Episode Overview

Podcast: New Books Network
Host: Yana Byers
Guest: Thomas Morel, Professor of History of Mathematics, University of Wuppertal, Germany
Book Discussed: Underground Mathematics: Craft Culture and Knowledge Production in Early Modern Europe (Cambridge University Press, 2022)
Release Date: November 21, 2025

This episode delves into the mathematical and craft cultures surrounding mining in early modern Europe, exploring how knowledge was developed, shared, and institutionalized among practitioners, scholars, and officials. Thomas Morel discusses the evolution of "underground mathematics"—a branch tailored for the unique challenges of mining—and how it bridged practical craft and scholarly disciplines. The conversation unpacks the book's key chapters, the messy and cross-disciplinary research process, and the transformation from artisanal knowledge to formal academic instruction.

Key Discussion Points & Insights

1. Thomas Morel’s Path to the Topic (02:58–04:33)

• Morel's initial research was on the institutional history of mathematics (universities, schools).
• His curiosity was piqued by the mining curriculum at the Freiberg Mining Academy.
• He asked: How was mining mathematics practiced before such academies existed?
  • “At some point I asked the question, okay…how were people working in the late Middle Ages and the Renaissance?...how are they doing maps, where they’re like really doing math stuff or whether [they were] just…trying their best?” (03:37)
• Years of archival rabbit holes led to the book.

2. The Geometria Subterranea and Its Challenges (05:04–12:14)

• The Book’s Iconic Frontispiece: Features a “mirror in the center with two persons around it” and “rocks,” highlighting mining's centrality (05:04).
• Mathematical instruments in the illustration indicate the real “treasure” is knowledge and skill, not just material wealth.
• Content of the Book:
  • Practical, practitioner-oriented rather than academic.
  • Sections: Descriptions of instruments; basic arithmetic; a series of down-to-earth ‘propositions’/problems; legal guidance for mining disputes.
  • Notably distinct from university geometry, focused on actual needs of miners.
  • “You will not find the kind of geometry that was being taught in universities...You will find it completely taught for the mathematics of mining.” (07:14)
• Audience:
  • Mining practitioners (underground surveyors, officials).
  • University mathematicians (such as Leibniz), patrons, professors—reflecting the book’s wide reach.
  • The book did not displace the manuscript tradition, but existed alongside it.
  • “We know that practitioners continued to mix these printed books with their own notes and this went on for a few generations.” (11:54)

3. Researching a Messy Subject (12:46–16:43)

• Mining mathematics falls between history of mathematics and history of technology—a neglected field.
• Sources used: Printed manuals, manuscripts, archive mining maps, legal/religious/literary references (Kafka is quoted at the book’s start).
  • “I have like printed sources, I have lots of manuscripts. I also sometimes looked even at religious stuff or even literary stuff...” (14:09)
• The book’s interdisciplinary, “anything goes” methodology reflects the hybrid nature of mining knowledge.

4. Why Mining Mattered in Early Modern Europe (16:57–19:12)

• Mining was economically and politically central—sources of currency, chemicals, materials.
• The Holy Roman Empire excelled due to training pools and rich mines (Saxony, Habsburgs).
• “You need to have the resources, but you also need the people. And that’s something pretty specific to the Holy Roman Empire....They kind of knew how to structure their training pool...” (18:11)

5. The Rise of Mathematical Practice—From “Scientific Revolution” to Mines (19:12–21:08)

• The rise of daily, practical mathematics (in mining) paralleled but differed from the “high science” of figures like Galileo, Newton.
  • “In several ways the story that I’m telling you runs along these lines but in a completely different direction...the daily work of technicians and engineers can also be shaped by mathematical laws.” (19:48)
• Early successes in mining mathematics helped foster broader social faith in mathematical approaches.

6. Renaissance Humanists and Mining (23:17–26:07)

• Example: Georgius Agricola—friend of Erasmus, physician-turned-mining-scholar, wrote De Re Metallica (1556).
• A gap existed between the scholarly discourse (printed books) and hands-on methods (archival maps and practitioner notes).
  • “What scholars were describing as the geometry of mining...did not exactly correspond to what practitioners were doing.” (25:02)
• Morel’s book compares these two spheres to illuminate a richer history.

7. Daily Mining Life and Mathematical Surveying (26:07–28:49)

• Typical miners: Hard, slow, dangerous work, but mining for precious metals less deadly than coal mining.
• Surveyors' geometry was essential for:
  • Efficient tunneling.
  • Mapping galleries and drainage tunnels.
  • Investor confidence and legal clarity.
• “If two galleries exist, how can they meet? Because sometimes you want them to meet. If you want to get rid of water, you have to dig special tunnels...” (27:29)

8. Boom Towns: Annaberg Case Study (28:56–31:13)

• Mining rushes rapidly built up towns like Annaberg (Saxony) in the 16th century.
• Rapid growth attracted miners, investors, scholars, printing presses, schools, etc.
• “...the biggest city of the Holy Roman Empire in just a few years.” (29:50)
• The lure: Fast riches, infused with a new role for mathematical expertise.

9. The Explosion of Cartographic Complexity (32:03–35:40)

• The 17th century saw parallel advances in both world and underground mapping.
• Mining maps were 3D, richly colored, sometimes figurative—for depicting depth, accidents, and galleries.
  • “You have to make maps… These maps have to be, in a way, 3D maps, because you cannot just map the surface of your mountain…” (32:38)
• Modern engineers can still use these old maps for their accuracy.

10. The Academic Institutionalization of Mining (35:57–39:06)

• 18th century: Founding of specialized mining academies (notably in the Holy Roman Empire and Paris).
• Challenge: How to convert a guild-like craft tradition into a formal discipline?
  • “Who can you formalize crafts and know-how that has been just transmitted with oral training and manuscripts for centuries?” (36:52)
• At first, practitioners and professors learned from each other, blending scholarship and hands-on experience.
  • “The first generations learn that both with a practitioner in the mind and also in a classroom with a professor. And only by combining the two approaches...you could make the most of it and produce the engineers...” (38:11)
• This hybrid model seeded the later rise of engineering education.

11. Capstone Case Study: The Deep George Drainage Tunnel (40:50–44:49)

• Massive 18th-century engineering project (10km+ underground drainage tunnel in the Harz region of Germany).
• Required:
  • Decades-long planning, mathematical calculations, and precise mapping.
  • International funding (King of England’s involvement via Hanover).
• The tunnel succeeded, demonstrating the cumulative value of systematic practical mathematics.
  • “This tunnel is the first time that on a distance of 10 kilometers you’re able to plan a thing from the beginning to the very end. And it works.” (42:27)
• “The idea of just keeping the cost and keeping the delays, it’s incredible. But at the time it worked and it worked...because you had this very long tradition of practical mathematics...” (43:44)

12. Morel’s Current Research (45:08–46:20)

• Returning to university studies in the Holy Roman Empire, 18th century.
• Focus on the teaching of practical mathematics (cartography, optics, bookkeeping) as university responsibilities.
• Investigates overlooked links between higher education and applied skills.

Notable Quotes & Memorable Moments

• On archival research:
  • “Anything goes, just take whatever you find and try to mix it together.”
    —Thomas Morel (14:02)
• On the impact of underground mathematics:
  • “One of the reasons why people began to trust mathematics...was what was happening in the mines, which is just the daily experience of the efficiency of this pretty elemental geometry.”
    —Thomas Morel (20:48)
• On craft and scholarship:
  • “Only by combining [practical and scholarly approaches], you could make the most of it and produce the engineers that would then...power the industrial revolution.”
    —Thomas Morel (38:16)
• On discipline-building:
  • “Can you imagine building a school? Wow. And building a discipline, building, you know, an idea around like this should be a discipline. It’s kind of amazing.”
    —Yana Byers (40:20)
• On perseverance and discovery:
  • “At some point you just have to say, okay, that’s enough. Now I need like the time to process it and write it down.”
    —Thomas Morel (16:36)
• On the Deep George Tunnel:
  • “After 22 years, like right at the end of the 18th century, the tunnel just opened. And...it’s pretty amazing if you’re comparing when nowadays the US or European states...build like an airport or any kind of major construction work. The idea of just keeping the cost and keeping the delays, it’s incredible. But at the time it worked...”
    —Thomas Morel (43:30)

Important Timestamps

| Time | Segment / Topic | |----------|--------------------------------------------------| | 02:58 | Morel’s entry into underground mathematics | | 05:04 | The Geometria Subterranea’s frontispiece & content| | 09:58 | Audience for mining mathematics books | | 12:46 | Crossing history of mathematics/technology divide | | 16:57 | Why mining was vital in early modern Europe | | 19:12 | Mines, math and the scientific revolution | | 23:17 | Renaissance humanists and mining | | 26:07 | Daily life and mathematical problems in mining | | 28:56 | Boom towns: Annaberg example | | 32:03 | Maps, cartography, and 3D challenges | | 35:57 | Rise of mining academies and hybrid learning | | 39:06 | Theory and practice in early education | | 40:50 | The Deep George Tunnel—project and impact | | 45:08 | Morel’s latest research—universities & practices |

Tone and Style

The conversation is collegial, lively, steeped in curiosity, and occasionally playful (“sounds dirty” about tunnel names, “neither fish nor fowl” about mixed genres). Both Morel and Byers approach the topic with accessible language, illustrating complex ideas through vivid analogies and historical anecdotes.

Summary for Non-Listeners

Thomas Morel offers an in-depth look at the interwoven worlds of mathematics and mining in early modern Europe—how practical problems underground forced new forms of expertise, documentation, and learning, which fed back into academic and institutional innovation. The episode traverses the nuts and bolts of practical geometry, profiles colorful characters and boom towns, and climaxes with the magisterial Deep George tunnel project as a symbol of emergent engineering discipline.

The episode will be valuable for anyone interested in the history of knowledge, the development of scientific disciplines, and the messy, vibrant world where hands-on craft and learned scholarship meet.