Pub Date : 2023-07-01DOI: 10.5642/jhummath.scyq4586
F. Larsen, Harald Moe
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Pub Date : 2023-07-01DOI: 10.5642/jhummath.tgsx1558
D. Monte-Serrat, C. Cattani
Synopsis Mathematics plays an important role in the linguistic structure of artificial intelligence (AI). We describe the linguistic process as a unique structure present both in human cognition and in cognitive computing. The close relationship with both AI and human cognition is due to this unique structure, which paves the way for AI to interfere with the behavior of those who interact with it. We highlight the role of mathematicians in designing algorithms—the core of the AI linguistic process—and in defining steps and instructions for AI. Because algorithms, through AI, interfere with the thought of those who interact with AI by providing anticipated solutions that prevent users from making free choices, we investigate how we can apply ethical principles to guide interactions between users and intelligent systems in order to address this issue. We contend that by integrating ethical principles in the mathematical modeling of algorithms, we can avoid manipulation, inequality, and black boxes in the protection of individual rights. As such, ethical considerations are highly important for those working with algorithms, which highlights the humanistic side of mathematics.
{"title":"Towards Ethical AI: Mathematics Influences Human Behavior","authors":"D. Monte-Serrat, C. Cattani","doi":"10.5642/jhummath.tgsx1558","DOIUrl":"https://doi.org/10.5642/jhummath.tgsx1558","url":null,"abstract":"Synopsis Mathematics plays an important role in the linguistic structure of artificial intelligence (AI). We describe the linguistic process as a unique structure present both in human cognition and in cognitive computing. The close relationship with both AI and human cognition is due to this unique structure, which paves the way for AI to interfere with the behavior of those who interact with it. We highlight the role of mathematicians in designing algorithms—the core of the AI linguistic process—and in defining steps and instructions for AI. Because algorithms, through AI, interfere with the thought of those who interact with AI by providing anticipated solutions that prevent users from making free choices, we investigate how we can apply ethical principles to guide interactions between users and intelligent systems in order to address this issue. We contend that by integrating ethical principles in the mathematical modeling of algorithms, we can avoid manipulation, inequality, and black boxes in the protection of individual rights. As such, ethical considerations are highly important for those working with algorithms, which highlights the humanistic side of mathematics.","PeriodicalId":42411,"journal":{"name":"Journal of Humanistic Mathematics","volume":" ","pages":""},"PeriodicalIF":0.3,"publicationDate":"2023-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42517325","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}
Pub Date : 2023-02-15DOI: 10.5642/jhummath.zruz1463
R. Buckmire, C. Eaton, Joseph E. Hibdon, Jr., Katherine M. Kinnaird, Drew Lewis, Jessica M. Libertini, Omayra Ortega, Rachel Roca, Andr'es R. Vindas-Mel'endez
The definition of who is or what makes a ``mathematician"is an important and urgent issue to be addressed in the mathematics community. Too often, a narrower definition of who is considered a mathematician (and what is considered mathematics) is used to exclude people from the discipline -- both explicitly and implicitly. However, using a narrow definition of a mathematician allows us to examine and challenge systemic barriers that exist in certain spaces of the community. This paper explores and illuminates tensions between narrow and broad definitions and how they can be used to promote both inclusion and exclusion simultaneously. In this article, we present a framework of definitions based on identity, function, and qualification and exploring several different meanings of ``mathematician". By interrogating various definitions, we highlight their risks and opportunities, with an emphasis on implications for broadening and/or narrowing participation of underrepresented groups.
{"title":"On Definitions of \"Mathematician\"","authors":"R. Buckmire, C. Eaton, Joseph E. Hibdon, Jr., Katherine M. Kinnaird, Drew Lewis, Jessica M. Libertini, Omayra Ortega, Rachel Roca, Andr'es R. Vindas-Mel'endez","doi":"10.5642/jhummath.zruz1463","DOIUrl":"https://doi.org/10.5642/jhummath.zruz1463","url":null,"abstract":"The definition of who is or what makes a ``mathematician\"is an important and urgent issue to be addressed in the mathematics community. Too often, a narrower definition of who is considered a mathematician (and what is considered mathematics) is used to exclude people from the discipline -- both explicitly and implicitly. However, using a narrow definition of a mathematician allows us to examine and challenge systemic barriers that exist in certain spaces of the community. This paper explores and illuminates tensions between narrow and broad definitions and how they can be used to promote both inclusion and exclusion simultaneously. In this article, we present a framework of definitions based on identity, function, and qualification and exploring several different meanings of ``mathematician\". By interrogating various definitions, we highlight their risks and opportunities, with an emphasis on implications for broadening and/or narrowing participation of underrepresented groups.","PeriodicalId":42411,"journal":{"name":"Journal of Humanistic Mathematics","volume":" ","pages":""},"PeriodicalIF":0.3,"publicationDate":"2023-02-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48818366","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}
Pub Date : 2023-01-01DOI: 10.5642/jhummath.becb4427
E. A. Marchisotto
Synopsis Anneli Lax (1922–1999) was my mentor and thesis advisor at New York University in the late 1980s. I was fortunate to be included among her circle of friends and collaborators in the ensuing years. Dr. Lax made important contributions to mathematics and mathematics education. This article describes her pioneering work in promoting good exposition of elementary mathematics in support of mathematics and its pedagogy. The design and implementation of her views illustrate her indefatigable spirit and impressive work ethic for causes she championed.
{"title":"Anneli Lax: They Think, Therefore We Are","authors":"E. A. Marchisotto","doi":"10.5642/jhummath.becb4427","DOIUrl":"https://doi.org/10.5642/jhummath.becb4427","url":null,"abstract":"Synopsis Anneli Lax (1922–1999) was my mentor and thesis advisor at New York University in the late 1980s. I was fortunate to be included among her circle of friends and collaborators in the ensuing years. Dr. Lax made important contributions to mathematics and mathematics education. This article describes her pioneering work in promoting good exposition of elementary mathematics in support of mathematics and its pedagogy. The design and implementation of her views illustrate her indefatigable spirit and impressive work ethic for causes she championed.","PeriodicalId":42411,"journal":{"name":"Journal of Humanistic Mathematics","volume":" ","pages":""},"PeriodicalIF":0.3,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44135678","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}
Pub Date : 2023-01-01DOI: 10.5642/jhummath.xpse6991
Virgilio A. Rivas
{"title":"Locked in Functions: A Short Poem for Robert Langlands","authors":"Virgilio A. Rivas","doi":"10.5642/jhummath.xpse6991","DOIUrl":"https://doi.org/10.5642/jhummath.xpse6991","url":null,"abstract":"","PeriodicalId":42411,"journal":{"name":"Journal of Humanistic Mathematics","volume":"1 1","pages":""},"PeriodicalIF":0.3,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42003745","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}
Pub Date : 2023-01-01DOI: 10.5642/jhummath.azev3747
G. Hanna, B. Larvor, Xiaoheng Yan
This paper argues that interactive theorem provers (ITPs) could play an important role in fostering students’ appreciation and understanding of proof and of mathematics in general. It shows that the ITP Lean has three features that mitigate existing difficulties in teaching and learning mathematical proof. One is that it requires students to identify a proof strategy at the start. The second is that it gives students instant feedback while still allowing them to explore with maximum autonomy. The third is that elementary formal logic finds a natural place in the activity of creating proofs. The challenge in using Lean is that students have to learn its command language, in addition to mathematics course content and elementary logic.
{"title":"Human-Machine Collaboration in the Teaching of Proof","authors":"G. Hanna, B. Larvor, Xiaoheng Yan","doi":"10.5642/jhummath.azev3747","DOIUrl":"https://doi.org/10.5642/jhummath.azev3747","url":null,"abstract":"This paper argues that interactive theorem provers (ITPs) could play an important role in fostering students’ appreciation and understanding of proof and of mathematics in general. It shows that the ITP Lean has three features that mitigate existing difficulties in teaching and learning mathematical proof. One is that it requires students to identify a proof strategy at the start. The second is that it gives students instant feedback while still allowing them to explore with maximum autonomy. The third is that elementary formal logic finds a natural place in the activity of creating proofs. The challenge in using Lean is that students have to learn its command language, in addition to mathematics course content and elementary logic.","PeriodicalId":42411,"journal":{"name":"Journal of Humanistic Mathematics","volume":" ","pages":""},"PeriodicalIF":0.3,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44825960","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}
Pub Date : 2023-01-01DOI: 10.5642/jhummath.kogv7900
W. Forbes, Joyce Mgombelo
Inspired by Brent Davis' conceptualization of listening and conversation in his book Teaching Mathematics: Toward a Sound Alternative, we propose how we as a mathematics education community may move forward by continuing in the conversation that emerged from COVID. We encourage all involved to listen rather than assume a discussion-oriented stance. Using an enactivist lens, we look at the pandemic learning space, give an overview of the education conversa-tion that emerged in Ontario, and offer a way to rethink Mathematics Education within the frame of a conversation. We believe that if mathematics education is to engage learners in a meaningful way, sustaining the progress made in math-ematics education, all stakeholders should embrace the changing context of our network within the environment and interact through listening.
{"title":"Teaching Mathematics After COVID: A Conversation not a Discussion","authors":"W. Forbes, Joyce Mgombelo","doi":"10.5642/jhummath.kogv7900","DOIUrl":"https://doi.org/10.5642/jhummath.kogv7900","url":null,"abstract":"Inspired by Brent Davis' conceptualization of listening and conversation in his book Teaching Mathematics: Toward a Sound Alternative, we propose how we as a mathematics education community may move forward by continuing in the conversation that emerged from COVID. We encourage all involved to listen rather than assume a discussion-oriented stance. Using an enactivist lens, we look at the pandemic learning space, give an overview of the education conversa-tion that emerged in Ontario, and offer a way to rethink Mathematics Education within the frame of a conversation. We believe that if mathematics education is to engage learners in a meaningful way, sustaining the progress made in math-ematics education, all stakeholders should embrace the changing context of our network within the environment and interact through listening.","PeriodicalId":42411,"journal":{"name":"Journal of Humanistic Mathematics","volume":" ","pages":""},"PeriodicalIF":0.3,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42964216","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}
Pub Date : 2023-01-01DOI: 10.5642/jhummath.cxug6663
{"title":"Astor Place Barber","authors":"","doi":"10.5642/jhummath.cxug6663","DOIUrl":"https://doi.org/10.5642/jhummath.cxug6663","url":null,"abstract":"","PeriodicalId":42411,"journal":{"name":"Journal of Humanistic Mathematics","volume":" ","pages":""},"PeriodicalIF":0.3,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43565603","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}
Pub Date : 2023-01-01DOI: 10.5642/jhummath.jbxg7428
T. Peres
Synopsis This paper presents a study on the extent to which creative literature been used as a vessel to carry forward the development of mathematical thought. The role of mathematics as a driving force for literature is highlighted
本文对创造性文学在多大程度上被用作推进数学思想发展的载体进行了研究。强调了数学作为文学推动力的作用
{"title":"The Use and Development of Mathematics Within Creative Literature","authors":"T. Peres","doi":"10.5642/jhummath.jbxg7428","DOIUrl":"https://doi.org/10.5642/jhummath.jbxg7428","url":null,"abstract":"Synopsis This paper presents a study on the extent to which creative literature been used as a vessel to carry forward the development of mathematical thought. The role of mathematics as a driving force for literature is highlighted","PeriodicalId":42411,"journal":{"name":"Journal of Humanistic Mathematics","volume":" ","pages":""},"PeriodicalIF":0.3,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43629690","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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