---
title: "avigad-mathematics-formal-turn"
description: "arXiv:2311.00007 (math) Submitted on 31 Oct 2023 (v1), last revised 4 Nov 2023 (this version, v2) Title:Mathematics and the formal turn Authors:Jeremy Avigad View PDF Abstract:Since the early twenti…"
doc_version: 1
last_updated: 2026-10-17
canonical_url: "http://parc.yolo.scapegoat.dev/note/research/institute/research/2026/04/16/philosophical-foundations-of-mathematics/sources/web/avigad-mathematics-formal-turn"
---

# avigad-mathematics-formal-turn

arXiv:2311.00007 (math) Submitted on 31 Oct 2023 (v1), last revised 4 Nov 2023 (this version, v2) Title:Mathematics and the formal turn Authors:Jeremy Avigad View PDF > Abstract:Since the early twenti…

## Content

**arXiv:2311.00007** (math)

$$Submitted on 31 Oct 2023 ([v1](https://arxiv.org/abs/2311.00007v1)), last revised 4 Nov 2023 (this version, v2)$$

## Title:Mathematics and the formal turn

Authors:[Jeremy Avigad](https://arxiv.org/search/math?searchtype=author&query=Avigad,+J)

[View PDF](https://arxiv.org/pdf/2311.00007)

> Abstract:Since the early twentieth century, it has been understood that mathematical definitions and proofs can be represented in formal systems systems with precise grammars and rules of use. Building on such foundations, computational proof assistants now make it possible to encode mathematical knowledge in digital form. This article enumerates some of the ways that these and related technologies can help us do mathematics.

| Subjects: | History and Overview (math.HO); Logic (math.LO) |
| --- | --- |
| MSC classes: | 03B35, 68V20 (Primary) 68Q60, 68V15, 68V25, 68V35, 68T01, 97U50 (Secondary) |
| Cite as: | [arXiv:2311.00007](https://arxiv.org/abs/2311.00007) $$math.HO$$ |
|  | (or [arXiv:2311.00007v2](https://arxiv.org/abs/2311.00007v2) $$math.HO$$ for this version) |
|  | [https://doi.org/10.48550/arXiv.2311.00007](https://doi.org/10.48550/arXiv.2311.00007)  arXiv-issued DOI via DataCite |

## Submission history

From: Jeremy Avigad $$[view email](https://arxiv.org/show-email/455ac2bc/2311.00007)$$  
**[$$v1$$](https://arxiv.org/abs/2311.00007v1)** Tue, 31 Oct 2023 00:05:12 UTC (26 KB)  
**$$v2$$** Sat, 4 Nov 2023 14:44:47 UTC (26 KB)  

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