applied mathematical modeling and problem solving

Academia.edu no longer supports Internet Explorer.

To browse Academia.edu and the wider internet faster and more securely, please take a few seconds to  upgrade your browser .

Enter the email address you signed up with and we'll email you a reset link.

• We're Hiring!
• Help Center

Applied mathematical problem solving, modelling, applications, and links to other subjects—State, trends and issues in mathematics instruction

1991, Educational Studies in Mathematics

Related Papers

Ceps Journal Center For Educational Policy Studies Journal

The Proceedings of the 12th International Congress on Mathematical Education

Zahra Gooya

Zdm – Mathematics Education

Manuel Santos-Trigo

Janine Remillard

The Journal of Mathematical Behavior

Joanna Mamona

ABSTRACT Introduces this special issue of the Journal of Mathematical Behavior. This special issue originated from the 10th International Congress of Mathematics Education's Topic Study Group 18: Problem Solving in Mathematics Education. The general aims of the Topic Study Group were to provide a forum for those who are interested in any aspect of problem-solving research at any educational level, to present recent findings, and to exchange ideas. We set up three specific goals for the Problem Solving Topic Study Group: (1) to examine the understanding of the complex cognitive processes involved in problem solving; (2) to explore the actual mechanisms by which students learn and make sense of mathematics through problem solving, and how this can be supported by teachers; and (3) to identify future directions of problem-solving research, including the use of information technology. The Topic Study Group received a good response. Most of the papers in this special issue are from those who presented at the Topic Study Group. In addition, we invited a few other researchers to submit papers in order to cover various aspects of problem-solving research that we wished to be represented in this issue. This special issue includes 12 papers, each addressing at least one of the three goals listed above. The first six papers that appear are empirically based; in these papers, the authors present the results of the fieldwork that they have conducted and also raise research questions for future studies. The remaining six papers are essays discussing issues about problem solving, and how these issues have been, or should be, the subjects of research. In this article, we briefly highlight the contributions of each of the 12 papers. (PsycINFO Database Record (c) 2012 APA, all rights reserved)

International Journal of Innovation and Applied Studies

R. M. Latif

Encyclopedia of Mathematics Education

Jerry Becker

The Mathematics Enthusiast

Journal of Marine Systems

Manish Tiwari

RELATED PAPERS

International Journal of Research in Engineering

Padma charan Sahu

Clinical Rheumatology

Gastrointestinal Endoscopy

Guido Missale

Cactaceas Y Suculentas Mexicanas

Beatriz Rendón

Engenharia Agrícola

Afonso Peche Filho

Anne Rothstein

hafize Kedir

Pattern Recognition

Giacomo Boracchi

Scientific Reports

Youngmi Kim Pak

Rheumatology

Laura Schanberg

Journal of Holistic Nursing and Midwifery

maryam niknamy

Journal of Ayub Medical College, Abbottabad : JAMC

Muhammad Suleman

Naeem khattak

Zulkafli B Othaman

Frontiers in neuroscience

Patricia Izilda Silva

Robert Veltri

Journal of the Turkish German Gynecological Association

Mohammad Ilyas

Environmental Science & Policy

margreet zwarteveen

Acta Physiologica Scandinavica

Stein Knardahl

RELATED TOPICS

•   We're Hiring!
•   Help Center
• Find new research papers in:
• Health Sciences
• Earth Sciences
• Cognitive Science
• Mathematics
• Computer Science
• Academia ©2024

May 31, 2024

10 min read

Math Can Help Solve Social Justice Problems

Mathematicians are working on ways to use their field to tackle major social issues, such as social inequality and the need for gender equity

By Rachel Crowell & Nature magazine

MicroStockHub/Getty Images

When Carrie Diaz Eaton trained as a mathematician, they didn’t expect their career to involve social-justice research. Growing up in Providence, Rhode Island, Diaz Eaton first saw social justice in action when their father, who’s from Peru, helped other Spanish-speaking immigrants to settle in the United States.

But it would be decades before Diaz Eaton would forge a professional path to use their mathematical expertise to study social-justice issues. Eventually, after years of moving around for education and training, that journey brought them back to Providence, where they collaborated with the Woonasquatucket River Watershed Council on projects focused on preserving the local environment of the river’s drainage basin, and bolstering resources for the surrounding, often underserved communities.

By “thinking like a mathematician” and leaning on data analysis, data science and visualization skills, they found that their expertise was needed in surprising ways, says Diaz Eaton, who is now executive director of the Institute for a Racially Just, Inclusive, and Open STEM Education at Bates College in Lewiston, Maine.

On supporting science journalism

If you're enjoying this article, consider supporting our award-winning journalism by subscribing . By purchasing a subscription you are helping to ensure the future of impactful stories about the discoveries and ideas shaping our world today.

For example, the council identified a need to help local people to better connect with community resources. “Even though health care and education don’t seem to fall under the purview of a watershed council, these are all interrelated issues,” Diaz Eaton says. Air pollution can contribute to asthma attacks, for example. In one project, Diaz Eaton and their collaborators built a quiz to help community members to choose the right health-care option, depending on the nature of their illness or injury, immigration status and health-insurance coverage.

“One of the things that makes us mathematicians, is our skills in logic and the questioning of assumptions”, and creating that quiz “was an example of logic at play”, requiring a logic map of cases and all of the possible branches of decision-making to make an effective quiz, they say.

Maths might seem an unlikely bedfellow for social-justice research. But applying the rigour of the field is turning out to be a promising approach for identifying, and sometimes even implementing, fruitful solutions for social problems.

Mathematicians can experience first-hand the messiness and complexity — and satisfaction — of applying maths to problems that affect people and their communities. Trying to work out how to help people access much-needed resources, reduce violence in communities or boost gender equity requires different technical skills, ways of thinking and professional collaborations compared with breaking new ground in pure maths. Even for an applied mathematician like Diaz Eaton, transitioning to working on social-justice applications brings fresh challenges.

Mathematicians say that social-justice research is difficult yet fulfilling — these projects are worth taking on because of their tremendous potential for creating real-world solutions for people and the planet.

Data-driven research

Mathematicians are digging into issues that range from social inequality and health-care access to racial profiling and predictive policing. However, the scope of their research is limited by their access to the data, says Omayra Ortega, an applied mathematician and mathematical epidemiologist at Sonoma State University in Rohnert Park, California. “There has to be that measured information,” Ortega says.

Fortunately, data for social issues abound. “Our society is collecting data at a ridiculous pace,” Ortega notes. Her mathematical epidemiology work has examined which factors affect vaccine uptake in different communities. Her work has found, for example, that, in five years, a national rotavirus-vaccine programme in Egypt would reduce disease burden enough that the cost saving would offset 76% of the costs of the vaccine. “Whenever we’re talking about the distribution of resources, there’s that question of social justice: who gets the resources?” she says.

Lily Khadjavi’s journey with social-justice research began with an intriguing data set.

About 15 years ago, Khadjavi, a mathematician at Loyola Marymount University in Los Angeles, California, was “on the hunt for real-world data” for an undergraduate statistics class she was teaching. She wanted data that the students could crunch to “look at new information and pose their own questions”. She realized that Los Angeles Police Department (LAPD) traffic-stop data fit that description.

At that time, every time that LAPD officers stopped pedestrians or pulled over drivers, they were required to report stop data. Those data included “the perceived race or ethnicity of the person they had stopped”, Khadjavi notes.

When the students analysed the data, the results were memorable. “That was the first time I heard students do a computation absolutely correctly and then audibly gasp at their results,” she says. The data showed that one in every 5 or 6 police stops of Black male drivers resulted in a vehicle search — a rate that was more than triple the national average, which was about one out of every 20 stops for drivers of any race or ethnicity, says Khadjavi.

Her decision to incorporate that policing data into her class was a pivotal moment in Khadjavi’s career — it led to a key publication and years of building expertise in using maths to study racial profiling and police practice. She sits on California’s Racial Identity and Profiling Advisory Board , which makes policy recommendations to state and local agencies on how to eliminate racial profiling in law enforcement.

In 2023, she was awarded the Association for Women in Mathematics’ inaugural Mary & Alfie Gray Award for Social Justice, named after a mathematician couple who championed human rights and equity in maths and government.

Sometimes, gaining access to data is a matter of networking. One of Khadjavi’s colleagues shared Khadjavi’s pivotal article with specialists at the American Civil Liberties Union. In turn, these specialists shared key data obtained through public-records requests with Khadjavi and her colleague. “Getting access to that data really changed what we could analyse,” Khadjavi says. “[It] allowed us to shine a light on the experiences of civilians and police in hundreds of thousands of stops made every year in Los Angeles.”

The data-intensive nature of this research can be an adjustment for some mathematicians, requiring them to develop new skills and approach problems differently. Such was the case for Tian An Wong, a mathematician at the University of Michigan-Dearborn who trained in number theory and representation theory.

In 2020, Wong wanted to know more about the controversial issue of mathematicians collaborating with the police, which involves, in many cases, using mathematical modelling and data analysis to support policing activities. Some mathematicians were protesting about the practice as part of a larger wave of protests around systemic racism , following the killing of George Floyd by police in Minneapolis, Minnesota. Wong’s research led them to a technique called predictive policing, which Wong describes as “the use of historical crime and other data to predict where future crime will occur, and [to] allocate policing resources based on those predictions”.

Wong wanted to know whether the tactics that mathematicians use to support police work could instead be used to critique it. But first, they needed to gain some additional statistics and data analysis skills. To do so, Wong took an online introductory statistics course, re-familiarized themself with the Python programming language, and connected with colleagues trained in statistical methods. They also got used to reading research papers across several disciplines.

Currently, Wong applies those skills to investigating the policing effectiveness of a technology that automatically locates gunshots by sound. That technology has been deployed in parts of Detroit, Michigan, where community members and organizations have raised concerns about its multimillion-dollar cost and about whether such police surveillance makes a difference to public safety.

Getting the lay of the land

For some mathematicians, social-justice work is a natural extension of their career trajectories. “My choice of mathematical epidemiology was also partially born out of out of my love for social justice,” Ortega says. Mathematical epidemiologists apply maths to study disease occurrence in specific populations and how to mitigate disease spread. When Ortega’s PhD adviser mentioned that she could study the uptake of a then-new rotovirus vaccine in the mid-2000s, she was hooked.

Mathematicians, who decide to jump into studying social-justice issues anew, must do their homework and dedicate time to consider how best to collaborate with colleagues of diverse backgrounds.

Jonathan Dawes, an applied mathematician at the University of Bath, UK, investigates links between the United Nations’ Sustainable Development Goals (SDGs) and their associated target actions. Adopted in 2015, the SDGs are “a universal call to action to end poverty, protect the planet, and ensure that by 2030 all people enjoy peace and prosperity,” according to the United Nations , and each one has a number of targets.

“As a global agenda, it’s an invitation to everybody to get involved,” says Dawes. From a mathematical perspective, analysing connections in the complex system of SDGs “is a nice level of problem,” Dawes says. “You’ve got 17 Sustainable Development Goals. Between them, they have 169 targets. [That’s] an amount of data that isn’t very large in big-data terms, but just big enough that it’s quite hard to hold all of it in your head.”

Dawes’ interest in the SDGs was piqued when he read a 2015 review that focused on how making progress on individual goals could affect progress on the entire set. For instance, if progress is made on the goal to end poverty how does that affect progress on the goal to achieve quality education for all, as well as the other 15 SDGs?

“If there’s a network and you can put some numbers on the strengths and signs of the edges, then you’ve got a mathematized version of the problem,” Dawes says. Some of his results describe how the properties of the network change if one or more of the links is perturbed, much like an ecological food web. His work aims to identify hierarchies in the SDG networks, pinpointing which SDGs should be prioritized for the health of the entire system.

As Dawes dug into the SDGs, he realized that he needed to expand what he was reading to include different journals, including publications that were “written in very different ways”. That involved “trying to learn a new language”, he explains. He also kept up to date with the output of researchers and organizations doing important SDG-related work, such as the International Institute for Applied Systems Analysis in Laxenburg, Austria, and the Stockholm Environment Institute.

Dawes’ research showed that interactions between the SDGs mean that “there are lots of positive reinforcing effects between poverty, hunger, health care, education, gender equity and so on.” So, “it’s possible to lift all of those up” when progress is made on even one of the goals. With one exception: managing and protecting the oceans. Making progress on some of the other SDGs could, in some cases, stall progress for, or even harm, life below water.

Collaboration care

Because social-justice projects are often inherently cross-disciplinary, mathematicians studying social justice say it’s key in those cases to work with community leaders, activists or community members affected by the issues.

Getting acquainted with these stakeholders might not always feel comfortable or natural. For instance, when Dawes started his SDG research, he realized that he was entering a field in which researchers already knew each other, followed each other’s work and had decades of experience. “There’s a sense of being like an uninvited guest at a party,” Dawes says. He became more comfortable after talking with other researchers, who showed a genuine interest in what he brought to the discussion, and when his work was accepted by the field’s journals. Over time, he realized “the interdisciplinary space was big enough for all of us to contribute to”.

Even when mathematicians have been invited to join a team of social-justice researchers, they still must take care, because first impressions can set the tone.

Michael Small is an applied mathematician and director of the Data Institute at the University of Western Australia in Perth. For much of his career, Small focused on the behaviour of complex systems, or those with many simple interacting parts, and dynamical systems theory, which addresses physical and mechanical problems.

But when a former vice-chancellor at the university asked him whether he would meet with a group of psychiatrists and psychologists to discuss their research on mental health and suicide in young people, it transformed his research. After considering the potential social impact of better understanding the causes and risks of suicide in teenagers and younger children, and thinking about how the problem meshed well with his research in complex systems and ‘non-linear dynamics’, Small agreed to collaborate with the group.

The project has required Small to see beyond the numbers. For the children’s families, the young people are much more than a single data point. “If I go into the room [of mental-health professionals] just talking about mathematics, mathematics, mathematics, and how this is good because we can prove this really cool theorem, then I’m sure I will get push back,” he says. Instead, he notes, it’s important to be open to insights and potential solutions from other fields. Listening before talking can go a long way.

Small’s collaborative mindset has led him to other mental-health projects, such as the Transforming Indigenous Mental Health and Wellbeing project to establish culturally sensitive mental-health support for Indigenous Australians.

Career considerations

Mathematicians who engage in social-justice projects say that helping to create real-world change can be tremendously gratifying. Small wants “to work on problems that I think can do good” in the world. Spending time pursuing them “makes sense both as a technical challenge [and] as a social choice”, he says.

However, pursuing this line of maths research is not without career hurdles. “It can be very difficult to get [these kinds of] results published,” Small says. Although his university supports, and encourages, his mental-health research, most of his publications are related to his standard mathematics research. As such, he sees “a need for balance” between the two lines of research, because a paucity of publications can be a career deal breaker.

Diaz Eaton says that mathematicians pursuing social-justice research could experience varying degrees of support from their universities. “I’ve seen places where the work is supported, but it doesn’t count for tenure [or] it won’t help you on the job market,” they say.

Finding out whether social-justice research will be supported “is about having some really open and transparent conversations. Are the people who are going to write your recommendation letters going to see that work as scholarship?” Diaz Eaton notes.

All things considered, mathematicians should not feel daunted by wading into solving the world’s messy problems, Khadjavi says: “I would like people to follow their passions. It’s okay to start small.”

This article is reproduced with permission and was first published on May 22, 2024 .

Help | Advanced Search

Computer Science > Artificial Intelligence

Title: mathchat: benchmarking mathematical reasoning and instruction following in multi-turn interactions.

Abstract: Large language models (LLMs) have demonstrated impressive capabilities in mathematical problem solving, particularly in single turn question answering formats. However, real world scenarios often involve mathematical question answering that requires multi turn or interactive information exchanges, and the performance of LLMs on these tasks is still underexplored. This paper introduces MathChat, a comprehensive benchmark specifically designed to evaluate LLMs across a broader spectrum of mathematical tasks. These tasks are structured to assess the models' abilities in multiturn interactions and open ended generation. We evaluate the performance of various SOTA LLMs on the MathChat benchmark, and we observe that while these models excel in single turn question answering, they significantly underperform in more complex scenarios that require sustained reasoning and dialogue understanding. To address the above limitations of existing LLMs when faced with multiturn and open ended tasks, we develop MathChat sync, a synthetic dialogue based math dataset for LLM finetuning, focusing on improving models' interaction and instruction following capabilities in conversations. Experimental results emphasize the need for training LLMs with diverse, conversational instruction tuning datasets like MathChatsync. We believe this work outlines one promising direction for improving the multiturn mathematical reasoning abilities of LLMs, thus pushing forward the development of LLMs that are more adept at interactive mathematical problem solving and real world applications.

Submission history

Access paper:.

• HTML (experimental)
• Other Formats

References & Citations

• Google Scholar
• Semantic Scholar

BibTeX formatted citation

Bibliographic and Citation Tools

Code, data and media associated with this article, recommenders and search tools.

• Institution

arXivLabs: experimental projects with community collaborators

arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website.

Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them.

Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs .

Applied mathematical problem solving, modelling, applications, and links to other subjects — State, trends and issues in mathematics instruction

• Published: February 1991
• Volume 22 , pages 37–68, ( 1991 )

Cite this article

• Werner Blum 1 , 2 &
• Mogens Niss 1 , 2  

3583 Accesses

320 Citations

3 Altmetric

Explore all metrics

The paper will consist of three parts. In part I we shall present some background considerations which are necessary as a basis for what follows. We shall try to clarify some basic concepts and notions, and we shall collect the most important arguments (and related goals) in favour of problem solving, modelling and applications to other subjects in mathematics instruction. In the main part II we shall review the present state, recent trends, and prospective lines of development, both in empirical or theoretical research and in the practice of mathematics instruction and mathematics education, concerning (applied) problem solving, modelling, applications and relations to other subjects. In particular, we shall identify and discuss four major trends: a widened spectrum of arguments, an increased globality, an increased unification, and an extended use of computers. In the final part III we shall comment upon some important issues and problems related to our topic.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price includes VAT (Russian Federation)

Instant access to the full article PDF.

Rent this article via DeepDyve

Institutional subscriptions

Similar content being viewed by others

Introduction to Mathematical Challenges for All Unraveling the Intricacy of Mathematical Challenge

Mathematical practices, in theory and practice

Author information

Authors and affiliations.

Dept. of Mathematics, Kassel University, Heinrich-Plett-Str. 40, D-3500, Kassel, Federal Republic of Germany

Werner Blum & Mogens Niss

Roskilde University IMFVFA, Postbox 260, DK-4000, Roskilde, Denmark

You can also search for this author in PubMed   Google Scholar

Additional information

Written version of a Survey Lecture given jointly at the Sixth International Congress on Mathematical Education (ICME-6, Budapest 1988). A condensation was published in a volume with contributions from the ICME-6 Theme Groups on Problem Solving, Modelling and Applications and on Mathematics and Other Subjects (Blum/Niss/Huntley 1989, pp. 1–21).

Rights and permissions

Reprints and permissions

About this article

Blum, W., Niss, M. Applied mathematical problem solving, modelling, applications, and links to other subjects — State, trends and issues in mathematics instruction. Educ Stud Math 22 , 37–68 (1991). https://doi.org/10.1007/BF00302716

Download citation

Issue Date : February 1991

DOI : https://doi.org/10.1007/BF00302716

Share this article

Anyone you share the following link with will be able to read this content:

Sorry, a shareable link is not currently available for this article.

Provided by the Springer Nature SharedIt content-sharing initiative

• Present State
• Basic Concept
• Mathematics Instruction
• Mathematical Problem
• Find a journal
• Publish with us
• Track your research

More From Forbes

5 concepts from physics that could give you an edge as a startup founder.

• Share to Facebook
• Share to Twitter
• Share to Linkedin

Physics concepts can provide valuable mental models for decision-making, strategy development, and ... [+] problem-solving. So, in this article, we discuss five essential ideas from physics that can be applied to the world of startups and entrepreneurship.

It’s hard to have a competitive edge as an entrepreneur and business manager if you are drawing your information from the same traditional business sources as all other entrepreneurs. Having a diverse knowledge base could help you see situations from a different angle, which could help you see threats and opportunities other founders could miss.

Certain physics concepts can provide valuable mental models for decision-making, strategy development, and problem-solving. So, in this article, we discuss five essential ideas coming from physics that can be applied to the world of startups and entrepreneurship.

1. Newton's First Law (Inertia)

Newton's First Law, also known as the law of inertia, states that an object at rest will remain at rest, and an object in motion will remain in motion unless acted upon by an external force. This principle, discovered by Sir Isaac Newton in the 17th century, describes the resistance of any physical object to a change in its state of motion.

In the context of entrepreneurship, inertia can be seen in the resistance to change within organizations and markets. For startups, overcoming inertia means finding ways to disrupt the status quo and motivate stakeholders to embrace new ideas.

For example, when introducing a disruptive product, entrepreneurs must identify and apply the necessary "force" to overcome market resistance, such as compelling marketing strategies, demonstrations of value, or strategic partnerships.

NSA Warns iPhone And Android Users To Turn It Off And On Again

A 3-point cheat sheet for creating romantic chemistry—by a psychologist, goldman sachs issues astonishing bitcoin and ethereum etf prediction after price turning point.

Understanding inertia helps entrepreneurs recognize that change requires deliberate effort and energy to shift established patterns and behaviors.

2. Newton's Second Law (F=ma)

Newton's Second Law states that the force acting on an object is equal to the mass of the object multiplied by its acceleration (F=ma). This law quantifies the relationship between an object's mass, the force applied to it, and the resulting acceleration.

For startups, this principle can be translated into the relationship between resources (mass), effort (force), and growth (acceleration). A startup with substantial resources (financial, human, technological) that applies significant effort (strategic planning, execution) will experience faster growth.

Conversely, a startup with limited resources must either find ways to increase efficiency or apply greater force to achieve acceleration. Entrepreneurs can use this model to assess their resource allocation and strategic efforts, ensuring that their actions are sufficient to drive the desired growth and momentum.

Combined with Newton’s first law, it follows that a huge amount of force is necessary to change the trajectory of a big corporation (a high-mass object) due to inertia. This is a big boon for startups, as they can react to shifting market conditions much quicker than established corporations that struggle to overcome their own inertia.

3. Thermodynamics And Conservation Of Energy

The first law of thermodynamics, also known as the law of conservation of energy, states that energy cannot be created or destroyed, only transformed from one form to another. This principle, established in the 19th century, emphasizes the constancy of energy within a closed system.

In a startup context, this concept could be interpreted as a restatement of the economic concept of opportunity cost - there is no free lunch in business. By investing your energy (time, resources, etc.) in something, you are necessarily taking it away from something else. You have a finite amount of energy, which means that you need to use it wisely.

4. Leverage

Leverage, in the physical sense, refers to the use of a lever to amplify force, allowing a smaller force to move a larger load. The concept of leverage has been known since ancient times, with early civilizations using simple machines like levers to perform tasks more efficiently.

In business, leverage refers to using various means to amplify the impact of efforts and resources. This can include financial leverage (using debt to finance growth), operational leverage (scaling processes to increase output), and strategic leverage (forming alliances to enhance market presence).

Entrepreneurs can apply the principle of leverage to identify opportunities where small actions or investments can lead to significant gains. By strategically leveraging resources and capabilities, startups can achieve exponential growth and competitive advantage with minimal initial input.

In fact, this is a crucial concept for early-stage startups. Initially, you have very little force to apply to your project. This means that in order to achieve a significant impact, you need to leverage it. Traditionally, this is done by using other people’s resources (capital) in addition to scalable technology, which presents another form of leverage for your efforts.

5. Momentum

Momentum, a concept from classical mechanics, is the product of an object's mass and velocity. It represents the quantity of motion an object has and is a measure of how difficult it is to stop that object.

In the entrepreneurial world, momentum signifies the progress and traction a startup gains over time. Once a startup begins to build momentum through early successes, customer acquisitions, or funding rounds, it becomes easier to sustain and accelerate growth. Maintaining momentum requires continuous effort and focus, ensuring that the startup does not lose its forward motion. Entrepreneurs should seek to build and sustain momentum by setting achievable milestones, celebrating wins, and maintaining a consistent pace of development and innovation.

• Editorial Standards
• Reprints & Permissions

Join The Conversation

One Community. Many Voices. Create a free account to share your thoughts. 

Forbes Community Guidelines

Our community is about connecting people through open and thoughtful conversations. We want our readers to share their views and exchange ideas and facts in a safe space.

In order to do so, please follow the posting rules in our site's  Terms of Service.   We've summarized some of those key rules below. Simply put, keep it civil.

Your post will be rejected if we notice that it seems to contain:

• False or intentionally out-of-context or misleading information
• Insults, profanity, incoherent, obscene or inflammatory language or threats of any kind
• Attacks on the identity of other commenters or the article's author
• Content that otherwise violates our site's  terms.

User accounts will be blocked if we notice or believe that users are engaged in:

• Continuous attempts to re-post comments that have been previously moderated/rejected
• Racist, sexist, homophobic or other discriminatory comments
• Attempts or tactics that put the site security at risk
• Actions that otherwise violate our site's  terms.

So, how can you be a power user?

• Stay on topic and share your insights
• Feel free to be clear and thoughtful to get your point across
• ‘Like’ or ‘Dislike’ to show your point of view.
• Protect your community.
• Use the report tool to alert us when someone breaks the rules.

Thanks for reading our community guidelines. Please read the full list of posting rules found in our site's  Terms of Service.

• Computer Vision
• Federated Learning
• Reinforcement Learning
• Natural Language Processing
• New Releases
• Advisory Board Members
• 🐝 Partnership and Promotion

Regarding performance, the InternLM2-Math-Plus models show significant improvement over existing models. The 1.8B model, for example, outperforms the MiniCPM-2B in the smallest size category. Similarly, the 7B model surpasses the Deepseek-Math-7B-RL, previously state-of-the-art open-source math reasoning models. Notably, the largest model, Mixtral8x22B, achieves top scores on MATH and GSM8K, indicating superior problem-solving capabilities.

The InternLM2-Math-Plus 1.8B model shows notable performance improvements with scores of 37.0 on MATH, 41.5 on MATH-Python, and 58.8 on GSM8K. The 7B variant enhances these results further, achieving 53.0 on MATH, 59.7 on MATH-Python, and 85.8 on GSM8K. The 20B model also performs impressively, scoring 53.8 on MATH, 61.8 on MATH-Python, and 87.7 on GSM8K. The largest model, Mixtral8x22B, achieves 68.5 on MATH and 91.8 on GSM8K.

Each variant of InternLM2-Math-Plus is designed to address specific needs in mathematical reasoning. The 1.8B model balances performance and efficiency, which is ideal for applications requiring robust yet compact models. The 7B model provides enhanced capabilities for more complex problem-solving tasks. The 20B model further pushes the boundaries of performance, making it suitable for highly demanding mathematical computations. The Mixtral8x22B model, with its extensive parameters, delivers unparalleled accuracy and precision, making it the go-to choice for the most challenging mathematical tasks.

In conclusion, the research on InternLM2-Math-Plus signifies a substantial advancement in the mathematical reasoning capabilities of LLMs. The models effectively address key challenges by integrating sophisticated training techniques and leveraging extensive datasets, enhancing performance on various mathematical benchmarks. 

• https://arxiv.org/pdf/2402.06332
• https://x.com/intern_lm/status/1795043367383859523
• https://github.com/InternLM/InternLM-Math
• https://huggingface.co/internlm/internlm2-math-plus-1_8b/
• https://huggingface.co/internlm/internlm2-math-plus-7b/
• https://huggingface.co/internlm/internlm2-math-plus-20b/
• https://huggingface.co/internlm/internlm2-math-plus-mixtral8x22b/

Asif Razzaq

Asif Razzaq is the CEO of Marktechpost Media Inc.. As a visionary entrepreneur and engineer, Asif is committed to harnessing the potential of Artificial Intelligence for social good. His most recent endeavor is the launch of an Artificial Intelligence Media Platform, Marktechpost, which stands out for its in-depth coverage of machine learning and deep learning news that is both technically sound and easily understandable by a wide audience. The platform boasts of over 2 million monthly views, illustrating its popularity among audiences.

MAP-Neo: A Fully Open-Source and Transparent Bilingual LLM Suite that Achieves Superior Performance to Close the Gap with Closed-Source Models

Researchers at stanford propose sleepfm: a new multi-modal foundation model for sleep analysis.

• The Emergence of Super Tiny Language Models (STLMs) for Sustainable AI Transforms the Realm of NLP
• Mistral AI Releases Codestral: An Open-Weight Generative AI Model for Code Generation Tasks and Trained on 80+ Programming Languages, Including Python

RELATED ARTICLES MORE FROM AUTHOR

Understanding system prompts and the power of zero-shot vs. few-shot prompting in artificial intelligence (ai), autocoder: the first large language model to surpass gpt-4 turbo (april 2024) and gpt-4o in pass@1 on the human eval benchmark test (90.9% vs...., dir-assistant: simplifying file management with local and api language models, anthropic’s claude ai takes a leap forward with tool use/function calling feature, map-neo: a fully open-source and transparent bilingual llm suite that achieves superior performance to..., understanding system prompts and the power of zero-shot vs. few-shot prompting in artificial intelligence..., autocoder: the first large language model to surpass gpt-4 turbo (april 2024) and gpt-4o....

• AI Magazine
• Privacy & TC
• Cookie Policy

🐝 🐝 Join the Fastest Growing AI Research Newsletter Read by Researchers from Google + NVIDIA + Meta + Stanford + MIT + Microsoft and many others...

Thank You 🙌

Privacy Overview