li>(All levels) Complete <a href=\"https:\/\/www.jpl.nasa.gov\/edu\/resources\/lesson-plan\/solar-system-scroll\/\">this 30-minute activity<\/a> from NASA about the relative distances in the solar system.<\/li>\n<\/ul>\n<p style=\"text-align: right\"><em>\u2014Max Levy<\/em><\/p>\n<hr \/>\n<h3><a id=\"3\" href=\"https:\/\/www.newscientist.com\/article\/mg26835690-600-the-19th-century-maths-that-can-help-you-deal-with-horrible-coffee\/\">The 19th-century maths that can help you deal with horrible coffee<\/a><\/h3>\n<p><em>New Scientist<\/em>, November 12, 2025<\/p>\n<p>If you\u2019re picking teams, or playing Connect 4, going first gives you an advantage. To mitigate that, you can \u201ctake turns at taking turns,\u201d writes Katie Steckles for <em>New Scientist<\/em>. In this article, Steckles unpacks the technique.<\/p>\n<p><strong>Classroom Activities: <\/strong><em>calculus, algebra<\/em><\/p>\n<ul>\n<li>(All levels) Read the article. If you recognize the tactic of \u201ctaking turns taking turns,\u201d share where you\u2019ve seen it before.\n<ul>\n<li>If there are 3 people sharing the badly brewed pot of coffee, how would you suggest they share it? Explain why.<\/li>\n<li>What if there are 3 captains picking players ranked 1-10 for sports teams? Calculate the total ranking of each team if your solution is followed.<\/li>\n<\/ul>\n<\/li>\n<li>(High level, Calculus) Imagine the pot of coffee is a perfect cylinder, and the coffee reaches a height of 10 cm. Now imagine that at a height $h$ centimeters from the bottom of the pot, the strength of the coffee is $1 \u2013 h\/10$.\n<ul>\n<li>What is the average strength of the coffee in the pot?<\/li>\n<li>If two people share the coffee normally (the first half of the pot in one cup, the second half in another) what is the average strength of the coffee in the two cups?<\/li>\n<li>What is the average strength if the two people follow Steckles\u2019 proposed solution?<\/li>\n<li>What is the average strength for 3 people sharing (1) normally, and (2) according to the solution you proposed earlier?<\/li>\n<li>Why is it important that the pot is a perfect cylinder?<\/li>\n<li>(Hard) Suppose the strength of the coffee at height $h$ is $1 \u2013 (h\/10)^2$. For ten minutes, try to figure out whether it\u2019s possible for two people to both get the same amount of coffee, and the same average strength. After the 10 minutes are up, make your best guess, and explain your reasoning.<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<p style=\"text-align: right\"><em>\u2014Leila Sloman<\/em><\/p>\n<hr \/>\n<h3><a id=\"4\" href=\"https:\/\/www.scientificamerican.com\/article\/how-to-identify-a-prime-number-without-a-computer\/\">How to Identify a Prime Number without a Computer<\/a><\/h3>\n<p><em>Scientific American<\/em>, November 12, 2025<\/p>\n<p>Two centuries ago, long before digital computers or calculators, one mathematician named \u00c9douard Lucas proved that a 39-digit number was prime. To do so, he relied on advanced mathematical theories\u2014but in the end, his procedure was relatively simple. (That doesn\u2019t mean easy!) In this article, Manon Bischoff explains Lucas\u2019s strategy.<\/p>\n<p><strong>Classroom Activities: <\/strong><em>prime numbers, sequences, arithmetic<\/em><\/p>\n<ul>\n<li>(Mid-level) Read the article. What are the two methods the article gives for deciding whether $2^p \u2013 1$ is prime?\n<ul>\n<li>Prove in two different ways that 127 is prime. Show your work. (Consult <a href=\"https:\/\/oeis.org\/wiki\/Lucas-Lehmer_sequence\">the Online Encyclopedia of Integer Sequences<\/a> to find the elements of the Lucas-Lehmer sequence.)<\/li>\n<li>Based on the article, how else can you deduce that 127 is prime?<\/li>\n<\/ul>\n<\/li>\n<li>(High level) Prove that if $n$ is not prime, then $2^n \u2013 1$ is not prime either.<\/li>\n<li>(High level) <a href=\"https:\/\/oeis.org\/A095847\">This sequence<\/a> tells you the remainder when you divide the entries of the Lucas-Lehmer sequence by the corresponding Mersenne number.\n<ul>\n<li>Explain in your own words how you can use this sequence to find prime numbers.<\/li>\n<li>Are the following numbers prime? Explain how you know.\n<ul>\n<li>2,047<\/li>\n<li>8,191<\/li>\n<li>32,767<\/li>\n<li>131,071<\/li>\n<li>524,287<\/li>\n<li>4,294,967,295<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<p style=\"text-align: right\"><em>\u2014Leila Sloman<\/em><\/p>\n<hr \/>\n<h3><a id=\"5\" href=\"https:\/\/apnews.com\/article\/trump-tariff-dividends-election-supreme-court-21ee2da1ab7966fa6566b81bc91b11d4\">What to know about Trump&#8217;s plan to give Americans a $2,000 tariff dividend<\/a><\/h3>\n<p><em>AP News<\/em>, November 11, 2025<\/p>\n<p>In November, President Trump suggested that the government could write Americans checks for \u201cat least $2,000\u201d with funds raised from his administration\u2019s controversial tariffs. But there may be a problem. \u201cThe numbers just don\u2019t check out,\u201d one policy expert told the <em>Associated Press<\/em>. This article describes Trump\u2019s proposal and uses math to analyze whether it makes sense.<\/p>\n<p><strong>Classroom Activities:<\/strong><em> economics, arithmetic, algebra <\/em><\/p>\n<ul>\n<li>(All levels) Answer the following questions based on your reading:\n<ul>\n<li>How much money had the tariffs raised by the end of the fiscal year? (September)<\/li>\n<li>How much <em>more<\/em> money was raised in that fiscal year compared to the previous year?<\/li>\n<li>If a \\$2000 dividend to every eligible American would cost \\$600 billion, then how many Americans are eligible?<\/li>\n<li>How much more would this dividend program cost than the money raised by tariffs?<\/li>\n<li>What dividend payment amount would total the money raised by tariffs in the fiscal year? (Assume the same number of eligible recipients.)<\/li>\n<\/ul>\n<\/li>\n<li>(Mid-level) Economists <a href=\"https:\/\/mathvoices.ams.org\/mathmedia\/math-digests-december-2024\/\">have argued<\/a> that tariffs ultimately hurt consumers, as they cause prices to increase.\n<ul>\n<li>Suppose your annual shopping expenses sum to \\$12,000. If tariffs raise prices by 20%, then how much do your expenses rise in one year? If the government promises a \\$2000 dividend, how much money would you gain from a tariff program <em>overall<\/em>?<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<p style=\"text-align: right\"><em>\u2014Max Levy<\/em><\/p>\n<hr \/>\n<h3>More of this month\u2019s math headlines<\/h3>\n<ul>\n<li><a href=\"https:\/\/www.ft.com\/content\/b05318d1-12e5-49f1-9950-47e8b0f809ae\">AI doesn\u2019t add up if you neglect the mathematicians<\/a><br \/>\n<em>Financial Times<\/em>, November 30, 2025<\/li>\n<li><a href=\"https:\/\/www.popularmechanics.com\/science\/a69514328\/mathematicians-just-figured-out-how-to-better-predict-the-future\/\">Mathematicians Just Figured Out How to Better Predict the Future<\/a><br \/>\n<em>Popular Mechanics<\/em>, November 25, 2025<\/li>\n<li><a href=\"https:\/\/www.smh.com.au\/national\/nsw\/the-sydney-mathematician-finding-a-better-way-to-keep-your-data-safe-20251118-p5nge4.html\">The Sydney mathematician finding a better way to keep your data safe<\/a><br \/>\n<em>The Sydney Morning Herald<\/em>, November 19, 2025<\/li>\n<li><a href=\"https:\/\/nation.cymru\/news\/welsh-mathematician-helps-unlock-new-model-that-could-transform-medical-treatments\/\">Welsh mathematician helps unlock new model that could transform medical treatments<\/a><br \/>\n<em>Cymru<\/em>, November 15, 2025<\/li>\n<li><a href=\"https:\/\/www.quantamagazine.org\/new-proofs-probe-soap-film-singularities-20251112\/\">New Proofs Probe Soap-Film Singularities<\/a><br \/>\n<em>Quanta Magazine<\/em>, November 12, 2025<\/li>\n<\/ul>\n","protected":false},"excerpt":{"rendered":"<p>November digests: Gerrymandering, &#8220;the problem of democracy,&#8221; in The New York Times The &#8220;unimaginably smooth&#8221; world, from The Rest is Science When turn-taking isn&#8217;t fair enough, in New Scientist How to find prime numbers, in Scientific American The math of tariffs, in the Associated Press Moon Duchin on the Math<span class=\"more-link\"><a href=\"https:\/\/mathvoices.ams.org\/mathmedia\/math-digests-november-2025\/\">Read More &rarr;<\/a><\/span><\/p>\n","protected":false},"author":13,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"advanced_seo_description":"","jetpack_seo_html_title":"","jetpack_seo_noindex":false,"jetpack_post_was_ever_published":false,"_jetpack_newsletter_access":"","_jetpack_dont_email_post_to_subs":false,"_jetpack_newsletter_tier_id":0,"_jetpack_memberships_contains_paywalled_content":false,"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[2],"tags":[6,155,143,127,105,72,80],"class_list":["entry","author-leilasloman","post-4102","post","type-post","status-publish","format-standard","category-math-in-the-media-digests","tag-algebra","tag-arithmetic","tag-calculus","tag-economics","tag-graph-theory","tag-prime-numbers","tag-sequences"],"jetpack_featured_media_url":"","jetpack_sharing_enabled":true,"jetpack_likes_enabled":true,"_links":{"self":[{"href":"https:\/\/mathvoices.ams.org\/mathmedia\/wp-json\/wp\/v2\/posts\/4102","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/mathvoices.ams.org\/mathmedia\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/mathvoices.ams.org\/mathmedia\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/mathvoices.ams.org\/mathmedia\/wp-json\/wp\/v2\/users\/13"}],"replies":[{"embeddable":true,"href":"https:\/\/mathvoices.ams.org\/mathmedia\/wp-json\/wp\/v2\/comments?post=4102"}],"version-history":[{"count":7,"href":"https:\/\/mathvoices.ams.org\/mathmedia\/wp-json\/wp\/v2\/posts\/4102\/revisions"}],"predecessor-version":[{"id":4111,"href":"https:\/\/mathvoices.ams.org\/mathmedia\/wp-json\/wp\/v2\/posts\/4102\/revisions\/4111"}],"wp:attachment":[{"href":"https:\/\/mathvoices.ams.org\/mathmedia\/wp-json\/wp\/v2\/media?parent=4102"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/mathvoices.ams.org\/mathmedia\/wp-json\/wp\/v2\/categories?post=4102"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/mathvoices.ams.org\/mathmedia\/wp-json\/wp\/v2\/tags?post=4102"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}