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Mathematics | NSF - National Science Foundation
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of images showing magnified views of organisms including the brain of a fruit fly larva, the cells and structure of a fruit fly eye, and equations describing some of the biological processes involved." data-credit="Richard Carthew/Northwestern University/U.S. National Science Foundation" data-component-id="nsf_theme:hero"> <picture class="hero__media hero__image"> <source srcset="https://nsf-gov-resources.nsf.gov/styles/hero/s3/media_hub/NITMB_Collage_v2_1400x800.jpg.webp?VersionId=JPcCFWDE3EK2BO1006Yf9jbccMQCNt_r&itok=31OwSrBt" media="(min-width: 1204px)" type="image/webp" /> <source srcset="https://nsf-gov-resources.nsf.gov/styles/hero_medium/s3/media_hub/NITMB_Collage_v2_1400x800.jpg.webp?VersionId=7BeZRqQ1fp82sm8ppC3odAEZpOIKBd_E&itok=0v3uU33i" media="(min-width: 580px)" type="image/webp" /> <img class="hero__image-image" src="https://nsf-gov-resources.nsf.gov/styles/hero_small/s3/media_hub/NITMB_Collage_v2_1400x800.jpg.webp?VersionId=tNLTGU2xO3bq8qcpkhE2pfD7lL8DwyIC&itok=kluK_XKc" alt="A collage of images showing magnified views of organisms including the brain of a fruit fly larva, the cells and structure of a fruit fly eye, and equations describing some of the biological processes involved." /> </picture> <span class="hero__overlay"></span> <div class="hero hero--default hero--style-dynamic-image-overlay hero--media-type-image"> <div class="hero__content hero__content--default "> <div class="hero__content-inner"> <div class="hero__meta"> </div> <h1 class="hero__title hero-heading">Mathematics</h1> <div class="hero__tagline"> Developing and exploring the language of the universe. </div> </div> </div> </div> <div class="hero-credit-caption__wrapper"> <div class="hero-credit-caption"> <div class="hero-credit-caption__content"> <span aria-hidden="true"> <div class="icon__camera"> <svg xmlns="http://www.w3.org/2000/svg" height="24" viewBox="0 0 24 24" width="24"><path d="M0 0h24v24H0z" fill="none"/><circle cx="12" cy="12" r="3.2" fill="#005EA2" /><path d="M9 2L7.17 4H4c-1.1 0-2 .9-2 2v12c0 1.1.9 2 2 2h16c1.1 0 2-.9 2-2V6c0-1.1-.9-2-2-2h-3.17L15 2H9zm3 15c-2.76 0-5-2.24-5-5s2.24-5 5-5 5 2.24 5 5-2.24 5-5 5z" fill="#005EA2"/></svg> </div> </span> <div class="hero-credit-caption__text"> <a class="credit__link" href="#image-caption-credit-block" > View image credit & caption</a> </div> </div> </div> </div> </section> </div> <section class="usa-section uswds-middle-section"> <div class="grid-container"> <div class="grid-row grid-gap-lg"> <div class="mobile-lg:grid-col-fill"> <div class="region region-breadcrumb"> <div id="block-nsf-theme-breadcrumbs" class="block block-system block-system-breadcrumb-block block-nsf-theme-breadcrumbs"> <nav aria-label="Breadcrumb" id="system-breadcrumb" class="breadcrumbs"> <ol class="breadcrumbs__list"> <li class="breadcrumbs__item"> <a href="/" class="breadcrumbs__item--url">Home</a> </li> <li class="breadcrumbs__item"> <a href="/focus-areas" class="breadcrumbs__item--url">Our Focus Areas</a> </li> <li class="breadcrumbs__item"> <span class="breadcrumbs__item--current" aria-current="page">Mathematics</span> </li> </ol> </nav> </div> </div> </div> </div> </div> </section> <main class="uswds-main-content-wrapper grid-container not-search-page three-col-layout"> <div class="grid-row"> </div> <div class="grid-row grid-gap-6"> <div class="region-content full-width-container tablet:grid-col-12"> <div id="content-article-wrap"> <div class="region region-content"> <div data-drupal-messages-fallback class="hidden"></div> <div id="block-nsf-theme-content" class="block block-system block-system-main-block block-nsf-theme-content"> <article class="node node--type-layout-builder-page node--promoted node--view-mode-full"> <div class="node__content"> <article class="node text__container node--type-layout-builder-page node--promoted node--view-mode-pre-layout-fields"> <div class="node_view"></div> </article> <div class="layout-container--wrapper nsf-layout nsf-layout--twocol-60-40 constrained-width"> <div class="nsf-layout--outer"> <div class="nsf-layout--inner"> </div> <div class="nsf-layout--inner"> <div class="layout__region layout__region--first"> <div class="block block-layout-builder block-inline-blockcomponent-text nsf-component"> <section class="text__container"> <div class="body-1"><p>We advance research in mathematics: the science of numbers, shapes, probability and change.</p></div> <div class="text__content text-formatted"><p>The U.S. National Science Foundation is the leading supporter of fundamental mathematics research in the United States.</p> <p>Whether it's unraveling the chaos of turbulence to better predict weather, accelerating the development of life-saving drugs, or improving the security and efficiency of the modern power grid, NSF research in mathematics keeps the U.S. at the leading edge of science and engineering.</p></div> </section> </div> </div> <div class="layout__region layout__region--second"> <section data-component-id="nsf_theme:related-links" class="block block-layout-builder block-inline-blockrelated-links-with-files nsf-component"> <div class="related-links nsf-component related-links--chevron"> <ul class="link-list"> <li class="link-list__item"> <div class="paragraph paragraph--type--attachment paragraph--view-mode--ief-table"> <div class="grid-col-fill"> <div class="field field-para-attachment-link"><a href="/funding/opportunities?f%5B0%5D=division%3A43">Find funding in mathematics</a></div> </div> </div> </li> <li class="link-list__item"> <div class="paragraph paragraph--type--attachment paragraph--view-mode--ief-table"> <div class="grid-col-fill"> <div class="field field-para-attachment-link"><a href="/mps/dms">Division of Mathematical Sciences</a></div> </div> </div> </li> <li class="link-list__item"> <div class="paragraph paragraph--type--attachment paragraph--view-mode--ief-table"> <div class="grid-col-fill"> <div class="field field-para-attachment-link"><a href="/mps">Directorate for Mathematical and Physical Sciences</a></div> </div> </div> </li> </ul> </div> </section> </div> </div> <div class="nsf-layout--inner"> </div> </div> </div> <div class="layout-container--wrapper nsf-layout nsf-layout--threecol full-browser-width"> <div class="nsf-layout--outer"> <div class="nsf-layout--inner"> <div class="layout__region layout__region--headline"> <div class="block block-layout-builder block-inline-blockcomponent-text nsf-component"> <section class="text__container"> <div class="body-1"><h2 id="what-we-support-dcc">What we support</h2></div> </section> </div> </div> </div> <div class="nsf-layout--inner"> <div class="layout__region layout__region--first"> <div class="cta block block-layout-builder block-inline-blockcomponent-cta nsf-component" class="block block-layout-builder block-inline-blockcomponent-cta nsf-component" data-media-id="9939" data-is-footer-caption-credit data-src="https://nsf-gov-resources.nsf.gov/2023-04/Cover3.jpg?VersionId=6gOBZOAGpBF4e64AYkU18TfDr2g5nT4s" data-footer-caption-credit-src="https://nsf-gov-resources.nsf.gov/styles/image_credit_caption_block_130x78_/s3/2023-04/Cover3.jpg?VersionId=DbTWj7oWvCJE94FD5lIkV1v0X4PCqDVJ&amp;itok=oDSoQrPX" data-caption="This visualization depicts state variables -- the variables used to describe the physical states of a dynamical system -- discovered by artificial intelligence and colored by their corresponding physical variables." data-credit="Boyuan Chen/Columbia Engineering" data-component-id="nsf_theme:cta"> <div class="cta__image"> <img class="cta__img--full" src="https://nsf-gov-resources.nsf.gov/styles/cta_image/s3/2023-04/Cover3.jpg?VersionId=V8zmpjPWqlkmxAAWvUD1H8pX7zDKYKjx&itok=-zmzGF2N" alt="" /> </div> <div class="cta__content"> <div class="clearfix text-formatted field field-block-cta-body"><h3>Innovation in mathematics and statistics</h3> <p>We support research on the properties of mathematical structures and how to use mathematics to solve problems in science, engineering and society at large.</p> </div> </div> </div> </div> <div class="layout__region layout__region--second"> <div class="cta block block-layout-builder block-inline-blockcomponent-cta nsf-component" class="block block-layout-builder block-inline-blockcomponent-cta nsf-component" data-media-id="9940" data-is-footer-caption-credit data-src="https://nsf-gov-resources.nsf.gov/2023-04/AwschalomLab.jpg?VersionId=gMkJnzFsKyBADgKOwgra_0MflphoKnPl" data-footer-caption-credit-src="https://nsf-gov-resources.nsf.gov/styles/image_credit_caption_block_130x78_/s3/2023-04/AwschalomLab.jpg?VersionId=XQnDu0sj8Ds8WLeyT__BHwb9ytOXwu5M&amp;itok=aulixo0m" data-caption="" data-credit="University of Chicago" data-component-id="nsf_theme:cta"> <div class="cta__image"> <img class="cta__img--full" src="https://nsf-gov-resources.nsf.gov/styles/cta_image/s3/2023-04/AwschalomLab.jpg?VersionId=5fV87x2CDVQ78KzUBVCyY9kpfuuEqCJb&itok=TOzV1dQk" alt="" /> </div> <div class="cta__content"> <div class="clearfix text-formatted field field-block-cta-body"><h3>World-class research institutes</h3> <p>We support national mathematical research institutes that advance fundamental research and address problems in other disciplines.</p> </div> </div> </div> </div> <div class="layout__region layout__region--third"> <div class="cta block block-layout-builder block-inline-blockcomponent-cta nsf-component" class="block block-layout-builder block-inline-blockcomponent-cta nsf-component" data-media-id="9420" data-is-footer-caption-credit data-src="https://nsf-gov-resources.nsf.gov/2023-04/QuICS%20image.JPG?VersionId=9xuQEhDRw7Qq1HxNTNNGygZiTSlR9lcE" data-footer-caption-credit-src="https://nsf-gov-resources.nsf.gov/styles/image_credit_caption_block_130x78_/s3/2023-04/QuICS%20image.JPG?VersionId=iGJyGejticc5NBLDNBIuQ.RQgO0soPqe&amp;itok=03VEBhvd" data-caption="Ph.D. Students working at the whiteboard in the QuICS space in the Atlantic Building. The Joint Center for Quantum Information and Computer Science (QulCS) recently received a renewal in federal funding that will allow the center to expand its research and educational activities, including additional support for postdocs and graduate students. UMD computer science Ph.D. student Manesi Shingane (left) discusses her work with postdoc Atul Mantri (right)." data-credit="John T. Consoli/University of Maryland" data-component-id="nsf_theme:cta"> <div class="cta__image"> <img class="cta__img--full" src="https://nsf-gov-resources.nsf.gov/styles/cta_image/s3/2023-04/QuICS%20image.JPG?VersionId=P7eUZg.PDh4zdrW3U7r8AlEaLibUoloC&itok=C0gl_xjC" alt="" /> </div> <div class="cta__content"> <div class="clearfix text-formatted field field-block-cta-body"><h3>Education and training</h3> <p>We support the next generation of mathematical scientists and statisticians through internships, fellowships, institutes and other programs.</p> </div> </div> </div> </div> </div> <div class="nsf-layout--inner"> </div> </div> </div> <div class="palette palette--light-gray layout-container--wrapper nsf-layout nsf-layout--base full-browser-width"> <div class = "nsf-layout--outer"> <div class = "nsf-layout--inner"> <div class="layout__region layout__region--main"> <div class="block block-layout-builder block-inline-blockcomponent-text nsf-component"> <section class="text__container"> <div class="body-1"><h2 id="latest-discoveries-960">Featured news</h2></div> </section> </div> <div class="block block-layout-builder block-inline-blocknsf-news nsf-component nsf-news-latest-news nsf-news--horizontal"> <div class="field field-nsfnews-latest-news"> <div class="views-element-container block block-views block-views-blocklatest-news-nsfnews-sciencematters block-views-block-latest-news-nsfnews-sciencematters--2" id="block-views-block-latest-news-nsfnews-sciencematters--2"> <div><!-- network: 0 - Sat, 22 Mar 2025 12:48:51 -0400 --> <div class="view view-latest-news view-id-latest_news view-display-id-nsfnews_sciencematters js-view-dom-id-13e258aa6eab4939bf10ce310c21c8933782aa983ba994cd778ebdfee73a6be6"> <div class="view-content"> <div class="views-row"> <div class="vertical-news-teaser " data-component-id="nsf_theme:vertical-news-teaser"> <span class="label-gray vertical-news-teaser__type"> NSF Stories </span> <div class="vertical-news-teaser__image"> <img class="" src="https://nsf-gov-resources.nsf.gov/styles/news_teaser/s3/media_hub/Bubblewrap_1%5B93%5D.jpg?VersionId=LDrAB20nsCBoGqMmC8poMFs3Nc44HV9l&itok=_iwem0nx" alt="supportive skeletal tissue" /> </div> <div class="vertical-news-teaser__content"> <div class="vertical-news-teaser__date"> <time datetime="2025-03-14T11:25:33-04:00" title="Friday, March 14, 2025 - 11:25" class="datetime">March 14, 2025</time> </div> <div class="vertical-news-teaser__headline"> <h3> <a href="/news/unique-skeletal-tissue-may-enable-new-regenerative-medical"> <span class="field field--name-title field--type-string field--label-hidden">Unique skeletal tissue may enable new regenerative medical treatments</span> </a> </h3> </div> </div> </div> </div> <div class="views-row"> <div class="vertical-news-teaser " data-component-id="nsf_theme:vertical-news-teaser"> <span class="label-gray vertical-news-teaser__type"> NSF Stories </span> <div class="vertical-news-teaser__image"> <img class="" src="https://nsf-gov-resources.nsf.gov/styles/news_teaser/s3/media_hub/pr05005xray1processed.jpg?VersionId=CZmfGIgscwKrPcceYJz9kw3I2RINcerP&itok=OU-1xezo" alt="x-ray" /> </div> <div class="vertical-news-teaser__content"> <div class="vertical-news-teaser__date"> <time datetime="2025-01-16T12:31:33-05:00" title="Thursday, January 16, 2025 - 12:31" class="datetime">January 16, 2025</time> </div> <div class="vertical-news-teaser__headline"> <h3> <a href="/news/chasing-sparks-unraveling-50-year-old-x-ray-mystery"> <span class="field field--name-title field--type-string field--label-hidden">Chasing sparks: Unraveling a 50-year-old X-ray mystery</span> </a> </h3> </div> </div> </div> </div> <div class="views-row"> <div class="vertical-news-teaser " data-component-id="nsf_theme:vertical-news-teaser"> <span class="label-gray vertical-news-teaser__type"> NSF Stories </span> <div class="vertical-news-teaser__image"> <img class="" src="https://nsf-gov-resources.nsf.gov/styles/news_teaser/s3/media_hub/AdobeStock_975925473.jpeg?VersionId=SAjh5AOm7UGrfSoFqAwH62oQ1tXlQ4gx&itok=pkflSyUj" alt="3D model of a human heart" /> </div> <div class="vertical-news-teaser__content"> <div class="vertical-news-teaser__date"> <time datetime="2025-01-10T14:37:56-05:00" title="Friday, January 10, 2025 - 14:37" class="datetime">January 10, 2025</time> </div> <div class="vertical-news-teaser__headline"> <h3> <a href="/news/ai-vs-supercomputers-new-ai-based-method-solves-complex"> <span class="field field--name-title field--type-string field--label-hidden">AI vs. supercomputers: New AI-based method solves complex equations faster and uses less computing power </span> </a> </h3> </div> </div> </div> </div> </div> </div> </div> </div> </div> </div> <div class="block block-layout-builder block-inline-blockbutton alignment-center nsf-component"> <a href="/news/releases?f%5B0%5D=group%3A43" title="Explore mathematics and statistics news" class="link-button usa-button usa-button--outline " > Explore mathematics and statistics news </a> </div> </div> </div> </div> </div> <div class="palette palette--dark-blue layout-container--wrapper nsf-layout nsf-layout--base full-browser-width"> <div class = "nsf-layout--outer"> <div class = "nsf-layout--inner"> <div class="layout__region layout__region--main"> <div class="card-dark-blue card-dark-blue--horizontal block block-layout-builder block-inline-blockcomponent-featured-content" class="block block-layout-builder block-inline-blockcomponent-featured-content" data-media-id="9944" data-is-footer-caption-credit data-src="https://nsf-gov-resources.nsf.gov/2023-04/Curve_graph_white.png?VersionId=DEz3FtIAoF8vXGmrDWNjxPE8dXmBRcuJ" data-footer-caption-credit-src="https://nsf-gov-resources.nsf.gov/styles/image_credit_caption_block_130x78_/s3/2023-04/Curve_graph_white.png?VersionId=GDJBL.b5OaAhWATOPkMZa0zQ_38uOo5C&amp;itok=Z09QqbiE" data-caption="Curve_graph_white" data-credit="U.S.National Science Foundation" data-component-id="nsf_theme:card-dark-blue"> <div class="card-dark-blue__inner"> <div class="card-dark-blue__content fullwidth"> <div class="card-dark-blue__image"> <div class="card-dark-blue__image--image"> <picture> <source srcset="https://nsf-gov-resources.nsf.gov/styles/featured_content_tablet/s3/2023-04/Curve_graph_white.png.webp?VersionId=TlX0XbJPtUE3ysm2X9B3SIo2yOiXaWNt&itok=M3MJ0dxL 1x" media="all and (min-width: 640px)" type="image/webp" width="500" height="324"/> <source srcset="https://nsf-gov-resources.nsf.gov/styles/featured_content_mobile/s3/2023-04/Curve_graph_white.png.webp?VersionId=qSxdYJjQNmx5ELcOOyrkIBU4OsZjsBpV&itok=Hv7zb-FM 1x" media="all and (min-width: 0)" type="image/webp" width="595" height="400"/> <source srcset="https://nsf-gov-resources.nsf.gov/styles/featured_content_tablet/s3/2023-04/Curve_graph_white.png?VersionId=TlX0XbJPtUE3ysm2X9B3SIo2yOiXaWNt&itok=M3MJ0dxL 1x" media="all and (min-width: 640px)" type="image/png" width="500" height="324"/> <source srcset="https://nsf-gov-resources.nsf.gov/styles/featured_content_mobile/s3/2023-04/Curve_graph_white.png.webp?VersionId=qSxdYJjQNmx5ELcOOyrkIBU4OsZjsBpV&itok=Hv7zb-FM 1x" media="all and (min-width: 0)" type="image/webp" width="595" height="400"/> <img src="https://nsf-gov-resources.nsf.gov/styles/featured_content_tablet/s3/2023-04/Curve_graph_white.png?VersionId=TlX0XbJPtUE3ysm2X9B3SIo2yOiXaWNt&itok=M3MJ0dxL" width="500" height="324" alt="curve graph icon" loading="lazy" /> </picture> </div> <span role="img" aria-label="curve graph icon" class="card-dark-blue__background-image" style="background-image: url(https://nsf-gov-resources.nsf.gov/styles/featured_content_tablet/s3/2023-04/Curve_graph_white.png?VersionId=TlX0XbJPtUE3ysm2X9B3SIo2yOiXaWNt&itok=M3MJ0dxL);"></span> </div> <div class="card-dark-blue__text"> <h3> <a href="/focus-areas/mathematics/educational-resources">Educational resources</a> </h3> <p>View lesson plans, 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