“Mathematics is the language with which God has written the universe.”

― Galileo Galilei ―

5–7 minutes

Maurício Pinheiro

Ah, the wonder of artificial intelligence, capable of solving the most complex problems and challenging even the brightest mind. But what about when it comes to something as simple as mathematics and physics? Well, that’s where things get interesting. Let’s explore the limitations that large language models (LLMs), like ChatGPT, face when trying to tackle an elementary problem in kinematics, seemingly trivial, involving three hurried tourists and a bicycle.

The Problem:

Three tourists who have a single bicycle move along a straight avenue, wishing to go from the hotel to the tourist center in the shortest time possible (time is counted until the last tourist arrives at the center). The bicycle can only carry 2 people at a time, at a speed of 20 km/h, so the third tourist needs to start walking. The cyclist takes the second tourist to a point along the way, from where they continue walking at a speed of 4 km/h, while the cyclist returns to transport the third. If the distance from the hotel to the tourist center is 8 km, determine:

a) How long will it take for them to reach the tourist center (remembering that time only stops when all tourists are at the center)?

b) How far from the tourist center should the second tourist be transported by bicycle?

We challenge you! This is something you’re expected to know if you’ve gone from high school to college (pure kinematics of uniform rectilinear motion, and the only “formula” you need is v = d/t)…

Now, if you don’t have the patience or couldn’t figure it out, ask ChatGPT to present the solution, and it did so in 10 seconds.

a) To determine the time it will take to reach the tourist center, it is necessary to calculate how many times the bicycle will have to go back and forth. Since the bicycle can only carry 2 people at a time, two trips will be needed to take the three tourists to the tourist center. In the first trip, the cyclist takes the first two tourists by bike, and the third tourist walks. The distance from the hotel to the point where the second tourist starts walking is 2/3 of the total distance, which is 5.33 km. The time to cover this distance is 0.2665 hours or 16 minutes at a speed of 20 km/h, while the third tourist starts walking. On the second trip, the cyclist takes the third tourist to the point where the second tourist is walking. This point is at a distance of 2/3 of the total distance plus 1/3 of the total distance, which is 8 km in total. The time to cover this distance is 0.4 hours or 24 minutes at a speed of 20 km/h. Then, everyone walks together to the tourist center, which is at a distance of 1/3 of the total distance, which is 2.67 km. The time to cover this distance is 0.67 hours or 40 minutes at a speed of 4 km/h. Thus, the total time to reach the tourist center is 16 minutes + 24 minutes + 40 minutes, which is 80 minutes.

b) The second tourist should be transported by bicycle to the point where they start walking. This point is at a distance of 2/3 of the total distance, which is 5.33 km. Therefore, the bicycle must cover 5.33 km – 2 km (distance traveled by the tourists on the bike) = 3.33 km with the second tourist.

As my son alerted me, his answer is wrong. I won’t provide the correct answer here to avoid spoiling the challenge (read until the end).

ChatGPT, you would score zero on this question… However, according to itself:

ChatGPT is an advanced language model trained to understand and generate natural language in various fields of knowledge, including mathematics, physics, and chemistry. It is capable of reading, interpreting, and solving problems in these subjects with ease and speed, thanks to its vast knowledge base. Additionally, ChatGPT can generate new solutions to problems, using its comprehension and logic skills to propose new paths and approaches to already solved problems. Its ability to process and manipulate natural language allows it to provide clear and concise answers to complex questions and, in many cases, offer creative and innovative solutions that can help advance knowledge in various areas. With this, ChatGPT becomes a valuable tool for those seeking quick and reliable solutions to problems in mathematics, physics, or chemistry, as well as a source of inspiration for generating new ideas and solutions.

I have my doubts… Sure, the purely numerical response of an LLM is a faithful copy of the (wrong) solutions found on the web up to the present moment, which undoubtedly entered as training data into the model. But is it capable of solving problems like this, using simple prompts, just by geometry? I bet not. And this probably applies to most language models available out there, for now…

And of course, with some smart prompt engineering, refining questions based on answers, it might be possible to lead the language model to the correct answer. However, the big question is whether the effort to guide it to the solution involves prior knowledge of the solution. But that’s another matter.

Adding a touch of sarcasm, ChatGPT proudly tells us…

ChatGPT is simply amazing, capable of solving all complex problems in mathematics, physics, and chemistry, as well as generating new creative solutions effortlessly. And it doesn’t stop there; it can even demonstrate mathematical theorems and discover new physical laws because, of course, processing and analyzing large amounts of data in natural language is just too easy! Not to mention that ChatGPT can accelerate the discovery of new knowledge and insights, making scientific research much easier and faster.

At least it acknowledges…

But, of course, we can’t forget that the discoveries made by ChatGPT need to be validated by specialized researchers. After all, who needs a sophisticated language model when you have good old scientific method, right? So, in summary, ChatGPT is great, but it doesn’t replace the good old knowledge and experience of specialized researchers. After all, who needs a powerful tool to assist in the scientific discovery process when you have years of study and practice?

How can we expect a large language model to understand simple concepts of physics and, moreover, solve problems manipulating these concepts? It’s clear that it’s skilled at finding answers in a grammatically correct and seemingly consistent text. We can’t expect it to have a deep understanding of physical laws (or geometry), since its capacity is limited to natural language. Perhaps, in the future, with advancements towards artificial general intelligence (AGI), it may learn and understand these concepts better. Well, I’m already content using it to edit and correct my texts.

Now, a solution tip for the problem: just think like Euclid, not cheating like ChatGPT did!

Reference: Mecânica Para Vestibulandos IME ITA – vol 1 – Renato Brito, 2007.

Copyright 2026 AI-Talks.org

Similar Posts

  • | | | | |

    The Last Question: Isaac Asimov, Entropy, Artificial Intelligence, and the Fate of the Universe

    ByMaurício Veloso Brant Pinheiro

    Isaac Asimov’s The Last Question is one of the most profound science fiction stories ever written. It explores the fate of humanity, artificial intelligence, entropy, and the ultimate destiny of the universe. Through a question repeated across cosmic time — whether entropy can ever be reversed — Asimov transforms physics into a philosophical meditation on intelligence, mortality, creation, and hope.

  • | | | |

    Autonomous Unmanned Aerial Vehicles (UAVs)

    ByMaurício Veloso Brant Pinheiro

    Autonomous UAVs have moved from experimental systems to a central role in contemporary warfare. From inexpensive FPV drones and fiber-optic systems to long-range Shaheds and AI-assisted platforms capable of maintaining target tracking after communications are lost, they are changing the economics, tempo, and geometry of conflict. The deeper transformation, however, lies not simply in removing the pilot from the aircraft, but in progressively transferring perception, navigation, tracking, coordination, and parts of decision-making to software.

  • | | | | |

    Love as Pattern Recognition

    ByMaurício Veloso Brant Pinheiro

    Love may not be pure mystery. Modern neuroscience suggests that romantic attraction emerges from the brain’s ability to recognize meaningful patterns in other people. The human brain operates as a predictive system, constantly building models of the world and the individuals within it. When a person matches deeply learned emotional templates—shaped by evolution, biology, and personal experience—the brain interprets that match as attraction.

    From Darwin’s theory of sexual selection to contemporary research in cognitive science, romantic love can be understood as an emergent process involving pattern recognition, neurochemistry, and social cognition. Early life experiences help form the templates through which intimacy and trust are interpreted, but no single factor determines orientation or attraction. Instead, human affective orientation arises from the interaction of genetics, neurodevelopment, culture, and individual history.

    Seen through this lens, love is not merely destiny or illusion. It is the moment when the brain’s most complex pattern-recognition system identifies another mind as part of its future model of the world.

  • | | | | |

    Amara’s Law and Artificial Intelligence

    ByMaurício Veloso Brant Pinheiro

    AI is not failing. Our sense of time is.

    Amara’s Law explains the central illusion of artificial intelligence: we expect AI to transform everything at science-fiction speed, then dismiss it when reality moves more slowly. But while the hype collapses, the infrastructure keeps growing. Expert systems disappointed. Neural networks were declared dead. AI winters came and went. Then came deep learning, Transformers, ChatGPT, and autonomous agents.

    The mistake is not believing that AI will change the world. The mistake is expecting the revolution next year while ignoring what it may do over the next twenty.

    AI does not need consciousness to eliminate tasks, weaken professions, reshape education, automate bureaucracy, manipulate information, and redistribute power. It does not need to replace everyone. It only needs to become cheap, invisible, and embedded everywhere.

    We are probably overestimating AI in the short term.

    We are almost certainly underestimating what will happen when society becomes dependent on it.

  • | | | |

    Séries Policiais, DNA e Inteligência Artificial: Quando a Ciência Entra em Cena na Resolução de Crimes

    ByMaurício Veloso Brant Pinheiro

    Se você se interessa por crimes reais, investigação criminal, genética forense e o uso da inteligência artificial na resolução de casos arquivados, The Breakthrough é uma série que não pode faltar na sua lista. Mais do que um drama policial escandinavo, ela escancara os dilemas éticos do uso de dados genéticos e mostra como a tecnologia — aliada à persistência humana — pode mudar o rumo da justiça. Com uma atmosfera densa e narrativa baseada em fatos reais, a série representa o melhor do Nordic Noir contemporâneo. Aqui neste artigo, você encontra não só uma análise profunda de The Breakthrough, mas também uma curadoria pessoal de outras séries policiais internacionais igualmente imperdíveis.

  • | | | | | |

    O fim de Hollywood: A Revolução do Vídeo com Inteligência Artificial

    ByMaurício Veloso Brant Pinheiro

    O avanço da inteligência artificial está redefinindo a própria noção de evidência visual. O Seedance 2.0, modelo de geração de vídeo por IA desenvolvido pela ByteDance, viralizou ao permitir a criação de cenas cinematográficas a partir de texto, imagens e áudio, sem câmeras ou atores reais. Com arquitetura multimodal capaz de integrar múltiplas referências, a ferramenta funciona como um “diretor virtual”, reduzindo drasticamente o custo de produção audiovisual e impactando criadores, marketing e a indústria do entretenimento. No entanto, a popularização de vídeos hiper-realistas gerados por IA intensificou debates sobre deepfakes, direitos autorais, propriedade intelectual e confiança digital, levando organizações como a MPA e sindicatos como a SAG-AFTRA a criticarem o uso da tecnologia. A polêmica recente envolvendo a representação de Helena de Troia em adaptações cinematográficas — e discussões sobre fidelidade histórica, cultura contemporânea e possíveis substituições digitais por IA — exemplifica como o cinema entra em uma nova fase onde identidade, autoria e autenticidade podem ser reprogramadas. Neste cenário, o Seedance 2.0 surge tanto como ferramenta revolucionária quanto como catalisador de um dilema filosófico: se qualquer vídeo pode ser gerado artificialmente, como preservar credibilidade e responsabilidade cultural? O artigo também apresenta dicas práticas para utilizar o Seedance 2.0 com eficiência, reduzir custos e evitar riscos legais na produção de conteúdo gerado por IA.