---
title: Represent — from counting to calculus
seo_title: Represent — from counting to calculus — video
description: How symbols, numbers, algebra and calculus made it possible to represent and manipulate the world, building the mathematical foundation of modern AI.
keywords: history of mathematics, symbolic representation, algebra, differential calculus, history of computing, Leibniz Newton, mathematical notation, origins of artificial intelligence
date: '2026-03-26T00:00:00+00:00'
robots: index,follow,max-snippet:-1,max-image-preview:large,max-video-preview:-1
hide:
- toc
- navigation
video_watch_page: true
---


<div class="s5-video-watch" data-s5-video-watch data-video-id="videos-series-from-cave-to-agi-01-representar-md">
  <header class="s5-video-watch__header">
    <div class="s5-video-watch__crumbs"><a href="https://5sigmas.com/en/videos/">All videos</a><span>History of AI</span><span>1:03</span></div>
    <h1>Represent — from counting to calculus</h1><p>How symbols, numbers, algebra and calculus made it possible to represent and manipulate the world, building the mathematical foundation of modern AI.</p>
  </header>
  <div class="s5-video-watch__player">
    <video controls crossorigin="anonymous" preload="metadata" poster="/en/series/from-cave-to-agi/01-representar.jpg" playsinline data-s5-watch-player><source src="/en/series/from-cave-to-agi/01-representar.mp4" type="video/mp4">Your browser does not support the video element.</video>
    <p>Links containing <code>?t=</code> open the video at a specific second.</p>
  </div>
  <section class="s5-video-watch__summary" aria-labelledby="video-summary-title">
    <div class="s5-video-watch__section-head"><span class="s5-eyebrow">Video summary</span><h2 id="video-summary-title">The ideas to retain</h2></div>
    <div class="s5-video-watch__snippet-grid"><article><span>01</span><h2>1. We invented languages to describe the world</h2></article>
<article><span>02</span><h2>Before writing, we were already counting</h2><p>The need to count is far older than writing. Paleolithic notched objects such as the Lebombo bone and the Ishango bone do not by themselves prove the existence of formal mathematics, but…</p></article>
<article><span>03</span><h2>Numbers, position and zero</h2><p>For millennia, different civilizations developed their own ways of representing quantities. The Egyptians used an additive system. The Romans did too. The Babylonians introduced a very…</p></article></div>
  </section>
  
  
  <aside class="s5-video-watch__source"><div><span class="s5-eyebrow">Context and evidence</span><h2>Continue with the full article</h2><p>The chapter develops the mechanism, primary sources, limitations and connections to the rest of the series.</p></div><a class="s5-video-watch__source-link" href="https://5sigmas.com/en/series/from-cave-to-agi/01-representar/">Read the article →</a></aside>
  <section class="s5-video-watch__related" aria-labelledby="related-videos-title"><div class="s5-video-watch__section-head"><span class="s5-eyebrow">Next step</span><h2 id="related-videos-title">Related videos</h2></div><div class="s5-video-watch__related-grid"><article><a href="https://5sigmas.com/en/videos/series/from-cave-to-agi/05-mas-alla/"><img src="https://5sigmas.com/en/series/from-cave-to-agi/05-mas-alla.jpg" alt="" loading="lazy" width="1280" height="720"><span>History of AI · 1:03</span><strong>Beyond the Transformer</strong></a></article>
<article><a href="https://5sigmas.com/en/videos/series/from-cave-to-agi/03-aprender/"><img src="https://5sigmas.com/en/series/from-cave-to-agi/03-aprender.jpg" alt="" loading="lazy" width="1280" height="720"><span>History of AI · 1:03</span><strong>Learn — from rules to data</strong></a></article>
<article><a href="https://5sigmas.com/en/videos/series/from-cave-to-agi/02-mecanizar/"><img src="https://5sigmas.com/en/series/from-cave-to-agi/02-mecanizar.jpg" alt="" loading="lazy" width="1280" height="720"><span>History of AI · 1:03</span><strong>Mechanize — from calculation to computing</strong></a></article></div></section>
</div>