What does ChatGPT Think About Maths?

The chances are you've heard of ChatGPT, but you might not know what it is. Just in case, I asked it what it was. It said:

"ChatGPT is a conversational artificial intelligence language model developed by OpenAI. It uses state-of-the-art machine learning algorithms and a massive dataset to generate human-like responses to natural language inputs. ChatGPT is trained on a diverse range of topics and can answer a wide range of questions, making it an extremely versatile AI system. It can be used for various applications, such as customer service, knowledge base, language translation, and more."

I didn't have an image for this post so I asked DALL·E 2 "what does ChatGPT look like?"

Essentially, it's a big blob of maths that's been given an enormous collection of texts to play with. When you ask it a question it analyses what you've typed and takes a statistical stab at writing something that you might classify as a 'correct' answer. Its 'training', in simple terms, involves being asked questions and providing an answer. These answers are scored against criteria such as whether it makes sense and, if so, whether it's relevant and true. Early answers are probably strings of gibberish but because it involves computers and clever algorithms it can work through them at a phenomenal rate, getting mostly bad scores at first but occasionally getting better scores by chance. Eventually, it works out what collections of symbols to output for any given input that will receive good scores.

This is a very similar idea to DALL·E 2 and craiyon (previously DALL·E mini), except it works with text rather than images. Peter Rowlett, blogging over at the Aperiodical, found out what craiyon thought mathematics and mathematicians look like, and I asked DALL·E 2 the same questions when I gained access a few weeks later. I thought it might be interesting to see what ChatGPT thinks of maths and mathematicians. The questions I asked are provided in the headings below; ChatGPT's responses have been copied and pasted beneath each one.

1. What is mathematics?

"Mathematics is the study of numbers, quantities, and shapes, and the relationships among them. It is an abstract subject that uses logical reasoning and critical thinking to solve problems and make predictions. Mathematics is widely considered to be a fundamental and universal language that is used in a variety of fields, including science, engineering, economics, and finance. It includes branches such as algebra, geometry, calculus, number theory, and statistics, and can be studied at different levels of depth and generality. Mathematics is also a creative and dynamic subject, with new theories and solutions constantly being developed."

2. Explain why mathematics is important to someone who doesn't like mathematics.

"Mathematics is not just about numbers and equations. It's a fundamental tool for understanding and describing the world around us. It's used in a wide range of fields, from science and engineering to finance, economics, and even the arts.

For someone who doesn't like mathematics, it might be difficult to see the practical applications of it in everyday life. But math is a critical part of solving real-world problems. It helps us to make better decisions, understand data, and communicate ideas more effectively.

In the business world, for example, math skills are essential for budgeting, forecasting, and analyzing market trends. In medicine, math is used to evaluate treatment options, understand the spread of diseases, and develop new technologies.

Moreover, math helps develop important skills such as problem-solving, critical thinking, and logic. These skills are valuable in many aspects of life and can help you to be successful in whatever career you choose.

In short, even if you don't like math, it's important to have a basic understanding of it as it's a critical part of our daily lives and essential for success in many areas."

3. What are the most common misconceptions about mathematics?

"There are several misconceptions about mathematics that are commonly held by students and even some adults:

1. Mathematics is just about memorizing formulas and rules: While there is some memorization involved, mathematics is much more about problem solving and critical thinking. It involves finding patterns, making connections, and logically deducing solutions.
2. Mathematics is not relevant to real-life: Mathematics is an integral part of our daily lives, from calculating our expenses and managing our finances, to designing and building structures and even understanding weather patterns.
3. Mathematics is a fixed subject with one right answer: In mathematics, there are often multiple methods to solve a problem and multiple answers that are considered correct. This allows for creative thinking and exploration.
4. Mathematics is only for people with a natural talent: While some people may have a natural affinity for mathematics, anyone can learn and excel at mathematics with hard work and dedication.
5. Mathematics is boring: While some people find mathematics dry and uninteresting, it can also be fascinating, beautiful, and fun. It's all about perspective and how the subject is taught.

These misconceptions can prevent individuals from fully appreciating the value and relevance of mathematics in their lives, and can also lead to a fear of mathematics. By addressing these misconceptions, students can develop a more positive attitude towards mathematics and find enjoyment in solving problems."

4. Describe a mathematician.

"A mathematician is a person who studies and practices the field of mathematics. This can include a wide range of subfields such as algebra, geometry, calculus, number theory, and more. Mathematicians use abstract reasoning, logical deduction, and problem-solving skills to understand mathematical concepts and develop new mathematical theories. They may work in academia, industry, government, or other settings, and often collaborate with other mathematicians and scientists to address complex mathematical problems. A successful mathematician is someone who is both highly knowledgeable about mathematics and able to apply this knowledge to real-world problems. They have strong critical thinking and analytical skills, and are able to think creatively and outside the box to find solutions to complex problems."

5. Who can do mathematics?

"Mathematics is a subject that can be studied and practiced by people of all ages, backgrounds, and abilities. It is a universal language that can be understood by people all over the world, regardless of culture, ethnicity, or language. With practice and dedication, anyone can develop the skills and knowledge necessary to excel in mathematics. It is a subject that requires patience, persistence, and a willingness to think logically and creatively. Whether you are a student, a teacher, an engineer, a scientist, or any other professional, mathematics has something to offer, and the opportunities for growth and discovery are limitless."

6. What's the best thing about mathematics?

"Mathematics has many great aspects, and what is considered the best thing can vary from person to person. Some people might appreciate the elegance and beauty of mathematical concepts and theorems. Others might appreciate the practical applications of mathematics, such as how it is used in engineering, science, and technology.

For some, the challenge of solving mathematical problems and the sense of accomplishment when they succeed is what makes mathematics so appealing.

Ultimately, the best thing about mathematics depends on one's individual perspective and interests. But it is safe to say that mathematics is a fascinating and rewarding field of study that offers endless opportunities for exploration and discovery."

What do you think? Did Chat GPT make any major mistakes here, or did it largely hit the mark? What questions should I have asked? Post them in the comments and I might do a 'part II'.