Reference Lists: Mathematical Articles on Fiber Arts

While these lists are intended to be comprehensive, they certainly are not. If you know of any other articles, either academic or non-, please send me references. Note that there is a substantial computer science literature not reflected here.
Last updated March 2026.

Articles/chapters appearing in academic publications

Knitting: Alphabetical

belcastro, s-m; Yackel, Carolyn. About Knitting. Math Horizons, November 2006.
belcastro, sarah-marie. Every Topological Surface Can Be Knit: A Proof, Journal of Mathematics and the Arts 3(2) June 2009, 67--83.
belcastro, sarah-marie. Generalized Helix Striping, in Crafting by Concepts, A K Peters (2011), pp. 28--49. (Focuses on knitting stripes.)
belcastro, sarah-marie. Knitting Torus Knots and Links, in Figuring Fibers, American Mathematical Society (2018), pp. 119--136.
belcastro, s-m; Szczepanski, Amy; Yackel, Carolyn. (K)not Cables, Braids, in Making Mathematics with Needlework, A K Peters (2007), pp. 118--134. Reprinted in Mitt. Dtsch. Math.-Ver. 16 (2008), no. 1, 26--34, and EMS newsletter, Issue 70, December 2008, pp. 19--25. (Focuses on knitting braid words.)
belcastro, s-m. Only Two Knit Stitches Can Create a Torus, in Making Mathematics with Needlework, A K Peters (2007), pp. 53--68.
belcastro, s-m; Yackel, Carolyn. Stop Those Pants!, in Making Mathematics with Needlework, A K Peters (2007), pp. 154--176. (Focuses on knitting a hyperbolic surface.)
Bernasconi, Anna; Bodei, Chiara; Pagli, Linda. Knitting for Fun: A Recursive Sweater. in Fun with Algorithms, Lecture Notes in Computer Science, Volume 4475, Springer, 2007, 53--65. article (.pdf)
Bernasconi, Anna; Bodei, Chiara; Pagli, Linda. On formal descriptions for knitting recursive patterns. Journal of Mathematics and the Arts, 2(1) March 2008, 9--27.
Cochrane, Paul. Knitting Maths. Mathematics Teaching September 1988, pp. 26--28.
Counts, Jared. Knitting with Directed Graphs. Thesis: M. Eng., Massachusetts Institute of Technology, Department of Electrical Engineering and Computer Science, 2018.
Crum Brown, Alexander. 'On a Case of Interlacing Surfaces'. Proceedings of the Royal Society of Edinburgh volume 13 (1885--6), pp. 382--386. (see related models.)
Dennett, Emily. Randomizing Your Digits: Generatively Knit Mittens, in Proceedings of Bridges 2022: Mathematics, Art, Music, Architecture, Culture, ed. D. Reimann, , D. Norton, and E. Torrence, 281--284.
Drukker, Nadav; Paznokas, Elise; Schrimpel, Dominik. Knitting Knots & the Framing Anomaly, in Proceedings of Bridges 2022: Mathematics, Art, Music, Architecture, Culture, ed. D. Reimann, , D. Norton, and E. Torrence, 245--252.
Funahashi, Tatsushi; Yamada, Masashi; Seki, Hirohisa; Itoh, Hidenori. A technique for representing cloth shapes and generating 3-dimensional knitting shapes. Forma 14 (1999), no. 3, 239--248.
Givens, Berit N. The Chinese Remainder Theorem and Knitting Stitch Patterns, in Figuring Fibers, American Mathematical Society (2018), pp. 101--117.
Givens, Berit Nilsen. The trinomial triangle knitted shawl. Journal of Mathematics and the Arts, 2023, Vol. 17, No. 1--2, 178--193.
Goldstine, Susan. A Recursion in Knitting, in Proceedings of Bridges 2016: Mathematics, Music, Art, Architecture, Education, Culture, ed. E. Torrence, B. Torrence, C. Sequin, D. McKenna, K. Fenyvesi, R. Sarhangi, 395--398.
Goldstine, Susan. Self-Diagramming Lace, in Proceedings of Bridges 2018: Mathematics, Art, Music, Architecture, Education, Culture, ed. E. Torrence, B. Torrence, C. Sequin, K. Fenyvesi, 519--522
Goldstine, Susan; Yackel, Carolyn. A mathematical analysis of mosaic knitting: constraints,combinatorics, and colour-swapping symmetries. Journal of Mathematics and the Arts, 2022, Vol. 16, No. 3, 183--217.
Grishanov, S.A.; Cassidy, T; Spencer, D.J. A model of the loop formation process on knitting machines using finite automata theory. Applied Mathematical Modelling 21(7) July 1997, 455--465.
Hofmann, Megan; Albaugh, Lea; Sethapakdi, Ticha; Hodgins, Jessica; Hudson, Scott; McCann, Jim; Mankoff, Jen. KnitPicking Textures: Programming and Modifying Complex Knitted Textures for Machine and Hand Knitting, UIST '19: Proceedings of the 32nd Annual ACM Symposium on User Interface Software and Technology, p. 5--16.
Holden, Lana. Picking Up Stitches and Diophantine Equations, in Making Mathematics with Needlework, A K Peters (2007), pp. 29--39. (Focuses on knitting in different directions.)
Igarashi, Yuki; Igarashi, Takeo; Suzuki, Hiromasa. Knitting a 3D Model. Computer Graphics Forum (Proceedings of Pacific Graphics 2008), 27(7), Oct. 2008, 1737--1743.
Irving, Claire. Making the Real Projective Plane. Math. Gazette November 2005, 417--423. (This focuses on knitted models.)
Isaksen, Daniel; Petrofsky, Al. Mobius knitting, in Bridges: Mathematical Connections in Art, Music, and Science, Conference Proceedings 1999, ed. R. Sarhangi, 1999, 67--76. article
Jensen, Sara. Sequence Knitting. Journal of Mathematics and the Arts, 2023, Vol. 17, No. 1--2, 111--139.
Kaldor, Jonathan M.; James, Doug L.; Marschner, Steve. Simulating knitted cloth at the yarn level. International Conference on Computer Graphics and Interactive Techniques, ACM SIGGRAPH 2008 papers, Article No. 65. ACM Press, 2008. two versions of the paper.
Kapllani, Levi; Amanatides, Chelsea; Dion, Genevieve; Shapiro, Vadim, Breen, David E. TopoKnit: A Process-Oriented Representation for Modeling the Topology of Yarns in Weft-Knitted Textiles, Graphical Models, Volume 118, 2021, 101114. (arXiv version.)
Knittel, Chelsea E.; Tanis, Michael; Stoltzfus, Amy L.; Castle, Toen; Kamien, Randall D.; Dion, Genevieve. Modelling textile structures using bicontinuous surfaces, Journal of Mathematics and the Arts, 14:4 (2020) , pp. 331--344.
Lin, Jenny; McCann, Jim. An Artin Braid Group Representation of Knitting Machine State with Applications to Validation and Optimization of Fabrication Plans, 2021 IEEE International Conference on Robotics and Automation (ICRA) p. 1147---1153. (NSF PAR PDF)
Lin, Jenny; Narayanan, Vidya; Ikarashi, Yuka; Ragan-Kelley, Jonathan; Bernstein, Gilbert; and James McCann. 2023. Semantics and Scheduling for Machine Knitting Compilers. ACM Trans. Graph. 42, 4, Article 143 (August 2023).
Mahmoudi, Sonia; Dresselhaus, Elizabeth; Dimitriyev, Michael. An Orbifold Framework for Classifying Layer Groups with an Application to Knitted Fabrics, arXiv preprint 2025.
Mallos, James. Triangle-Strip Knitting. Hyperseeing: Proceedings of ISAMA 2010 Summer 2010, 111--116.
Markande, Shashank; Matsumoto, Elisabetta. Knotty Knits are Tangles in Tori, in Proceedings of Bridges 2020: Mathematics, Art, Music, Architecture, Education, Culture, ed. C. Yackel, R. Bosch, E. Torrence, and K. Fenyvesi, 103--112.
Matsumoto, Elisabetta; Segerman, Henry; Serriere, Fabienne. Mobius Cellular Automata Scarves, in Proceedings of Bridges 2018: Mathematics, Art, Music, Architecture, Education, Culture, ed. E. Torrence, B. Torrence, C. Sequin, K. Fenyvesi, 523--526.
McCann, James; Albaugh, Lea; Narayanan, Vidya; Grow, April; Matusik, Wojciech; Mankoff, Jennifer; Hodgins, Jessica. A compiler for 3D machine knitting. ACM Transactions on Graphics (TOG) - Proceedings of ACM SIGGRAPH 2016 Volume 35 Issue 4, July 2016, Article No. 49.
Mitra, Rahul; Couplet, Matte; Wang, Tongtong; Hoffman, Megan; Wu, Kui; Chien, Edward. Curl Quantization for Automatic Placement of Knit Singularities, in SIGGRAPH Conference Papers '25: Proceedings of the Special Interest Group on Computer Graphics and Interactive Techniques Conference Conference Papers, 2025, Article No.: 158, pp. 1--10.
Narayanan, Vidya; Albaugh, Lea; Hodgins, Jessica; Coros, Stelian; McCann, James. Automatic Machine Knitting of 3D Meshes, ACM Transactions on Graphics, Volume 37, Issue 3, June 2018, Article No.: 35, pp. 1--15.
Narayanan, Vidya; Wu, Kui; Yuksel, Cem; McCann, James. Visual Knitting Machine Programming, ACM Trans. Graph. 38, 4, Article 63 (July 2019), 13 pages.
Peters, Emily. A Knitted Cross-Cap, in Crafting by Concepts, A K Peters (2011), pp. 50--57.
Reid, Miles. The Knitting of Surfaces. Eureka - The Journal of the Archimedeans 34 (1971), pp. 21--26.
Reid, Miles. Needlework Section: Knitting 2-Manifolds, 1. 2-Manifold 2, Autumn 1982, 9--14.
Reid, Miles. Needlework Section: Knitting 2-Manifolds, 2: the Boy's Surface. 2-Manifold, (the next issue), 10--21.
Roth, Kimberly. A mathematician knits an afghan and counts the number of possible patterns. Journal of Mathematics and the Arts, 2023, Vol. 17, No. 1--2, 85--98.
Seaton, Katherine. Devising a `Purist Knitting Aesthetic' Six-Colored Mobius Band, in Proceedings of Bridges 2021: Mathematics, Art, Music, Architecture, Culture, ed. D. Swart, F. Farris, and E. Torrence, 355--358.
Shimamoto, Daisuke; Shimamoto, Keiko; Mahmoudi, Sonia; Poincloux, Samuel. Topological Defect Propagation to Classify Knitted Fabrics, arXiv preprint 2025.
Szczepanski, Amy. Knit Knit Revolution, in Crafting by Concepts, A K Peters (2011), pp. 1--27.
Taalman, Laura. Knit Knots: Large-Scale Soft Conformations of Minimum-Ropelength Knots and Links., in Proceedings of Bridges 2023: Mathematics, Art, Music, Architecture, Culture, ed J. Holdener,, E. Torrence, C. Fong, and K. Seaton, 369--372.
Vandermonde, Alexandre-The'ophile. Remarques sur les Probl`emes de Situation. Histoire de l' Acade'mie des Sciences (Paris) (1771), 566--574. (Mainly about knight's tours on chessboards, he does describe paths through space for rows of stockinette.)
Wilmer, Elizabeth. Knitted Origami. Journal of Mathematics and the Arts, 2023, Vol. 17, No. 1--2, 9--21.
Wu, Kui; Gao, Xifeng; Ferguson, Zachary; Panozzo, Daniele; Yuksel, Cem. Stitch Meshing. ACM Trans. Graph. 37, 4, Article 130 (August 2018), 14 pages.
Wu, Kui; Swan, Hannah; Yuksel, Cem. Knittable Stitch Meshes. ACM 82 Trans. Graph. 36, 4, Article 1 (July 2018), 13 pages.
Yackel, Carolyn. Socks with Algebraic Structure, in Making Mathematics with Needlework, A K Peters (2007), pp. 90--103. (Focuses on knitting and group theory.)
Yackel, Carolyn. Templeton Square Truchet Tiles, in Figuring Fibers, American Mathematical Society (2018), pp. 59--80.
Yuksel, Cem; Kaldor, Jonathan; James, Doug L.; Marschner, Steve. Stitch Meshes for Modeling Knitted Clothing with Yarn-level Detail. ACM Transactions on Graphics (TOG), Volume 31, Issue 4 (July 2012) Article No.: 37, pp. 1--12

Knitting: Chronological

Prior to 2000

Vandermonde, Alexandre-The'ophile. Remarques sur les Probl`emes de Situation. Histoire de l' Acade'mie des Sciences (Paris) (1771), 566--574. (Mainly about knight's tours on chessboards, he does describe paths through space for rows of stockinette.)
Crum Brown, Alexander. 'On a Case of Interlacing Surfaces'. Proceedings of the Royal Society of Edinburgh volume 13 (1885--6), pp. 382--386. (see related models.)
Reid, Miles. The Knitting of Surfaces. Eureka - The Journal of the Archimedeans 34 (1971), pp. 21--26.
Reid, Miles. Needlework Section: Knitting 2-Manifolds, 1. 2-Manifold 2, Autumn 1982, 9--14.
Reid, Miles. Needlework Section: Knitting 2-Manifolds, 2: the Boy's Surface. 2-Manifold, (the next issue), 10--21.
Cochrane, Paul. Knitting Maths. Mathematics Teaching September 1988, pp. 26--28.
Isaksen, Daniel; Petrofsky, Al. Mobius knitting, in Bridges: Mathematical Connections in Art, Music, and Science, Conference Proceedings 1999, ed. R. Sarhangi, 1999, 67--76. article
Grishanov, S.A.; Cassidy, T; Spencer, D.J. A model of the loop formation process on knitting machines using finite automata theory. Applied Mathematical Modelling 21(7) July 1997, 455--465.
Funahashi, Tatsushi; Yamada, Masashi; Seki, Hirohisa; Itoh, Hidenori. A technique for representing cloth shapes and generating 3-dimensional knitting shapes. Forma 14 (1999), no. 3, 239--248.

2000--2009

Irving, Claire. Making the Real Projective Plane. Math. Gazette November 2005, 417--423. (This focuses on knitted models.)
belcastro, s-m; Yackel, Carolyn. About Knitting. Math Horizons, November 2006.
belcastro, s-m; Szczepanski, Amy; Yackel, Carolyn. (K)not Cables, Braids, in Making Mathematics with Needlework, A K Peters (2007), pp. 118--134. Reprinted in Mitt. Dtsch. Math.-Ver. 16 (2008), no. 1, 26--34, and EMS newsletter, Issue 70, December 2008, pp. 19--25. (Focuses on knitting braid words.)
belcastro, s-m. Only Two Knit Stitches Can Create a Torus, in Making Mathematics with Needlework, A K Peters (2007), pp. 53--68.
belcastro, s-m; Yackel, Carolyn. Stop Those Pants!, in Making Mathematics with Needlework, A K Peters (2007), pp. 154--176. (Focuses on knitting a hyperbolic surface.)
Holden, Lana. Picking Up Stitches and Diophantine Equations, in Making Mathematics with Needlework, A K Peters (2007), pp. 29--39. (Focuses on knitting in different directions.)
Yackel, Carolyn. Socks with Algebraic Structure, in Making Mathematics with Needlework, A K Peters (2007), pp. 90--103. (Focuses on knitting and group theory.)
Bernasconi, Anna; Bodei, Chiara; Pagli, Linda. Knitting for Fun: A Recursive Sweater. in Fun with Algorithms, Lecture Notes in Computer Science, Volume 4475, Springer, 2007, 53--65. article (.pdf)
Bernasconi, Anna; Bodei, Chiara; Pagli, Linda. On formal descriptions for knitting recursive patterns. Journal of Mathematics and the Arts, 2(1) March 2008, 9--27.
Igarashi, Yuki; Igarashi, Takeo; Suzuki, Hiromasa. Knitting a 3D Model. Computer Graphics Forum (Proceedings of Pacific Graphics 2008), 27(7), Oct. 2008, 1737--1743.
Kaldor, Jonathan M.; James, Doug L.; Marschner, Steve. Simulating knitted cloth at the yarn level. International Conference on Computer Graphics and Interactive Techniques, ACM SIGGRAPH 2008 papers, Article No. 65. ACM Press, 2008. two versions of the paper.
belcastro, sarah-marie. Every Topological Surface Can Be Knit: A Proof, Journal of Mathematics and the Arts 3(2) June 2009, 67--83.

2010--2019

Mallos, James. Triangle-Strip Knitting. Hyperseeing: Proceedings of ISAMA 2010, Summer 2010, 111--116.
belcastro, sarah-marie. Generalized Helix Striping, in Crafting by Concepts, A K Peters (2011), pp. 28--49. (Focuses on knitting stripes.)
Peters, Emily. A Knitted Cross-Cap, in Crafting by Concepts, A K Peters (2011), pp. 50--57.
Szczepanski, Amy. Knit Knit Revolution, in Crafting by Concepts, A K Peters (2011), pp. 1--27.
Yuksel, Cem; Kaldor, Jonathan; James, Doug L.; Marschner, Steve. Stitch Meshes for Modeling Knitted Clothing with Yarn-level Detail. ACM Transactions on Graphics (TOG), Volume 31, Issue 4 (July 2012) Article No.: 37, pp. 1--12
Goldstine, Susan. A Recursion in Knitting, in Proceedings of Bridges 2016: Mathematics, Music, Art, Architecture, Education, Culture, ed. E. Torrence, B. Torrence, C. Sequin, D. McKenna, K. Fenyvesi, R. Sarhangi, 395--398.
McCann, James; Albaugh, Lea; Narayanan, Vidya; Grow, April; Matusik, Wojciech; Mankoff, Jennifer; Hodgins, Jessica. A compiler for 3D machine knitting. ACM Transactions on Graphics (TOG) - Proceedings of ACM SIGGRAPH 2016 Volume 35 Issue 4, July 2016, Article No. 49.
Counts, Jared. Knitting with Directed Graphs. Thesis: M. Eng., Massachusetts Institute of Technology, Department of Electrical Engineering and Computer Science, 2018.
Narayanan, Vidya; Albaugh, Lea; Hodgins, Jessica; Coros, Stelian; McCann, James. Automatic Machine Knitting of 3D Meshes, ACM Transactions on Graphics, Volume 37, Issue 3, June 2018, Article No.: 35, pp. 1--15.
Wu, Kui; Swan, Hannah; Yuksel, Cem. Knittable Stitch Meshes. ACM 82 Trans. Graph. 36, 4, Article 1 (July 2018), 13 pages.
Matsumoto, Elisabetta; Segerman, Henry; Serriere, Fabienne. Mobius Cellular Automata Scarves, in Proceedings of Bridges 2018: Mathematics, Art, Music, Architecture, Education, Culture, ed. E. Torrence, B. Torrence, C. Sequin, K. Fenyvesi, 523--526.
Goldstine, Susan. Self-Diagramming Lace, in Proceedings of Bridges 2018: Mathematics, Art, Music, Architecture, Education, Culture, ed. E. Torrence, B. Torrence, C. Sequin, K. Fenyvesi, 519--522
Wu, Kui; Gao, Xifeng; Ferguson, Zachary; Panozzo, Daniele; Yuksel, Cem. Stitch Meshing. ACM Trans. Graph. 37, 4, Article 130 (August 2018), 14 pages.
Yackel, Carolyn. Templeton Square Truchet Tiles, in Figuring Fibers, American Mathematical Society (2018), pp. 59--80.
Givens, Berit N. The Chinese Remainder Theorem and Knitting Stitch Patterns, in Figuring Fibers, American Mathematical Society (2018), pp. 101--117.
belcastro, sarah-marie. Knitting Torus Knots and Links, in Figuring Fibers, American Mathematical Society (2018), pp. 119--136.
Hofmann, Megan; Albaugh, Lea; Sethapakdi, Ticha; Hodgins, Jessica; Hudson, Scott; McCann, Jim; Mankoff, Jen. KnitPicking Textures: Programming and Modifying Complex Knitted Textures for Machine and Hand Knitting, UIST '19: Proceedings of the 32nd Annual ACM Symposium on User Interface Software and Technology, p. 5--16.
Narayanan, Vidya; Wu, Kui; Yuksel, Cem; McCann, James. Visual Knitting Machine Programming, ACM Trans. Graph. 38, 4, Article 63 (July 2019), 13 pages.

2021--2024

Markande, Shashank; Matsumoto, Elisabetta. Knotty Knits are Tangles in Tori, in Proceedings of Bridges 2020: Mathematics, Art, Music, Architecture, Education, Culture, ed. C. Yackel, R. Bosch, E. Torrence, and K. Fenyvesi, 103--112.
Knittel, Chelsea E.; Tanis, Michael; Stoltzfus, Amy L.; Castle, Toen; Kamien, Randall D.; Dion, Genevieve. Modelling textile structures using bicontinuous surfaces, Journal of Mathematics and the Arts, 14:4 (2020) , pp. 331--344.
Kapllani, Levi; Amanatides, Chelsea; Dion, Genevieve; Shapiro, Vadim, Breen, David E. TopoKnit: A Process-Oriented Representation for Modeling the Topology of Yarns in Weft-Knitted Textiles, Graphical Models, Volume 118, 2021, 101114. (arXiv version.)
Seaton, Katherine. Devising a `Purist Knitting Aesthetic' Six-Colored Mobius Band, in Proceedings of Bridges 2021: Mathematics, Art, Music, Architecture, Culture, ed. D. Swart, F. Farris, and E. Torrence, 355--358.
Lin, Jenny; McCann, Jim. An Artin Braid Group Representation of Knitting Machine State with Applications to Validation and Optimization of Fabrication Plans, 2021 IEEE International Conference on Robotics and Automation (ICRA) p. 1147---1153. (NSF PAR PDF)
Goldstine, Susan; Yackel, Carolyn. A mathematical analysis of mosaic knitting: constraints,combinatorics, and colour-swapping symmetries. Journal of Mathematics and the Arts, 2022, Vol. 16, No. 3, 183--217.
Drukker, Nadav; Paznokas, Elise; Schrimpel, Dominik. Knitting Knots & the Framing Anomaly, in Proceedings of Bridges 2022: Mathematics, Art, Music, Architecture, Culture, ed. D. Reimann, , D. Norton, and E. Torrence, 245--252.
Dennett, Emily. Randomizing Your Digits: Generatively Knit Mittens, in Proceedings of Bridges 2022: Mathematics, Art, Music, Architecture, Culture, ed. D. Reimann, , D. Norton, and E. Torrence, 281--284.
Givens, Berit Nilsen. The trinomial triangle knitted shawl. Journal of Mathematics and the Arts, 2023, Vol. 17, No. 1--2, 178--193.
Gray, Kathryn; Bell, Brian; Kobourov, Stephen. A Graph Model and a Layout Algorithm for Knitting Patterns. preprint cs > arXiv:2406.13800.
Gray, Kathryn; Bell, Brian; Sieper, Diana; Kobourov, Stephen; Schreiber, Falk; Klein, Karsten; Hong, Seokhee. Wooly Graphs : A Mathematical Framework For Knitting. preprint cs > arXiv:2407.00511.
Jensen, Sara. Sequence Knitting. Journal of Mathematics and the Arts, 2023, Vol. 17, No. 1--2, 111--139.
Roth, Kimberly. A mathematician knits an afghan and counts the number of possible patterns. Journal of Mathematics and the Arts, 2023, Vol. 17, No. 1--2, 85--98.
Wilmer, Elizabeth. Knitted Origami. Journal of Mathematics and the Arts, 2023, Vol. 17, No. 1--2, 9--21.
Taalman, Laura. Knit Knots: Large-Scale Soft Conformations of Minimum-Ropelength Knots and Links., in Proceedings of Bridges 2023: Mathematics, Art, Music, Architecture, Culture, ed J. Holdener,, E. Torrence, C. Fong, and K. Seaton, 369--372.
Lin, Jenny; Narayanan, Vidya; Ikarashi, Yuka; Ragan-Kelley, Jonathan; Bernstein, Gilbert; and James McCann. 2023. Semantics and Scheduling for Machine Knitting Compilers. ACM Trans. Graph. 42, 4, Article 143 (August 2023).
Gray, Kathryn; Bell, Brian; Kobourov, Stephen. A Graph Model and a Layout Algorithm for Knitting Patterns. preprint cs > arXiv:2406.13800.
Gray, Kathryn; Bell, Brian; Sieper, Diana; Kobourov, Stephen; Schreiber, Falk; Klein, Karsten; Hong, Seokhee. Wooly Graphs : A Mathematical Framework For Knitting. preprint cs > arXiv:2407.00511.

2025--

Mitra, Rahul; Couplet, Matte; Wang, Tongtong; Hoffman, Megan; Wu, Kui; Chien, Edward. Curl Quantization for Automatic Placement of Knit Singularities, in SIGGRAPH Conference Papers '25: Proceedings of the Special Interest Group on Computer Graphics and Interactive Techniques Conference Conference Papers, 2025, Article No.: 158, pp. 1--10.
Shimamoto, Daisuke; Shimamoto, Keiko; Mahmoudi, Sonia; Poincloux, Samuel. Topological Defect Propagation to Classify Knitted Fabrics, arXiv preprint 2025.
Mahmoudi, Sonia; Dresselhaus, Elizabeth; Dimitriyev, Michael. An Orbifold Framework for Classifying Layer Groups with an Application to Knitted Fabrics, arXiv preprint 2025.

Everything Recent (2024-- ): Chronological

Gray, Kathryn; Bell, Brian; Kobourov, Stephen. A Graph Model and a Layout Algorithm for Knitting Patterns. preprint cs > arXiv:2406.13800.
Gray, Kathryn; Bell, Brian; Sieper, Diana; Kobourov, Stephen; Schreiber, Falk; Klein, Karsten; Hong, Seokhee. Wooly Graphs : A Mathematical Framework For Knitting. preprint cs > arXiv:2407.00511.
Defant, Colin; Kravitz, Noah. Loops and regions in Hitomezashi patterns. Discrete Mathematics Volume 347, Issue 1, January 2024, 113693.
Alhaddad, Shemsi. Best Practices for Data Embroidery, Proceedings of Bridges 2024: Mathematics, Art, Music, Architecture, Culture, ed H. Verrill, K. Kattchee, S.L. Gould, and E. Torrence, 243--250.
Gerofsky, Susan; Milner, Samuel. Sprang: Exploring an Ancient Form of Textile Weaving Through Handwork, Movement and Poetry, Proceedings of Bridges 2024: Mathematics, Art, Music, Architecture, Culture, ed H. Verrill, K. Kattchee, S.L. Gould, and E. Torrence, 573--580.
Marks, Lisa; Rohm, Owen. Connected Weaving: What Computational Patterning Can Contribute to Complex Weaving Utilization, Proceedings of Bridges 2024: Mathematics, Art, Music, Architecture, Culture, ed H. Verrill, K. Kattchee, S.L. Gould, and E. Torrence, 235--242.
Sen, Antara; Martinez, Megan. Attainable Symmetry in Generalized Hitomezashi Patterns, Proceedings of Bridges 2024: Mathematics, Art, Music, Architecture, Culture, ed H. Verrill, K. Kattchee, S.L. Gould, and E. Torrence, 227--234.
Stecher, Bobby; Yackel, Carolyn. Dyeing to Make an Orbifold, Proceedings of Bridges 2024: Mathematics, Art, Music, Architecture, Culture, ed H. Verrill, K. Kattchee, S.L. Gould, and E. Torrence, 545--552.
Wildstrom, D. Jacob. Enclave Depth in Hitomezashi Stitchery, Proceedings of Bridges 2024: Mathematics, Art, Music, Architecture, Culture, ed H. Verrill, K. Kattchee, S.L. Gould, and E. Torrence, 357--360.
Mahmoudi, Sonia. On the classification of periodic weaves and universal cover of links in thickened surfaces, Commun. Korean Math. Soc. 2024; 39(4): 997--1025.
Wu, Jiangmei. The artistry and algorithms in fabric origami tessellations. Journal of Mathematics and the Arts, 2024, Vol. 18, No. 3--4, 201--221.
Knoll, Eva; McLellan, Karyn; Cox, Danielle. The rhizomic tiles at Shooter's Hill: an application of Truchet tiles. Journal of Mathematics and the Arts, 2024, Vol. 18, No. 3--4, 222--243.
Thomas, R.S.D. Colouring isonemal fabrics with more than two colours and non-twilly redundancy, preprint 2024.
Ren, Qiuyu; Zhang, Shengtong. Toroidal Hitomezashi patterns. Discrete Mathematics Volume 348, Issue 1, January 2025, 114231
Ren, Qiuyu; Zhang, Shengtong. A Succinct Proof of Defant and Kravitz's Theorem on the Length of Hitomezashi Loops. Ann. Comb. 29, 117--122 (2025).
Seaton, Katherine. A stitch in line: mathematics and one-stitch Sashiko. AK Peters/CRC Press, 2025, 182 pp., ISBN: 9781032487205.
Fisher, Gwen. Book Review: A stitch in line: mathematics and one-stitch Sashiko. Journal of Mathematics and the Arts, 2025, Vol. 19, No. 1--2, 64--66.
Mitra, Rahul; Couplet, Matte; Wang, Tongtong; Hoffman, Megan; Wu, Kui; Chien, Edward. Curl Quantization for Automatic Placement of Knit Singularities, in SIGGRAPH Conference Papers '25: Proceedings of the Special Interest Group on Computer Graphics and Interactive Techniques Conference Conference Papers, 2025, Article No.: 158, pp. 1--10.
Dong, Shiying. Topological Crochet, Proceedings of Bridges 2025: Mathematics and the Arts, ed. T. Verhoeff, D. Swart, S.L. Gould, and E. Torrence, 77--84.
Gielen, Alice Yukari. Sliver Fiber Printer: Sequence Coloring on Yarn, Proceedings of Bridges 2025: Mathematics and the Arts, ed. T. Verhoeff, D. Swart, S.L. Gould, and E. Torrence, 415--418.
Inglis, Tiffany. Soccer Ball Torus: From Theory Crafting to Fibre Crafting, Proceedings of Bridges 2025: Mathematics and the Arts, ed. T. Verhoeff, D. Swart, S.L. Gould, and E. Torrence, 161--168.
Lipschütz, Henriette-Sophie; Reitebuch, Ulrich; Polthier, Konrad; Skrodzki, Martin. Braidings from Braids and Weavings, Proceedings of Bridges 2025: Mathematics and the Arts, ed. T. Verhoeff, D. Swart, S.L. Gould, and E. Torrence, 199--206.
Seaton, Katherine. Dilute Hitomezashi on the Isometric Grid, Proceedings of Bridges 2025: Mathematics and the Arts, ed. T. Verhoeff, D. Swart, S.L. Gould, and E. Torrence, 451--454.
Wildstrom, D. Jacob. Single-Strand, Two-Sided Cross-Stitch, Proceedings of Bridges 2025: Mathematics and the Arts, ed. T. Verhoeff, D. Swart, S.L. Gould, and E. Torrence, 365--372.
Zinn, Charles. Crocheting Knots with Curved Surfaces, Proceedings of Bridges 2025: Mathematics and the Arts, ed. T. Verhoeff, D. Swart, S.L. Gould, and E. Torrence, 381--386.
Shimamoto, Daisuke; Shimamoto, Keiko; Mahmoudi, Sonia; Poincloux, Samuel. Topological Defect Propagation to Classify Knitted Fabrics, arXiv preprint 2025.
Mahmoudi, Sonia; Dresselhaus, Elizabeth; Dimitriyev, Michael. An Orbifold Framework for Classifying Layer Groups with an Application to Knitted Fabrics, arXiv preprint 2025.

Articles appearing in nonacademic publications

sarah-marie belcastro, Adventures in Mathematical Knitting. American Scientist, 101(2), March--April 2013, 124--133.

sarah-marie belcastro, You Do the Math. KnitNet, Winter 2001.

Brandon-Guiguet, Méthode des Initiales: Un aspect mathématique du tissage à lames, Lyon, Joanne Desvigne & Co, eds., 1938.

Brenda Dayne, Geek chic. Interweave Knits Fall 2003 pp.68--71+118. Now freely available online.

Edouard Gand. Le Transpositeur ou l'Improvisateur de Tissus, Paris 1871. (This has no theoretical mathematics in it, but it is mathematical in the sense that Gand introduces a diagrammatic notation and implies using modular arithmetic to describe repeats.)

Mary Griffin, Wear Your Own Theory; A Beginner's Guide to Random Knitting. New Scientist, March 26, 1987, pp. 69--70.

Janice Hornicek, Color By Numbers. knitsimple, Spring/Summer 2006, pp. 22--25.

W.D. and Janet Hoskins. Satin and long-eyed heddles, Weavers Journal, 6 (1981) 25--26.

Olivier Masson and Francois Roussel, Shaft Weaving and Graph Design, 1988. (Accompanying notes

by Anne Wells, 2000.)

Debbie New, Celluar Automaton Knitting. Knitter's Magazine Number 49, Winter 1997, pp. 82--83.

Meg Swanson, Rita Buchanan, Möbius and Möbius II. Knitter's Magazine Winter 1991, pages 38 and 49.

Rachel Thomas, Career Interview: Fashion Designer, Plus magazine, Issue 53.

Margaret Wertheim, Crocheting the Hyperbolic Plane: An Interview with David Henderson and Daina Taimina. Cabinet: A Quarterly Magazine of Art & Culture Issue 16, Winter 2004. The article is available online here. (There are lots of articles that feature Daina's work, but this is the best one available online.)