For many years, I have been collecting math jokes and posting them on my website. I have more than 400 jokes there. In this paper, which is an extended version of my talk at the G4G15, I would like to present 66 of them.
{"title":"My Favorite Math Jokes","authors":"Tanya Khovanova","doi":"arxiv-2403.01010","DOIUrl":"https://doi.org/arxiv-2403.01010","url":null,"abstract":"For many years, I have been collecting math jokes and posting them on my\u0000website. I have more than 400 jokes there. In this paper, which is an extended\u0000version of my talk at the G4G15, I would like to present 66 of them.","PeriodicalId":501462,"journal":{"name":"arXiv - MATH - History and Overview","volume":"72 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140033734","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Group theory involves the study of symmetry, and its inherent beauty gives it the potential to be one of the most accessible and enjoyable areas of mathematics, for students and non-mathematicians alike. Unfortunately, many students never get a glimpse into the more alluring parts of this field because "traditional" algebra classes are often taught in a dry axiomatic fashion, devoid of visuals. This article will showcase aesthetic pictures that can bring this subject to life. It will also leave the reader with some (intentionally) unanswered puzzles that undergraduate students, hobbyists, and mathematical artists can explore and answer, and even create new versions themselves.
{"title":"Revealing the hidden beauty of finite groups with Cayley graphs","authors":"Matthew Macauley","doi":"arxiv-2402.19438","DOIUrl":"https://doi.org/arxiv-2402.19438","url":null,"abstract":"Group theory involves the study of symmetry, and its inherent beauty gives it\u0000the potential to be one of the most accessible and enjoyable areas of\u0000mathematics, for students and non-mathematicians alike. Unfortunately, many\u0000students never get a glimpse into the more alluring parts of this field because\u0000\"traditional\" algebra classes are often taught in a dry axiomatic fashion,\u0000devoid of visuals. This article will showcase aesthetic pictures that can bring\u0000this subject to life. It will also leave the reader with some (intentionally)\u0000unanswered puzzles that undergraduate students, hobbyists, and mathematical\u0000artists can explore and answer, and even create new versions themselves.","PeriodicalId":501462,"journal":{"name":"arXiv - MATH - History and Overview","volume":"80 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-02-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140019334","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
On 13-01-2024 the annual wintersymposium of the Koninlijk Wiskundig Genootschap (KWG) was held in the academiegebouw in Utrecht. The symposium had the theme ``inzichtelijk abstract''. Thomas Rot gave a lecture on his favourite theorem from topology. This article is a written account of this lecture. Audience comprised mostly of high school teachers and that is also the target audience of this article. The slides (in Dutch), which contain more pictures, are available~[8].
{"title":"Ropes have an even number of ends","authors":"Thomas O. Rot","doi":"arxiv-2402.18200","DOIUrl":"https://doi.org/arxiv-2402.18200","url":null,"abstract":"On 13-01-2024 the annual wintersymposium of the Koninlijk Wiskundig\u0000Genootschap (KWG) was held in the academiegebouw in Utrecht. The symposium had\u0000the theme ``inzichtelijk abstract''. Thomas Rot gave a lecture on his favourite\u0000theorem from topology. This article is a written account of this lecture.\u0000Audience comprised mostly of high school teachers and that is also the target\u0000audience of this article. The slides (in Dutch), which contain more pictures,\u0000are available~[8].","PeriodicalId":501462,"journal":{"name":"arXiv - MATH - History and Overview","volume":"46 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-02-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140006521","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In this note we explore the relationship between the operation of convolution of functions and the Eulerian integrals. This approach allow us to obtain some expressions for the convolution of a certain class of functions in terms of the Gamma Function as well as to derive some well known properties of the Gamma Function by using the concept and properties of the convolution.
{"title":"A Note on Gamma Function and Convolution","authors":"Francisco Mota","doi":"arxiv-2402.15842","DOIUrl":"https://doi.org/arxiv-2402.15842","url":null,"abstract":"In this note we explore the relationship between the operation of convolution\u0000of functions and the Eulerian integrals. This approach allow us to obtain some\u0000expressions for the convolution of a certain class of functions in terms of the\u0000Gamma Function as well as to derive some well known properties of the Gamma\u0000Function by using the concept and properties of the convolution.","PeriodicalId":501462,"journal":{"name":"arXiv - MATH - History and Overview","volume":"282 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-02-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139980796","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
This article presents a source list to support departments in creating more equitable, diverse, and inclusive mathematics classrooms. Included are relevant general-interest books, as well as articles and books presenting research results about how matters of inequity, exclusion, and homogeneity surface in educational contexts. We also present sources more specifically focused on research about the past and present of relationships between mathematics and gender, (dis)ability, race, and class, as well as articles proposing approaches and case studies in mathematics classrooms.
{"title":"A source list to support DEI/EDI work in mathematical sciences","authors":"Deborah Kent, Emilie Aebischer, Stuart Neave","doi":"arxiv-2402.15612","DOIUrl":"https://doi.org/arxiv-2402.15612","url":null,"abstract":"This article presents a source list to support departments in creating more\u0000equitable, diverse, and inclusive mathematics classrooms. Included are relevant\u0000general-interest books, as well as articles and books presenting research\u0000results about how matters of inequity, exclusion, and homogeneity surface in\u0000educational contexts. We also present sources more specifically focused on\u0000research about the past and present of relationships between mathematics and\u0000gender, (dis)ability, race, and class, as well as articles proposing approaches\u0000and case studies in mathematics classrooms.","PeriodicalId":501462,"journal":{"name":"arXiv - MATH - History and Overview","volume":"49 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-02-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139980801","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
This paper, to appear in the ``Notices of the AMS'' 2024, is a modified version of a text already appeared in this journal, Feb. 2007 after a first publication in French, in ``La Gazette des Math{'e}maticiens'' 97 (2003) on the occasion of Sato's reception of the 2002/2003 Wolf prize.
这篇论文将发表在2024年的《美国数学会通报》（Notices of the AMS）上，是对2007年2月佐藤获得2002/2003年度沃尔夫奖时发表在《数学公报》第97期（2003年）上的法文论文的修改。
{"title":"Mikio Sato, a visionary of mathematics","authors":"Pierre Schapira","doi":"arxiv-2402.15553","DOIUrl":"https://doi.org/arxiv-2402.15553","url":null,"abstract":"This paper, to appear in the ``Notices of the AMS'' 2024, is a modified\u0000version of a text already appeared in this journal, Feb. 2007 after a first\u0000publication in French, in ``La Gazette des Math{'e}maticiens'' 97 (2003) on\u0000the occasion of Sato's reception of the 2002/2003 Wolf prize.","PeriodicalId":501462,"journal":{"name":"arXiv - MATH - History and Overview","volume":"16 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-02-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139980511","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Ke Wang, Junting Pan, Weikang Shi, Zimu Lu, Mingjie Zhan, Hongsheng Li
Recent advancements in Large Multimodal Models (LMMs) have shown promising results in mathematical reasoning within visual contexts, with models approaching human-level performance on existing benchmarks such as MathVista. However, we observe significant limitations in the diversity of questions and breadth of subjects covered by these benchmarks. To address this issue, we present the MATH-Vision (MATH-V) dataset, a meticulously curated collection of 3,040 high-quality mathematical problems with visual contexts sourced from real math competitions. Spanning 16 distinct mathematical disciplines and graded across 5 levels of difficulty, our dataset provides a comprehensive and diverse set of challenges for evaluating the mathematical reasoning abilities of LMMs. Through extensive experimentation, we unveil a notable performance gap between current LMMs and human performance on MATH-V, underscoring the imperative for further advancements in LMMs. Moreover, our detailed categorization allows for a thorough error analysis of LMMs, offering valuable insights to guide future research and development. The project is available at https://mathvision-cuhk.github.io
{"title":"Measuring Multimodal Mathematical Reasoning with MATH-Vision Dataset","authors":"Ke Wang, Junting Pan, Weikang Shi, Zimu Lu, Mingjie Zhan, Hongsheng Li","doi":"arxiv-2402.14804","DOIUrl":"https://doi.org/arxiv-2402.14804","url":null,"abstract":"Recent advancements in Large Multimodal Models (LMMs) have shown promising\u0000results in mathematical reasoning within visual contexts, with models\u0000approaching human-level performance on existing benchmarks such as MathVista.\u0000However, we observe significant limitations in the diversity of questions and\u0000breadth of subjects covered by these benchmarks. To address this issue, we\u0000present the MATH-Vision (MATH-V) dataset, a meticulously curated collection of\u00003,040 high-quality mathematical problems with visual contexts sourced from real\u0000math competitions. Spanning 16 distinct mathematical disciplines and graded\u0000across 5 levels of difficulty, our dataset provides a comprehensive and diverse\u0000set of challenges for evaluating the mathematical reasoning abilities of LMMs.\u0000Through extensive experimentation, we unveil a notable performance gap between\u0000current LMMs and human performance on MATH-V, underscoring the imperative for\u0000further advancements in LMMs. Moreover, our detailed categorization allows for\u0000a thorough error analysis of LMMs, offering valuable insights to guide future\u0000research and development. The project is available at\u0000https://mathvision-cuhk.github.io","PeriodicalId":501462,"journal":{"name":"arXiv - MATH - History and Overview","volume":"48 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-02-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139950752","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
This is a survey of characterizations and relationships between some properties of lattices, particularly the modular, Arguesian, linear, and distributive properties, but also some other related properties. The survey emphasizes finite and finitary lattices and deemphasizes complemented lattices.
{"title":"A survey of lattice properties: modular, Arguesian, linear, and distributive","authors":"Dale R. Worley","doi":"arxiv-2403.19677","DOIUrl":"https://doi.org/arxiv-2403.19677","url":null,"abstract":"This is a survey of characterizations and relationships between some\u0000properties of lattices, particularly the modular, Arguesian, linear, and\u0000distributive properties, but also some other related properties. The survey\u0000emphasizes finite and finitary lattices and deemphasizes complemented lattices.","PeriodicalId":501462,"journal":{"name":"arXiv - MATH - History and Overview","volume":"28 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-02-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140574052","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Alison Litherland, Patrick Litherland, Sam Nelson, Steven Wallace
Richard A. Litherland was born in 1953 in England. He received his PhD at Trinity College in Cambridge in 1979 and moved to the USA in 1983. He had a lengthy and distinguished career as a professor of mathematics and researcher of low-dimensional topology, based primarily at Louisiana State University (LSU) in Baton Rouge until his untimely passing in November 2022. In this paper we (Rick's family and students) recount some memories of Rick, his life and his mathematics.
{"title":"Richard A. Litherland: A Brief Biography","authors":"Alison Litherland, Patrick Litherland, Sam Nelson, Steven Wallace","doi":"arxiv-2402.13010","DOIUrl":"https://doi.org/arxiv-2402.13010","url":null,"abstract":"Richard A. Litherland was born in 1953 in England. He received his PhD at\u0000Trinity College in Cambridge in 1979 and moved to the USA in 1983. He had a\u0000lengthy and distinguished career as a professor of mathematics and researcher\u0000of low-dimensional topology, based primarily at Louisiana State University\u0000(LSU) in Baton Rouge until his untimely passing in November 2022. In this paper\u0000we (Rick's family and students) recount some memories of Rick, his life and his\u0000mathematics.","PeriodicalId":501462,"journal":{"name":"arXiv - MATH - History and Overview","volume":"2 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-02-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139928013","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In 1911, Alfred North Whitehead published a short book "Introduction to Mathematics" (IM) intended for students wanting an explanation of the fundamental ideas of mathematics. Whitehead's IM has enduring value because it was written not long after he and Bertrand Russell published their monumental three-volume work "Principia Mathematica" (PM) -- a publication of immense historical significance for mathematics. IM sheds light on Whitehead's view of mathematics at that time. Whitehead's book places proofs in predicate logic as the mythical starting point of mathematics, although Whitehead himself was slow to understand the significance of symbolic predicate logic.
{"title":"A review of Alfred North Whitehead's \"Introduction to Mathematics\"","authors":"Thomas Hales","doi":"arxiv-2403.19675","DOIUrl":"https://doi.org/arxiv-2403.19675","url":null,"abstract":"In 1911, Alfred North Whitehead published a short book \"Introduction to\u0000Mathematics\" (IM) intended for students wanting an explanation of the\u0000fundamental ideas of mathematics. Whitehead's IM has enduring value because it\u0000was written not long after he and Bertrand Russell published their monumental\u0000three-volume work \"Principia Mathematica\" (PM) -- a publication of immense\u0000historical significance for mathematics. IM sheds light on Whitehead's view of\u0000mathematics at that time. Whitehead's book places proofs in predicate logic as\u0000the mythical starting point of mathematics, although Whitehead himself was slow\u0000to understand the significance of symbolic predicate logic.","PeriodicalId":501462,"journal":{"name":"arXiv - MATH - History and Overview","volume":"60 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-02-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140574002","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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