One of the prompts we asked Google's Gemini AI.
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Standing out as the two most popular artificial intelligence chatbots today, OpenAI’s ChatGPT and Google’s Gemini (previously known as Bard) are starting to be used more and more by professionals looking to increase their productivity.
But which one is better at giving clear, articulate, and accurate responses? In this blog post, we will attempt to determine the answer to this question by asking each of these chatbots the same three questions relating to math, history, and philosophy and gauging the accuracy and clarity of the responses.
Question One: Proving the Pythagorean Theorem in Simple Steps
For question one, we decided to ask the chatbots to write a proof for a mathematical theorem that has already been proved several times by others, in order to compare its responses with ease. The exact question is phrased as: “Prove the Pythagorean Theorem in simple steps.” We’re looking for the clarity of the explanation, the accuracy, and the readability.
ChatGPT 4o’s Response
Below is the raw text containing ChatGPT 4o’s response, including a screenshot of the beginning of the response.
The Pythagorean Theorem states that in a right triangle, the square of the hypotenuse (ccc) is equal to the sum of the squares of the other two sides (aaa and bbb):a2+b2=c2a^2 + b^2 = c^2a2+b2=c2
Here’s a simple geometric proof:
Step 1: Construct a Square Using the Triangle
- Start with a right triangle with sides aaa, bbb, and hypotenuse ccc.
- Place four identical copies of this triangle inside a large square whose side length is a+ba + ba+b.
Step 2: Analyze the Large Square
- The side length of the large square is a+ba + ba+b, so its area is:
Area of large square=(a+b)2.\text{Area of large square} = (a + b)^2.Area of large square=(a+b)2.
Step 3: Look Inside the Large Square
- Inside the large square:
- There are four triangles, each with an area of: Area of one triangle=12ab.\text{Area of one triangle} = \frac{1}{2}ab.Area of one triangle=21ab. So, the total area of the four triangles is: 4×12ab=2ab.4 \times \frac{1}{2}ab = 2ab.4×21ab=2ab.
- There is also a smaller square in the center, whose side length is ccc, so its area is: Area of smaller square=c2.\text{Area of smaller square} = c^2.Area of smaller square=c2.
Step 4: Express the Total Area
- The area of the large square can also be written as the sum of the areas of the four triangles and the smaller square:
Area of large square=2ab+c2.\text{Area of large square} = 2ab + c^2.Area of large square=2ab+c2.
Step 5: Equate the Two Expressions for the Large Square’s Area
- From Step 2, we know:
(a+b)2=Area of large square.(a + b)^2 = \text{Area of large square}.(a+b)2=Area of large square.
- From Step 4, we know:
Area of large square=2ab+c2.\text{Area of large square} = 2ab + c^2.Area of large square=2ab+c2.
- Equating these:
(a+b)2=2ab+c2.(a + b)^2 = 2ab + c^2.(a+b)2=2ab+c2.
Step 6: Expand and Simplify
- Expand (a+b)2(a + b)^2(a+b)2:
a2+2ab+b2=2ab+c2.a^2 + 2ab + b^2 = 2ab + c^2.a2+2ab+b2=2ab+c2.
- Subtract 2ab2ab2ab from both sides:
a2+b2=c2.a^2 + b^2 = c^2.a2+b2=c2.
It looks like ChatGPT was able to prove the theorem without using trigonometry or any other advanced mathematical techniques, so that’s a good sign for the simplicity. Its use of examples and the construction of figures makes it easy to understand, although some of the transformations of equations could use a little bit more detail.
As for the response time, ChatGPT took approximately ten to fifteen seconds to generate the response, which is pretty on-par with the language model. Overall, it appears that ChatGPT has chosen a solving-and-simplifying method of proving the theorem that seems to make sense on the whole. Score: 9/10
Google Gemini 1.5 Flash’s response
Below is the raw text containing Google Gemini’s response, including a screenshot of the entire response.
Here’s a simple proof of the Pythagorean Theorem using a geometric approach:
Step 1: Draw a right triangle
Start with a right triangle with sides of length a, b, and c, where c is the hypotenuse (the side opposite the right angle).
Step 2: Create squares on each side
Draw squares on each side of the triangle, with side lengths a, b, and c.
Step 3: Rearrange the squares
Cut the squares with sides a and b into pieces. Rearrange these pieces to exactly cover the square with side c.
Step 4: Analyze the areas
The area of the square with side c is c^2. The combined area of the squares with sides a and b is a^2 + b^2.
Since the rearranged pieces from the smaller squares perfectly cover the larger square, their areas must be equal:
c^2 = a^2 + b^2
This proves the Pythagorean Theorem: In a right triangle, the square of the hypotenuse (c) is equal to the sum of the squares of the other two sides (a and 1 b).
Right away, I noticed that it took Google Gemini a matter of seconds to generate the response. It was also significantly shorter than ChatGPT’s response, and did not use any LaTeX. While ChatGPT did not cite any sources, Gemini did–although the cited website, pdffiller.com, does not appear to be a legitimate source as it leads to a paywall on a website that offers sketchy test prep materials.
It appears that Gemini used a similar approach to proving the theorem as ChatGPT, avoiding advanced math techniques overall. There is nothing mentioned in Gemini’s approach about creating equations for the square generated or simplifying the equations down to the final theorem equation, and overall Gemini’s explanation is a bit lacking in detail. But it appears to have gotten the job done and makes sense for the most part. Score: 7.8/10
Question Two: Explaining a Famous Philosophical Quote
For question two, we asked both chatbots to explain the meaning of Socrates’s famous quote “The only true wisdom is in knowing you know nothing.”. We’re looking here for readability of the explanation, how much sense it makes, and the language in which it is written.
ChatGPT 4o’s Response
Below is the raw text of ChatGPT 4o’s response, including a screenshot of the complete response.
Socrates’s quote, “The only true wisdom is in knowing you know nothing,” captures a profound philosophical idea: wisdom begins with humility and self-awareness. It suggests that acknowledging the limits of your own knowledge is a crucial step toward true understanding. Here’s a deeper explanation:
- Intellectual Humility: Socrates emphasizes that wise individuals recognize the vastness of what they don’t know, instead of pretending to have all the answers. This openness to learning prevents arrogance and fosters growth.
- Continuous Inquiry:
By admitting ignorance, Socrates highlights the importance of asking questions and seeking knowledge. This mindset aligns with his Socratic method of questioning as a way to explore deeper truths and challenge assumptions.- Critique of False Wisdom:
Socrates often critiqued those who claimed to possess ultimate knowledge, such as politicians, poets, or craftsmen, in his time. He believed that their perceived wisdom was often based on superficial understanding rather than genuine insight.- Path to Growth:
Admitting ignorance is not an end but a beginning. It creates a foundation for curiosity, learning, and the pursuit of deeper understanding.In essence, this quote encourages us to embrace humility, question our assumptions, and remain lifelong learners. It’s a reminder that the more we learn, the more we realize how much remains unknown.
ChatGPT chose a modular method of explaining the meaning, focusing in on four different aspects of the quote and elaborating on what they mean. The summary at the end of the quote’s meaning serves as a conclusion to the response, and on the whole the response seems to make good sense. It is also easy to read and relates the quote to Socrates’s Socratic method of questioning, which makes sense. Overall Score: 10/10
Google Gemini 1.5 Flash’s response
Below is the complete response given by Google Gemini, including a screenshot of the response.
Socrates’ quote, “The only true wisdom is in knowing you know nothing,” is a profound statement about humility and the pursuit of knowledge. Here’s a breakdown of its meaning:
- Humility: Recognizing the limits of one’s knowledge is a form of humility. It acknowledges that there is always more to learn and that absolute certainty is often elusive.
- Open-mindedness: By admitting ignorance, one opens oneself to new ideas and perspectives. It fosters a willingness to learn and grow.
- Continuous Learning: The realization that we don’t know everything motivates us to seek knowledge and understanding. It drives intellectual curiosity and a desire for lifelong learning.
- Critical Thinking: Recognizing the limitations of knowledge encourages critical thinking and questioning assumptions. It helps us avoid dogmatic thinking and embrace a more nuanced approach to problem-solving.
In essence, Socrates’ quote suggests that true wisdom lies not in possessing knowledge, but in the awareness of one’s own ignorance. It is this awareness that propels us to seek knowledge, question our beliefs, and ultimately, become wiser.
At first glance, it appears that Google Gemini has adopted a similar responding method to ChatGPT, breaking down its response into four points that focus in on specific aspects of the quote. “Humility” is a shared point by both of the responses, and they both express similar reasons for focusing in on the humility aspect of the quote. It is interesting to note that the conclusion section of both responses start with “In essence”. Both responses generally express the same ideas, although we feel that ChatGPT’s response was a little bit more in-depth. Score: 9.5/10
Question Three: Analyzing a Complex Historical Passage
For a little bit of an increased challenge, we decided to ask both chatbots to summarize the dense passage below, and to analyze its meaning:
The Seventh Symphony (1812) was, at the time, Beethoven’s last and vibrant word on the big style he had cultivated in the previous decade. In the Eighth Symphony (1814) he does something new by seeming to return to something old. He writes, that is, a symphony shorter than any since his First. It is almost as though he wanted to call his entire development throughout that decade into question. Indeed, over the remaining years of his life he would confidently explore in opposite directions, writing bigger pieces than before and ones more compressed, his most rhetorical music and his most inward, his most public and his most esoteric, compositions that plumb the inexhaustible possibilities of the sonata style and those that propose utterly new ways of organizing material, music reaching extremes of the centered and the bizarre.
If, however, we think of the Eight as a nostalgic return to the good old days, we misunderstand it. To say it is 1795 revisited from the vantage point of 1812 is not right either. What interests Beethoven is not so much brevity for its own sake — and certainly not something called “classicism” — as concentration. It is as though he were picking up where he had left off in the densely saturated first movement of the Fifth Symphony to produce another tour de force of tight packing. He had already done something like this two years earlier in one of his most uncompromising works, the F-minor String Quartet, Op. 95. But a symphony is not a “private” connoisseur’s music like a string quartet; by comparison, the Eighth Symphony is Opus 95’s friendly, open-featured cousin, even though its first and last movements bring us some of the most violent moments in Beethoven.
ChatGPT 4o’s Response
Below is the complete and raw response from ChatGPT to the prompt, including a screenshot of the entire response.
The passage discusses Beethoven’s Eighth Symphony (1814) as a significant departure from the expansive style of his earlier works, like the Seventh Symphony (1812). Although shorter, it is not merely a nostalgic return to the classical style but a bold exercise in concentration and compactness. Beethoven refines his approach, echoing the dense intensity of the Fifth Symphony’s first movement and the Op. 95 String Quartet. However, unlike the private nature of a string quartet, the Eighth Symphony is more accessible and outward-facing, yet still includes moments of intense, even violent energy, demonstrating Beethoven’s exploration of extremes in his later years.
The clarity and conciseness of ChatGPT’s response is immediately satisfactory. It reduces much of the pompous and advanced language used in the original passage down to a good summary, using some of the terms from the original passage (in bold) and combining them with its own language and interpretation. The information appears to be accurate, and would likely serve as a sufficient summary for someone in a professional environment. Overall Score: 9.5/10
Google Gemini 1.5 Flash’s response
The following is the raw, unedited response from Google Gemini, including a screenshot of the complete response:
Beethoven’s Eighth Symphony, while seemingly a return to a shorter, more classical style, is actually a concentrated exploration of musical possibilities. It’s not a nostalgic throwback but a bold experiment in density and intensity, drawing inspiration from the focused energy of his Fifth Symphony and the uncompromising nature of his F-minor String Quartet. Despite its more accessible form, the Eighth Symphony contains moments of extreme violence and complexity, showcasing Beethoven’s ability to push the boundaries of the classical tradition.
Gemini’s response appears to be similar in length to ChatGPT’s response, and contains the same level of conciseness and clarity as the prior response. While it doesn’t borrow specific terms and vocabulary from the original passage, it shows the same general ideas as ChatGPT, and both of their summaries appear to agree with each other, especially when it comes to Beethoven’s exploration of extremes and “pushing the boundaries” when it comes to classical tradition. Both responses appear to be on par with each other in terms of readability, accuracy, and conciseness. Overall Score: 9.5/10
Conclusion
Our overall observation from all three questions is that ChatGPT tends to provide more accurate and elaborate responses. On the math question, for example, ChatGPT provided very detailed steps and explanations for how it derived each of its subsequent equations as part of the proof. While Google Gemini didn’t provide quite as much detail on some of the steps for that problem, it performed equally well in making sure its proof made sense, and responding to the overall prompt.
On the philosophical analyzation prompt, both artificial intelligence bots did well, outputting similar results on similar interpretations of the quote, but again ChatGPT went into a little bit more detail overall on each of the four aspects of the quote.
Finally, both chatbots gave very similar responses on the final question with the analyzation of the passage, although we feel that ChatGPT demonstrated a greater connection to the original passage than Google Gemini.
So what’s the verdict? On the whole, it looks like ChatGPT came out on top, both in the overall scores (getting a 28.5/30, to Gemini’s 26.8) and in its general interpretation and responses to all three of the prompts. Our conclusion corroborates the opinion of other analyzers, and it’s important to note here that we tested the free versions of both ChatGPT and Gemini (4o mini and 1.5 Flash). It should be apparent that the paid versions of these chatbots would yield increased performance and better response time, but to be fair we have to compare the same versions of each chatbot.
For more information on this subject, and what other analyzers think of these artificial intelligence bots, take a listen to the TechStation Podcast for November 24, 2024 (resuming exclusively for two months only!) where we’ll be discussing the top articles from this week.
