<?xml version="1.0" encoding="UTF-8"?><rss xmlns:dc="http://purl.org/dc/elements/1.1/" xmlns:content="http://purl.org/rss/1.0/modules/content/" xmlns:atom="http://www.w3.org/2005/Atom" version="2.0" xmlns:itunes="http://www.itunes.com/dtds/podcast-1.0.dtd" xmlns:googleplay="http://www.google.com/schemas/play-podcasts/1.0"><channel><title><![CDATA[A Mathematician Lurking in the TechUnderWorld: Exclusive on Substack]]></title><description><![CDATA[Unpublished hot material on the crucial impact of current tech developments. Essential reading for developers, advanced users, and engineers.]]></description><link>https://www.josecrespophd.org/s/exclusive-on-substack</link><image><url>https://substackcdn.com/image/fetch/$s_!gOaz!,w_256,c_limit,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F56c7ab0d-ed6f-4d23-83dc-074a72323366_720x720.png</url><title>A Mathematician Lurking in the TechUnderWorld: Exclusive on Substack</title><link>https://www.josecrespophd.org/s/exclusive-on-substack</link></image><generator>Substack</generator><lastBuildDate>Tue, 07 Jul 2026 11:29:05 GMT</lastBuildDate><atom:link href="https://www.josecrespophd.org/feed" rel="self" type="application/rss+xml"/><copyright><![CDATA[Jose Crespo, PhD]]></copyright><language><![CDATA[en]]></language><webMaster><![CDATA[josecrespo@substack.com]]></webMaster><itunes:owner><itunes:email><![CDATA[josecrespo@substack.com]]></itunes:email><itunes:name><![CDATA[Jose Crespo PhD]]></itunes:name></itunes:owner><itunes:author><![CDATA[Jose Crespo PhD]]></itunes:author><googleplay:owner><![CDATA[josecrespo@substack.com]]></googleplay:owner><googleplay:email><![CDATA[josecrespo@substack.com]]></googleplay:email><googleplay:author><![CDATA[Jose Crespo PhD]]></googleplay:author><itunes:block><![CDATA[Yes]]></itunes:block><item><title><![CDATA[GTA 6 Spoilers: 2026’s Most Ambitious Game Doesn’t Need AI to Think]]></title><description><![CDATA[The best obsolete game ever made is about to show a hundred million players what the AI industry is missing]]></description><link>https://www.josecrespophd.org/p/gta-6-rockstar-builds-a-world-that</link><guid isPermaLink="false">https://www.josecrespophd.org/p/gta-6-rockstar-builds-a-world-that</guid><dc:creator><![CDATA[Jose Crespo PhD]]></dc:creator><pubDate>Tue, 07 Jul 2026 07:58:49 GMT</pubDate><enclosure url="https://substackcdn.com/image/fetch/$s_!Br9i!,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F87bcd356-b572-4e74-8647-ebf42d6832da_1512x1512.png" length="0" type="image/jpeg"/><content:encoded><![CDATA[<div class="captioned-image-container"><figure><a class="image-link image2 is-viewable-img" target="_blank" href="https://substackcdn.com/image/fetch/$s_!Br9i!,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F87bcd356-b572-4e74-8647-ebf42d6832da_1512x1512.png" data-component-name="Image2ToDOM"><div class="image2-inset"><picture><source type="image/webp" srcset="https://substackcdn.com/image/fetch/$s_!Br9i!,w_424,c_limit,f_webp,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F87bcd356-b572-4e74-8647-ebf42d6832da_1512x1512.png 424w, https://substackcdn.com/image/fetch/$s_!Br9i!,w_848,c_limit,f_webp,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F87bcd356-b572-4e74-8647-ebf42d6832da_1512x1512.png 848w, https://substackcdn.com/image/fetch/$s_!Br9i!,w_1272,c_limit,f_webp,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F87bcd356-b572-4e74-8647-ebf42d6832da_1512x1512.png 1272w, https://substackcdn.com/image/fetch/$s_!Br9i!,w_1456,c_limit,f_webp,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F87bcd356-b572-4e74-8647-ebf42d6832da_1512x1512.png 1456w" sizes="100vw"><img src="https://substackcdn.com/image/fetch/$s_!Br9i!,w_1456,c_limit,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F87bcd356-b572-4e74-8647-ebf42d6832da_1512x1512.png" width="1456" height="1456" data-attrs="{&quot;src&quot;:&quot;https://substack-post-media.s3.amazonaws.com/public/images/87bcd356-b572-4e74-8647-ebf42d6832da_1512x1512.png&quot;,&quot;srcNoWatermark&quot;:null,&quot;fullscreen&quot;:null,&quot;imageSize&quot;:null,&quot;height&quot;:1456,&quot;width&quot;:1456,&quot;resizeWidth&quot;:null,&quot;bytes&quot;:4402483,&quot;alt&quot;:null,&quot;title&quot;:null,&quot;type&quot;:&quot;image/png&quot;,&quot;href&quot;:null,&quot;belowTheFold&quot;:false,&quot;topImage&quot;:true,&quot;internalRedirect&quot;:&quot;https://www.josecrespophd.org/i/205498645?img=https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F87bcd356-b572-4e74-8647-ebf42d6832da_1512x1512.png&quot;,&quot;isProcessing&quot;:false,&quot;align&quot;:null,&quot;offset&quot;:false}" class="sizing-normal" alt="" srcset="https://substackcdn.com/image/fetch/$s_!Br9i!,w_424,c_limit,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F87bcd356-b572-4e74-8647-ebf42d6832da_1512x1512.png 424w, https://substackcdn.com/image/fetch/$s_!Br9i!,w_848,c_limit,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F87bcd356-b572-4e74-8647-ebf42d6832da_1512x1512.png 848w, https://substackcdn.com/image/fetch/$s_!Br9i!,w_1272,c_limit,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F87bcd356-b572-4e74-8647-ebf42d6832da_1512x1512.png 1272w, https://substackcdn.com/image/fetch/$s_!Br9i!,w_1456,c_limit,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F87bcd356-b572-4e74-8647-ebf42d6832da_1512x1512.png 1456w" sizes="100vw" fetchpriority="high"></picture><div class="image-link-expand"><div class="pencraft pc-display-flex pc-gap-8 pc-reset"><button tabindex="0" type="button" class="pencraft pc-reset pencraft icon-container restack-image"><svg role="img" width="20" height="20" viewBox="0 0 20 20" fill="none" stroke-width="1.5" stroke="var(--color-fg-primary)" stroke-linecap="round" stroke-linejoin="round" xmlns="http://www.w3.org/2000/svg"><g><title></title><path d="M2.53001 7.81595C3.49179 4.73911 6.43281 2.5 9.91173 2.5C13.1684 2.5 15.9537 4.46214 17.0852 7.23684L17.6179 8.67647M17.6179 8.67647L18.5002 4.26471M17.6179 8.67647L13.6473 6.91176M17.4995 12.1841C16.5378 15.2609 13.5967 17.5 10.1178 17.5C6.86118 17.5 4.07589 15.5379 2.94432 12.7632L2.41165 11.3235M2.41165 11.3235L1.5293 15.7353M2.41165 11.3235L6.38224 13.0882"></path></g></svg></button><button tabindex="0" type="button" class="pencraft pc-reset pencraft icon-container view-image"><svg xmlns="http://www.w3.org/2000/svg" width="20" height="20" viewBox="0 0 24 24" fill="none" stroke="currentColor" stroke-width="2" stroke-linecap="round" stroke-linejoin="round" class="lucide lucide-maximize2 lucide-maximize-2"><polyline points="15 3 21 3 21 9"></polyline><polyline points="9 21 3 21 3 15"></polyline><line x1="21" x2="14" y1="3" y2="10"></line><line x1="3" x2="10" y1="21" y2="14"></line></svg></button></div></div></div></a></figure></div><h3>A Mind-Blowingly Realistic World Built Without Modern AI</h3><p>Let me start with what GTA 6 is not, because almost everyone online right now is about to sell you the wrong idea without bothering to check whether their claims are credible.</p><p>One thing already seems clear: if you are waiting for NPCs with a next-generation brain, forget it. The people walking through Vice City will still be stereotypes with scripts. They will talk, panic, drive, fight, flee, and forget you five seconds later. They will not become tiny conscious agents living inside your console.</p><p><strong>And that is not a failure. It may be the smartest thing Rockstar has done.</strong></p><div class="pullquote"><p>Because the real leap in GTA 6 is not that pedestrians suddenly turn into hallucination-prone chatbots on legs. The leap is Leonida itself: a world so detailed, so physically alive in its light, motion, rotation, weight, and atmosphere, that almost no other video game can touch it.</p></div><p>And the machinery behind that illusion is not magic. It is the old recipe that has always worked: mathematics, geometry, graphs, manifolds, hierarchies, control systems, and classical programming, meaning algorithms and data structures, all shaped by clear goals and better design.</p><p>I heard you&#8230;. <em>how damn can be you so sure if the game still not has been releasead&#8230;. are you making just cheap advertisement disguised with a click-bait title?</em></p><p>Fair question. And yes, you are right to ask it.</p><p>What I can say with confidence about GTA 6 is not based only on Rockstar&#8217;s marketing campaign. It is based mainly on what its own patent filings quietly reveal about essential features and technical innovations, and on the mathematics behind those features.</p><p>That is the material I am using here: public footage, public patents, and the mathematical constraints any world like Leonida must obey.</p><p>Transparent, genuine, and readable for anyone willing to look at the evidence instead of the hype.</p><p>And before we dive into the nuts and bolts behind Leonida, let me say one more thing clearly: GTA 6 may become the reference point for the entire industry for years to come, and it does not need the other great hype of our age: transformer AI stuffed into everything and sold as the future of everything.</p><p>Because the real miracle of GTA 6 is hidden somewhere else.</p><p>In its structure. You will see it for yourself. Enjoy</p><div class="pullquote"><p>GTA 6 is not the triumph of new AI. It is the triumph of old mathematics.</p></div><h3>GTA 6 Is Not Just Bigger. It Is a Bigger Mathematical Problem</h3><p>Rockstar&#8217;s Leonida is its Florida: Vice City, the Keys, wetlands, highways, small towns, rural regions, beaches, interiors, traffic, water, bodies, reflections, light, and thousands of objects that all need to appear continuous.</p><p>And this is where the problem becomes more interesting than the marketing.</p><p>Because bigger worlds already exist. Of course they do. <a href="https://elderscrolls.bethesda.net/en-US/daggerfall">Daggerfall</a> is often cited with its 160K-plus square kilometers of procedural sprawl. <a href="https://bethesda.net/en/game/starfield">Starfield</a> gives you more than a thousand algorithmic planets. <a href="https://www.nomanssky.com/">No Man&#8217;s Sky</a> went completely cosmic with eighteen quintillion worlds. But that kind of scale is bought through generation, not authorship.</p><p>Denser worlds exist too, but they usually shrink the map to make density possible. <a href="https://www.cyberpunk.net/us/en/">Cyberpunk </a>2077&#8217;s Night City is one of the great modern density machines, a city where the open-world formula is compressed so hard that the wilderness almost disappears.</p><p>And hand-authored worlds of huge ambition exist as well, but they often solve the problem by division: different regions, separate maps, stitched continents, repeated activities, controlled transitions. <a href="https://www.thewitcher.com/us/en">The Witcher 3</a> gives you Velen, Novigrad, Skellige, and Toussaint. <a href="https://www.ubisoft.com/en-us/game/assassins-creed">Assassin&#8217;s Creed</a> gives you enormous historical playgrounds, but often through repetition, segmentation, and scale tricks.</p><p>So no, if Rockstar delivers what the trailers, patents, mapping evidence, and its own marketing imply, GTA 6 will not be the largest world ever made. That is not the interesting claim.</p><p>The interesting claim is harder. Leonida may be one continuous world large enough to read as geography, dense enough to behave like a city, and simulated deeply enough to feel alive at that scale.</p><p>That is the rare combination: not a world that is merely big, or merely dense, or merely beautiful&#8230;</p><p>But a continuous, authored, dense, physically convincing space, built to make the hours you spend inside it feel less like playing through a map and more like inhabiting a living world.</p><p><strong>And that is where Leonida stops being only a map and becomes a mathematical problem.</strong></p><p>Because once you compare it with GTA 5&#8217;s San Andreas, the real difficulty appears.</p><p>A larger map is not just extra land. It means every system is under pressure at once: space, traffic, interiors, physics, lighting, reflections, water, pedestrians, vehicles, and the invisible streaming machinery that keeps the illusion from falling apart.</p><p>So here is the first real question behind GTA 6:</p><p>How can a console stitch together patches of geography without gaps, misplacements, trembling edges, broken roads, or objects popping out of existence, when there is no single global map sitting in memory?</p><p>That question sounds technical.</p><p>It is actually the doorway into the whole miracle.</p><div class="captioned-image-container"><figure><a class="image-link image2 is-viewable-img" target="_blank" href="https://substackcdn.com/image/fetch/$s_!33Gb!,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F0429dadf-851c-4db8-83c3-86da341a5042_1512x1512.png" data-component-name="Image2ToDOM"><div class="image2-inset"><picture><source type="image/webp" srcset="https://substackcdn.com/image/fetch/$s_!33Gb!,w_424,c_limit,f_webp,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F0429dadf-851c-4db8-83c3-86da341a5042_1512x1512.png 424w, https://substackcdn.com/image/fetch/$s_!33Gb!,w_848,c_limit,f_webp,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F0429dadf-851c-4db8-83c3-86da341a5042_1512x1512.png 848w, https://substackcdn.com/image/fetch/$s_!33Gb!,w_1272,c_limit,f_webp,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F0429dadf-851c-4db8-83c3-86da341a5042_1512x1512.png 1272w, https://substackcdn.com/image/fetch/$s_!33Gb!,w_1456,c_limit,f_webp,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F0429dadf-851c-4db8-83c3-86da341a5042_1512x1512.png 1456w" sizes="100vw"><img src="https://substackcdn.com/image/fetch/$s_!33Gb!,w_1456,c_limit,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F0429dadf-851c-4db8-83c3-86da341a5042_1512x1512.png" width="1456" height="1456" data-attrs="{&quot;src&quot;:&quot;https://substack-post-media.s3.amazonaws.com/public/images/0429dadf-851c-4db8-83c3-86da341a5042_1512x1512.png&quot;,&quot;srcNoWatermark&quot;:null,&quot;fullscreen&quot;:null,&quot;imageSize&quot;:null,&quot;height&quot;:1456,&quot;width&quot;:1456,&quot;resizeWidth&quot;:null,&quot;bytes&quot;:4402483,&quot;alt&quot;:null,&quot;title&quot;:null,&quot;type&quot;:&quot;image/png&quot;,&quot;href&quot;:null,&quot;belowTheFold&quot;:true,&quot;topImage&quot;:false,&quot;internalRedirect&quot;:&quot;https://www.josecrespophd.org/i/205498645?img=https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F0429dadf-851c-4db8-83c3-86da341a5042_1512x1512.png&quot;,&quot;isProcessing&quot;:false,&quot;align&quot;:null,&quot;offset&quot;:false}" class="sizing-normal" alt="" srcset="https://substackcdn.com/image/fetch/$s_!33Gb!,w_424,c_limit,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F0429dadf-851c-4db8-83c3-86da341a5042_1512x1512.png 424w, https://substackcdn.com/image/fetch/$s_!33Gb!,w_848,c_limit,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F0429dadf-851c-4db8-83c3-86da341a5042_1512x1512.png 848w, https://substackcdn.com/image/fetch/$s_!33Gb!,w_1272,c_limit,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F0429dadf-851c-4db8-83c3-86da341a5042_1512x1512.png 1272w, https://substackcdn.com/image/fetch/$s_!33Gb!,w_1456,c_limit,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2F0429dadf-851c-4db8-83c3-86da341a5042_1512x1512.png 1456w" sizes="100vw" loading="lazy"></picture><div class="image-link-expand"><div class="pencraft pc-display-flex pc-gap-8 pc-reset"><button tabindex="0" type="button" class="pencraft pc-reset pencraft icon-container restack-image"><svg role="img" width="20" height="20" viewBox="0 0 20 20" fill="none" stroke-width="1.5" stroke="var(--color-fg-primary)" stroke-linecap="round" stroke-linejoin="round" xmlns="http://www.w3.org/2000/svg"><g><title></title><path d="M2.53001 7.81595C3.49179 4.73911 6.43281 2.5 9.91173 2.5C13.1684 2.5 15.9537 4.46214 17.0852 7.23684L17.6179 8.67647M17.6179 8.67647L18.5002 4.26471M17.6179 8.67647L13.6473 6.91176M17.4995 12.1841C16.5378 15.2609 13.5967 17.5 10.1178 17.5C6.86118 17.5 4.07589 15.5379 2.94432 12.7632L2.41165 11.3235M2.41165 11.3235L1.5293 15.7353M2.41165 11.3235L6.38224 13.0882"></path></g></svg></button><button tabindex="0" type="button" class="pencraft pc-reset pencraft icon-container view-image"><svg xmlns="http://www.w3.org/2000/svg" width="20" height="20" viewBox="0 0 24 24" fill="none" stroke="currentColor" stroke-width="2" stroke-linecap="round" stroke-linejoin="round" class="lucide lucide-maximize2 lucide-maximize-2"><polyline points="15 3 21 3 21 9"></polyline><polyline points="9 21 3 21 3 15"></polyline><line x1="21" x2="14" y1="3" y2="10"></line><line x1="3" x2="10" y1="21" y2="14"></line></svg></button></div></div></div></a><figcaption class="image-caption"><strong>GTA 6 Is Not Just a Bigger Game. It Is a Bigger Mathematical Problem:</strong>Leonida, the new world of GTA 6, is estimated to be up to 2.5 times larger than GTA 5&#8217;s San Andreas. That scale is not just a bigger surface; it is a larger computational universe. Roads, traffic, pedestrians, buildings, interiors, water, lighting, reflections, object interactions, and environmental behavior all have to work together without collapsing under their own complexity. Continuous navigation must stay precise. Ray tracing and mirror effects must remain stable. Fluids must behave believably. Objects, environments, and characters must react in ways that feel alive. This is why GTA 6 appears to rely less on &#8220;AI magic&#8221; than on advanced mathematics, geometry, algorithms, and classical programming. The evidence comes from Rockstar patents, implementation clues, leaks, trailer analysis, and the hard computational constraints that any world like Leonida must solve</figcaption></figure></div><h4>The answer is not simply more storage. The answer is representation</h4>
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