# \[WSS25\] Searching for holes in the proof space **URL:** \ **Category:** Staff Picks\ **Tags:** ruliology, discrete-mathematics, graphics-and-visualization, graphs-and-networks, group-theory, staff-pick, wolfram-summer-research-institute, mathematics-and-foundations\ **Created:** [July 10, 2025, 12:30am UTC](https://community.wolfram.com/t/wss25-searching-for-holes-in-the-proof-space/25664 "2025-07-10T00:30:27Z")\ **Posts on this page:** 9\ **Page:** 1
**Author:** ![sauldurdenbateman](https://yyz1.discourse-cdn.com/wolfram/user_avatar/community.wolfram.com/sauldurdenbateman/32/32330_2.png) [@sauldurdenbateman](https://community.wolfram.com/u/sauldurdenbateman)\ **Post date:** [July 10, 2025, 12:30am UTC](https://community.wolfram.com/t/wss25-searching-for-holes-in-the-proof-space/25664/1 "2025-07-10T00:30:27Z")
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**Author:** ![wolframcommunity](https://yyz1.discourse-cdn.com/wolfram/user_avatar/community.wolfram.com/wolframcommunity/32/8335_2.png) [@wolframcommunity](https://community.wolfram.com/u/wolframcommunity)\ **Post date:** [July 11, 2025, 11:14pm UTC](https://community.wolfram.com/t/wss25-searching-for-holes-in-the-proof-space/25664/2 "2025-07-11T23:14:05Z")
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**Author:** ![sauldurdenbateman](https://yyz1.discourse-cdn.com/wolfram/user_avatar/community.wolfram.com/sauldurdenbateman/32/32330_2.png) [@sauldurdenbateman](https://community.wolfram.com/u/sauldurdenbateman)\ **Post date:** [July 12, 2025, 6:12pm UTC](https://community.wolfram.com/t/wss25-searching-for-holes-in-the-proof-space/25664/3 "2025-07-12T18:12:24Z")
I am very grateful to you Wolfram Editorial Board, it is an honor to receive this recognition!! ---
**Author:** ![pietroribeiropepe](https://yyz1.discourse-cdn.com/wolfram/user_avatar/community.wolfram.com/pietroribeiropepe/32/38857_2.png) [@pietroribeiropepe](https://community.wolfram.com/u/pietroribeiropepe)\ **Post date:** [July 15, 2025, 1:19am UTC](https://community.wolfram.com/t/wss25-searching-for-holes-in-the-proof-space/25664/4 "2025-07-15T01:19:21Z")
Clever definitions! Seems like the most interesting aspect of this project is exploring this sort of “similarity” relation between proofs, rather than holes themselves. I wonder what else we can tell from a proof (or group of proofs) based on the number of holes in their proof space… Thanks for taking the time to make the post easy to follow! ---
**Author:** ![sauldurdenbateman](https://yyz1.discourse-cdn.com/wolfram/user_avatar/community.wolfram.com/sauldurdenbateman/32/32330_2.png) [@sauldurdenbateman](https://community.wolfram.com/u/sauldurdenbateman)\ **Post date:** [July 15, 2025, 2:06am UTC](https://community.wolfram.com/t/wss25-searching-for-holes-in-the-proof-space/25664/5 "2025-07-15T02:06:06Z")
I really appreciate your comment, Pietro. As you said, while searching for holes in the proof space, I discovered a very interesting phenomenon: the continuous transformation among the proofs for a theorem and, therefore, the equivalence among them. ---
**Author:** ![anon21378091](https://avatars.discourse-cdn.com/v4/letter/a/bcef8e/32.png) [@anon21378091](https://community.wolfram.com/u/anon21378091)\ **Post date:** [July 15, 2025, 3:16pm UTC](https://community.wolfram.com/t/wss25-searching-for-holes-in-the-proof-space/25664/6 "2025-07-15T15:16:22Z")
Lovely writeup, Saul! Glad to see another great metamathematics project come out of WSS. ---
**Author:** ![sauldurdenbateman](https://yyz1.discourse-cdn.com/wolfram/user_avatar/community.wolfram.com/sauldurdenbateman/32/32330_2.png) [@sauldurdenbateman](https://community.wolfram.com/u/sauldurdenbateman)\ **Post date:** [July 15, 2025, 6:50pm UTC](https://community.wolfram.com/t/wss25-searching-for-holes-in-the-proof-space/25664/7 "2025-07-15T18:50:00Z")
Thank you for the compliement!! I really enjoyed working on this project!! ---
**Author:** ![tjanawalkar74](https://yyz1.discourse-cdn.com/wolfram/user_avatar/community.wolfram.com/tjanawalkar74/32/11548_2.png) [@tjanawalkar74](https://community.wolfram.com/u/tjanawalkar74)\ **Post date:** [July 16, 2025, 2:03am UTC](https://community.wolfram.com/t/wss25-searching-for-holes-in-the-proof-space/25664/8 "2025-07-16T02:03:40Z")
A beautiful post and fascinating project on mathematical proofs. Amazing work Saúl, a very well deserved staff pick! ---
**Author:** ![sauldurdenbateman](https://yyz1.discourse-cdn.com/wolfram/user_avatar/community.wolfram.com/sauldurdenbateman/32/32330_2.png) [@sauldurdenbateman](https://community.wolfram.com/u/sauldurdenbateman)\ **Post date:** [July 16, 2025, 11:27am UTC](https://community.wolfram.com/t/wss25-searching-for-holes-in-the-proof-space/25664/9 "2025-07-16T11:27:30Z")
Thank you Tarang!! I truly appreciate your words