Undergraduate Upends a 40-Year-Old Data Science Conjecture

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class='theme__background-background theme__text'> <section class='post__title__wrapper relative '> <section class='outer fill-h relative outer--content '> <div class='mha container--s'> <div class='header-spacer'></div> <div class='post__title pv1 scale1 mha'> <div class='scale0'> <div class='mb1 pb025 mt0 h6t post__title__kicker '> <a class="kicker theme__accent theme__text-hover uppercase" href="/tag/algorithms/">algorithms</a> </div> <h1 class='post__title__title mv025 noe theme__text' >Undergraduate Upends a 40-Year-Old Data Science Conjecture</h1> <div class='post__title__author-date h5 mt1'> <div class='byline relative flex flex-items-start merriweather mv025 mr1 gray3 h6t theme__text-hover'> <em class='byline__by gray4 mr075'>By </em> <a href='https://www.quantamagazine.org/authors/nadis_steven/'> <span class='byline__author uppercase kern light small'>Steve Nadis</span> </a> </div> <p class="h6 mv1 pv025 o6"><em>February 10, 2025</em></p> </div> <div class='post__title__meta flex flex-wrap flex-items-start'> <div class='post__title__excerpt wysiwyg p italic mb1 mt025 pr2 o4 theme__text ' > A young computer scientist and two colleagues show that searches within data structures called hash tables can be much faster than previously deemed possible. </div> <div class='post__title__actions h5 mt025 flex-auto flex flex-items-center'> <div class='comments-button mr05 flex flex-items-center theme__accent-hover h5 theme__accent' data-name='comment-bubble' > <a href='#comments' class='flex flex-items-center pangram'> <svg viewbox='0 0 50 50' enable-background='new 0 0 50 50' xmlns='http://www.w3.org/2000/svg' class=''><title>Comment</title><path fill='currentColor' d='M9.4 4.2h31.2c8.6 0 9.4 7 9.4 15.6s-.7 15.6-9.4 15.6h-2.2l-.9 9.4-18.8-9.4H9.4c-8.6 0-9.4-7-9.4-15.6S.7 4.2 9.4 4.2z'></path></svg> <div> <span class='comments-button__count ml075 small mbold disqus-comment-count' data-disqus-identifier='146421 https://www.quantamagazine.org/?p=146421'></span> </div> </a> </div> <span class='o-divider mh075 relative'></span> <div class='relative'> <button class='bookmark-button mh05 flex flex-items-center theme__accent-hover ' data-toggle-hover='tooltip' data-id='146421' data-active-class='' aria-expanded='false'> <svg class="icon" viewbox="0 0 50 50" enable-background="new 0 0 50 50" xmlns="http://www.w3.org/2000/svg"><title>Save Article</title><path fill="currentColor" d="M2.1 0h45.8v50L25.5 37.5 2.1 50V0z"></path></svg> </button> <div class='q-tooltip hidden force-mobile-placement w-32 ml-n16 -top-10'> <div class='q-tooltip-content'> <div class='q-tooltip-arrow -bottom-3'></div> <div class='q-tooltip-inner py-1 pl-1' role='tooltip'> <div class='h6t relative z1 uppercase kern--w mx025'> <span class='small no-wrap'>Read Later</span> </div> </div> </div> </div> </div> </div> </div> </div> </div> </div> </section> </section> <figure class='leading-0 w-full my-0 mx-auto flex items-center justify-center flex-col max-w-img-large py-0 px-0 l:px-0 l:mb-20'> <div class='w-full flex justify-center max-w-mod-large m:max-w-unset image--module s:flex-col s:m-auto'> <div class='w-auto mr-2 last:mr-0 s:m-0 s:flex s:flex-col flex-1'> <img width="2560" height="1440" src="https://www.quantamagazine.org/wp-content/uploads/2025/02/Hash-Tables-Redux_cr_Nash-Weerasekera-Lede.webp" class="mb-6 w-full s:mb-4" alt="A tool chest with a tray full of different sized arrows against a red-orange backdrop." decoding="async" fetchpriority="high" srcset="https://www.quantamagazine.org/wp-content/uploads/2025/02/Hash-Tables-Redux_cr_Nash-Weerasekera-Lede.webp 2560w, https://www.quantamagazine.org/wp-content/uploads/2025/02/Hash-Tables-Redux_cr_Nash-Weerasekera-Lede-1720x968.webp 1720w, https://www.quantamagazine.org/wp-content/uploads/2025/02/Hash-Tables-Redux_cr_Nash-Weerasekera-Lede-520x293.webp 520w, https://www.quantamagazine.org/wp-content/uploads/2025/02/Hash-Tables-Redux_cr_Nash-Weerasekera-Lede-768x432.webp 768w, https://www.quantamagazine.org/wp-content/uploads/2025/02/Hash-Tables-Redux_cr_Nash-Weerasekera-Lede-1536x864.webp 1536w, https://www.quantamagazine.org/wp-content/uploads/2025/02/Hash-Tables-Redux_cr_Nash-Weerasekera-Lede-2048x1152.webp 2048w" sizes="(max-width: 2560px) 100vw, 2560px" /> </div> </div> <figcaption class='block my-0 mx-auto w-full'> <section class='py-0 px-12 s:p-0 m:px-16'> <div class='w-full my-0 mx-auto flex flex-col s:mx-5 s:w-full-minus-25 s:max-w-mod-inline m:max-w-mod-inline l:flex-row l:max-w-mod-large justify-end s:mb-4'> <div class='caption wysiwyg h5 theme__anchors--solid fill-h w-auto l:w-140'> <p>“Tiny pointers,” which show the way to a piece of stored data, inspired the creation of a new kind of faster hash table.</p> </div> <div class='attribution theme__anchors--solid wysiwyg pangram h6 mb1 fill-h text-left w-auto before:block l:before:hidden l:w-half-minus-17 l:text-right l:pl-24'> <p>Nash Weerasekera for <em>Quanta Magazine</em></p> </div> </div> </section> </figcaption> </figure> <div class='acf-content scale1 mt2'> <h2 class='screen-reader-text'>Introduction</h2> <div class='post__wrapper scale0 show-dropcap'> <div class='mha container--m'> <div class='post__content relative flex flex-items-start flex-justify-between'> <aside class='post__sidebar hide flex flex-justify-center '> <div class='post__sidebar__content'> <div class='post__sidebar__content__inner'> <div class='align-c mb075'> <div class='sidebar__author'> <a class='theme__accent-hover transition--color ' href='https://www.quantamagazine.org/authors/nadis_steven/'> <div class='sidebar__author__avatar mha mb1'> <div class='image mx0 relative image--circle '> <div class='image__inner absolute fit-x is-loaded'> <img width="1654" height="1720" src="https://www.quantamagazine.org/wp-content/uploads/2023/01/nadis-1654x1720.jpg" class="absolute fit-x fill-h fill-v mxa" alt="" decoding="async" srcset="https://www.quantamagazine.org/wp-content/uploads/2023/01/nadis-1654x1720.jpg 1654w, https://www.quantamagazine.org/wp-content/uploads/2023/01/nadis-500x520.jpg 500w, https://www.quantamagazine.org/wp-content/uploads/2023/01/nadis-768x798.jpg 768w, https://www.quantamagazine.org/wp-content/uploads/2023/01/nadis-1477x1536.jpg 1477w, https://www.quantamagazine.org/wp-content/uploads/2023/01/nadis-1970x2048.jpg 1970w" sizes="(max-width: 1654px) 100vw, 1654px" /> </div> </div> </div> <div class='h3t mv05'> <span class='screen-reader-text'>By </span>Steve Nadis </div> <p class="o8 theme__text h5 mt05 mb1"><em>Contributing Writer</em></p> </a> </div> <hr class='mb075 o1'> <p class="h6 mv1 pv025 o6"><em>February 10, 2025</em></p> </div> <form action='https://www.quantamagazine.org/undergraduate-upends-a-40-year-old-data-science-conjecture-20250210' method='get' class='sidebar__actions'> <hr class='mt075 mb1 o1'> <input type='hidden' id='print' name='print' value='1' /> <button 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transition--color relative'>computer science</span></a> <a class='sidebar__tag h6 pangram medium inline-block mb0 relative float-left' href='/tag/data'> <span class='absolute fit-x theme__text-background o1'></span> <span class='theme__text theme__accent-hover transition--color relative'>data</span></a> <a class='sidebar__tag h6 pangram medium inline-block mb0 relative theme__accent w-full' href='/topics'> <span class='absolute fit-x theme__text-background o1'></span> <span class='theme__text-hover transition--color relative'>All topics</span> <svg class='icon ml05' viewbox='0 0 50 50' enable-background='new 0 0 50 50'><path fill='currentColor' d='M50 25l-17.4-8.7v6.5H0v4.4h32.6v6.5'></path></svg> </a> </div> </div> <div class='sidebar__poster'> <a href='https://www.quantabooks.org/' title='' target='_blank' class=''> <img width="640" height="1100" src="https://www.quantamagazine.org/wp-content/uploads/2025/01/D-Article-Qbooks-Jan2025-1.png" class="fill-h" alt="" decoding="async" srcset="https://www.quantamagazine.org/wp-content/uploads/2025/01/D-Article-Qbooks-Jan2025-1.png 640w, https://www.quantamagazine.org/wp-content/uploads/2025/01/D-Article-Qbooks-Jan2025-1-303x520.png 303w" sizes="(max-width: 640px) 100vw, 640px" /></a> </div> </div> </aside> <section class='outer mha js-router-anchors outer--content'> <div class='flex-auto mha container--xs '> <div class='post__content__section wysiwyg p theme__anchors--underline' data-role='selectable'> <div class='post__content wysiwyg p theme__anchors--underline '> <p>Sometime in the fall of 2021, Andrew Krapivin, an undergraduate at Rutgers University, encountered a paper that would change his life. At the time, Krapivin didn’t give it much thought. But two years later, when he finally set aside time to go through the paper (“just for fun,” as he put it), his efforts would lead to a rethinking of a widely used tool in computer science.</p> <p>The paper’s title, “<a href="https://arxiv.org/abs/2111.12800">Tiny Pointers</a>,” referred to arrowlike entities that can direct you to a piece of information, or element, in a computer’s memory. Krapivin soon came up with a potential way to further miniaturize the pointers so they consumed less memory. However, to achieve that, he needed a better way of organizing the data that the pointers would point to.</p> <p>He turned to a common approach for storing data known as a hash table. But in the midst of his tinkering, Krapivin realized that he had invented a new kind of hash table, one that worked faster than expected — taking less time and fewer steps to find specific elements.</p> <p><a href="https://engineering.nyu.edu/faculty/martin-farach-colton">Martín Farach-Colton</a>, a co-author of the “Tiny Pointers” paper and Krapivin’s former professor at Rutgers, was initially skeptical of Krapivin’s new design. Hash tables are among the most thoroughly studied data structures in all of computer science; the advance sounded too good to be true. But just to be sure, he asked a frequent collaborator (and a “Tiny Pointers” co-author), <a href="https://csd.cmu.edu/people/faculty/william-kuszmaul">William Kuszmaul</a> of Carnegie Mellon University, to check out his student’s invention. Kuszmaul had a different reaction. “You didn’t just come up with a cool hash table,” he remembers telling Krapivin. “You’ve actually completely wiped out a 40-year-old conjecture!”</p> </div> </div> </div> </section> <aside class='post__sidebar hide flex flex-justify-center theme__anchors--solid '> <div class='post__sidebar__content'> <div class='post__sidebar__content__inner'> <div class='h3t mt0'> Share this article </div> <div data-id='social-links'> <div class='social-links social-links--share flex flex-justify-between'> <a href='http://www.facebook.com/sharer.php?u=https://www.quantamagazine.org/undergraduate-upends-a-40-year-old-data-science-conjecture-20250210/' class='social-links__link flex flex-items-center relative' target="_blank" > <div class='icon-button inline-block relative pointer theme__accent-hover-child'> <div class='absolute fit-x mxa o2 hover--opaque theme__text'> </div> <svg class="absolute fit-x mxa theme__text" viewbox="0 0 50 50" enable-background="new 0 0 50 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https://www.quantamagazine.org/wp-content/uploads/2025/02/Andrew-Krapivin-cr.PhilippAmmon-Posing-1720x1191.webp 1720w, https://www.quantamagazine.org/wp-content/uploads/2025/02/Andrew-Krapivin-cr.PhilippAmmon-Posing-520x360.webp 520w, https://www.quantamagazine.org/wp-content/uploads/2025/02/Andrew-Krapivin-cr.PhilippAmmon-Posing-768x532.webp 768w, https://www.quantamagazine.org/wp-content/uploads/2025/02/Andrew-Krapivin-cr.PhilippAmmon-Posing-1536x1063.webp 1536w, https://www.quantamagazine.org/wp-content/uploads/2025/02/Andrew-Krapivin-cr.PhilippAmmon-Posing-2048x1418.webp 2048w" sizes="(max-width: 2560px) 100vw, 2560px" /> </div> </div> <figcaption class='block my-0 mx-auto w-full l:max-w-mod-inline'> <section class='p-0 m:py-0 m:px-16'> <div class='w-full my-0 mx-auto flex flex-col s:mx-5 s:w-full-minus-25 s:max-w-mod-inline m:max-w-mod-inline l:m-0 l:p-0 max-w-mod-inline s:mb-4'> <div class='caption wysiwyg h5 theme__anchors--solid fill-h '> <p>Without setting out to do so, Andrew Krapivin upended the common thinking around hash tables — one of the best-studied tools in computer science.</p> </div> <div class='attribution theme__anchors--solid wysiwyg pangram h6 mb1 fill-h '> <p>Phillip Ammon for <em>Quanta Magazine</em></p> </div> </div> </section> </figcaption> </figure> <div class='acf-content scale1 mt2'> <section class='outer mha js-router-anchors outer--content'> <div class='flex-auto mha container--xs '> <div class='post__content__section wysiwyg p theme__anchors--underline' data-role='selectable'> <div class='post__content wysiwyg p theme__anchors--underline '> <p>Together, Krapivin (now a graduate student at the University of Cambridge), Farach-Colton (now at New York University) and Kuszmaul demonstrated in a <a href="https://arxiv.org/abs/2501.02305">January 2025 paper</a> that this new hash table can indeed find elements faster than was considered possible. ln so doing, they had disproved a conjecture long held to be true.</p> <p>“It’s an important paper,” said <a href="https://ajhconway.com/">Alex Conway</a> of Cornell Tech in New York City. “Hash tables are among the oldest data structures we have. And they’re still one of the most efficient ways to store data.” Yet open questions remain about how they work, he said. “This paper answers a couple of them in surprising ways.”</p> <p>Hash tables have become ubiquitous in computing, partly because of their simplicity and ease of use. They’re designed to allow users to do exactly three things: “query” (search for) an element, delete an element, or insert one into an empty slot. The first hash tables date back to the early 1950s, and computer scientists have studied and used them ever since. Among other things, researchers wanted to figure out the speed limits for some of these operations. How fast, for example, could a new search or insertion possibly be?</p> <aside class="post__aside mb2 relative post__aside--right"><figure class='mb2 mt1 image--shortcode s:mt-0'> <div class='relative image mx0'> <img width="1298" height="1571" src="https://www.quantamagazine.org/wp-content/uploads/2025/02/Martin-Farach-Colton_crAndrew-Farach-Colton.webp" class="block fit-x fill-h fill-v is-loaded mxa large-print-img vertical" alt="Martín Farach-Colton in a gray shirt stands in front of green plants" decoding="async" srcset="https://www.quantamagazine.org/wp-content/uploads/2025/02/Martin-Farach-Colton_crAndrew-Farach-Colton.webp 1298w, https://www.quantamagazine.org/wp-content/uploads/2025/02/Martin-Farach-Colton_crAndrew-Farach-Colton-430x520.webp 430w, https://www.quantamagazine.org/wp-content/uploads/2025/02/Martin-Farach-Colton_crAndrew-Farach-Colton-768x930.webp 768w, https://www.quantamagazine.org/wp-content/uploads/2025/02/Martin-Farach-Colton_crAndrew-Farach-Colton-1269x1536.webp 1269w" sizes="(max-width: 1298px) 100vw, 1298px" /> </div> <figcaption class='image__meta mt1'> <div class='caption wysiwyg h5 theme__anchors--solid fill-h post__aside__caption post__aside__caption--shortcode'> <p>Martín Farach-Colton helped Krapivin prove that his new hash table contradicted a longstanding conjecture.</p> </div> <div class='attribution theme__anchors--solid wysiwyg pangram h6 mb1 fill-h post__aside__attribution'> <p>Andrew Farach-Colton</p> </div> </figcaption> </figure> </aside> <p>The answer generally depends on the amount of time it takes to find an empty spot in a hash table. This, in turn, typically depends on how full the hash table is. Fullness can be described in terms of an overall percentage — this table is 50% full, that one’s 90% — but researchers often deal with much fuller tables. So instead, they may use a whole number, denoted by <em>x</em>, to specify how close the hash table is to 100% full. If <em>x</em> is 100, then the table is 99% full. If <em>x</em> is 1,000, the table is 99.9% full. This measure of fullness offers a convenient way to evaluate how long it should take to perform actions like queries or insertions.<strong> </strong></p> <p>Researchers have long known that for certain common hash tables, the expected time required to make the worst possible insertion — putting an item into, say, the last remaining open spot — is proportional to <em>x</em>. “If your hash table is 99% full,” Kuszmaul said, “it makes sense that you would have to look at around 100 different positions to find a free slot.”</p> <p>In a <a href="https://dl.acm.org/doi/10.1145/3828.3836">1985 paper</a>, the computer scientist <a href="https://amturing.acm.org/award_winners/yao_1611524.cfm">Andrew Yao</a>, who would go on to win the A.M. Turing Award, asserted that among hash tables with a specific set of properties, the best way to find an individual element or an empty spot is to just go through potential spots randomly — an approach known as uniform probing. He also stated that, in the worst-case scenario, where you’re searching for the last remaining open spot, you can never do better than <em>x</em>. for 40 years, most computer scientists assumed that Yao’s conjecture was true.</p> <p>Krapivin was not held back by the conventional wisdom for the simple reason that he was unaware of it. “I did this without knowing about Yao’s conjecture,” he said. His explorations with tiny pointers led to a new kind of hash table — one that did not rely on uniform probing. And for this new hash table, the time required for worst-case queries and insertions is proportional to (log <em>x</em>)<sup>2</sup> — far faster than <em>x</em>. This result directly contradicted Yao’s conjecture. Farach-Colton and Kuszmaul helped Krapivin show that (log <em>x</em>)<sup>2</sup> is the optimal, unbeatable bound for the popular class of hash tables Yao had written about.</p> <p>“This result is beautiful in that it addresses and solves such a classic problem,” said <a href="http://www.cs.cmu.edu/~guyb/">Guy Blelloch</a> of Carnegie Mellon.</p> <p>“It’s not just that they disproved [Yao’s conjecture], they also found the best possible answer to his question,” said <a href="https://cs.uwaterloo.ca/about/people/sassadi">Sepehr Assadi</a> of the University of Waterloo. “We could have gone another 40 years before we knew the right answer.”</p> </div> </div> </div> </section> </div> <figure class='leading-0 w-full my-0 mx-auto flex items-center justify-center flex-col max-w-img-large py-0 px-0 l:px-0 '> <div class='w-full flex justify-center max-w-mod-large m:max-w-unset image--module s:flex-col s:m-auto'> <div class='w-auto mr-2 last:mr-0 s:m-0 s:flex s:flex-col flex-1'> <img width="2560" height="1621" src="https://www.quantamagazine.org/wp-content/uploads/2025/02/Andrew-Krapivin-cr.PhilippAmmon-Bridge-scaled.webp" class="mb-6 w-full s:mb-4" alt="Andrew Krapivin in a blue checkered shirt leans on a bridge in front of impressive school buildings" decoding="async" srcset="https://www.quantamagazine.org/wp-content/uploads/2025/02/Andrew-Krapivin-cr.PhilippAmmon-Bridge-scaled.webp 2560w, https://www.quantamagazine.org/wp-content/uploads/2025/02/Andrew-Krapivin-cr.PhilippAmmon-Bridge-1720x1089.webp 1720w, https://www.quantamagazine.org/wp-content/uploads/2025/02/Andrew-Krapivin-cr.PhilippAmmon-Bridge-520x329.webp 520w, https://www.quantamagazine.org/wp-content/uploads/2025/02/Andrew-Krapivin-cr.PhilippAmmon-Bridge-768x486.webp 768w, https://www.quantamagazine.org/wp-content/uploads/2025/02/Andrew-Krapivin-cr.PhilippAmmon-Bridge-1536x973.webp 1536w, https://www.quantamagazine.org/wp-content/uploads/2025/02/Andrew-Krapivin-cr.PhilippAmmon-Bridge-2048x1297.webp 2048w" sizes="(max-width: 2560px) 100vw, 2560px" /> </div> </div> <figcaption class='block my-0 mx-auto w-full'> <section class='py-0 px-12 s:p-0 m:px-16'> <div class='w-full my-0 mx-auto flex flex-col s:mx-5 s:w-full-minus-25 s:max-w-mod-inline m:max-w-mod-inline l:flex-row l:max-w-mod-large justify-end s:mb-4'> <div class='caption wysiwyg h5 theme__anchors--solid fill-h w-auto l:w-140'> <p>Krapivin on the King’s College Bridge at the University of Cambridge. His new hash table can find and store data faster than researchers ever thought possible.</p> </div> <div class='attribution theme__anchors--solid wysiwyg pangram h6 mb1 fill-h text-left w-auto before:block l:before:hidden l:w-half-minus-17 l:text-right l:pl-24'> <p>Phillip Ammon for <em>Quanta Magazine</em></p> </div> </div> </section> </figcaption> </figure> <div class='acf-content scale1 mt2'> <section class='outer mha js-router-anchors outer--content'> <div class='flex-auto mha container--xs '> <div class='post__content__section wysiwyg p theme__anchors--underline' data-role='selectable'> <div class='post__content wysiwyg p theme__anchors--underline '> <p>In addition to refuting Yao’s conjecture, the new paper also contains what many consider an even more astonishing result. It pertains to a related, though slightly different, situation: In 1985, Yao looked not only at the worst-case times for queries, but also at the average time taken across all possible queries. He proved that hash tables with certain properties — including those that are labeled “greedy,” which means that new elements must be placed in the first available spot — could never achieve an average time better than log <em>x</em>.</p> <div class="related-list"> <aside class="post__aside mb2 relative hide-on-print post__aside--right"> <h2 class="mv0 h5 bold uppercase kern">Related:</h2> <hr class="mt1 o2"> <ol class="post__aside__list theme__anchors--none pt05"> <li class="mv075 flex"> <h3 class="h5t mt0 mb025 medium"> <a class="theme__accent theme__text-hover" href="https://www.quantamagazine.org/scientists-find-optimal-balance-of-data-storage-and-time-20240208/"> <span class="' . $span_class . '">Scientists Find Optimal Balance of Data Storage and Time</span> </a> </h3> </li> <li class="mv075 flex"> <h3 class="h5t mt0 mb025 medium"> <a class="theme__accent theme__text-hover" href="https://www.quantamagazine.org/new-book-sorting-algorithm-almost-reaches-perfection-20250124/"> <span class="' . $span_class . '">New Book-Sorting Algorithm Almost Reaches Perfection</span> </a> </h3> </li> <li class="mv075 flex"> <h3 class="h5t mt0 mb025 medium"> <a class="theme__accent theme__text-hover" href="https://www.quantamagazine.org/researchers-approach-new-speed-limit-for-seminal-problem-20240129/"> <span class="' . $span_class . '">Researchers Approach New Speed Limit for Seminal Problem</span> </a> </h3> </li> <li class="mv075 flex"> <h3 class="h5t mt0 mb025 medium"> <a class="theme__accent theme__text-hover" href="https://www.quantamagazine.org/computer-scientists-invent-an-efficient-new-way-to-count-20240516/"> <span class="' . $span_class . '">Computer Scientists Invent an Efficient New Way to Count</span> </a> </h3> </li> </ol> </aside> </div> <p>Farach-Colton, Krapivin and Kuszmaul wanted to see if that same limit also applied to non-greedy hash tables. They showed that it did not by providing a counterexample, a non-greedy hash table with an average query time that’s much, much better than log <em>x</em>. In fact, it doesn’t depend on <em>x</em> at all. “You get a number,” Farach-Colton said, “something that is just a constant and doesn’t depend on how full the hash table is.” The fact that you can achieve a constant average query time, regardless of the hash table’s fullness, was wholly unexpected — even to the authors themselves.</p> <p>The team’s results may not lead to any immediate applications, but that’s not all that matters, Conway said. “It’s important to understand these kinds of data structures better. You don’t know when a result like this will unlock something that lets you do better in practice.”</p> </div> </div> </div> </section> </div> <div class='pv2'></div> <div class='post__footer'> <div class='mha container--m'> <div class='flex flex-wrap flex-items-stretch'> <div class='post__footer__col fill-h pv2 flex flex-items-center flex-justify-center'> <section class='outer'> <aside class='post__sidebar hide flex flex-justify-center post__sidebar--footer'> <div class='post__sidebar__content'> <div class='post__sidebar__content__inner'> <div class='align-c mb075'> <div class='sidebar__author'> <a class='theme__accent-hover transition--color ' href='https://www.quantamagazine.org/authors/nadis_steven/'> <div class='sidebar__author__avatar mha mb1'> <div class='image mx0 relative image--circle '> <div class='image__inner absolute fit-x is-loaded'> <img width="1654" height="1720" src="https://www.quantamagazine.org/wp-content/uploads/2023/01/nadis-1654x1720.jpg" class="absolute fit-x 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