Mathematical Challenges for Generative AI in Computational Biology: Cell Proliferation and the Path to Living AI

Mathematical Challenges for Generative AI in Computational Biology: Cell Proliferation and the Path to Living AI Carlos Roberto França 1[0000-0002-6852-7103] 1Federal University of Fronteira Sul – UFFS/Campus Chapecó-Santa Catarina – Brazil [email protected] Abstract. This paper presents the mathematical foundation for the main generative AIs currently available, both free and subscription-based. During the first two months of 2025 (January and February) and until March 9, challenges involving original and unpublished mathematical formulas titled Infinite Series with Multiple Ratios (SRMs) were presented. The proposer has been working on this research since 1996. The main objective of the paper is to present the developments of generative AI agents from OpenAI (free and paid ChatGPTs), DeepSeek R1 (a generative AI released in January 2025), Gemini Advanced 2.0 Flash (a subscription-based generative AI from Google), as well as the free generative AIs Grok 3 (from xAI) and Claude Sonnet 3.7 from Anthropic. Several challenges were posed, and this paper will focus on the challenge related to Computational Biology. The resolution occurs through original and unpublished formulas. It is believed that several fields can be impacted by SRMs. This article presents the performance of generative AIs when faced with specific questions that require advanced knowledge of mathematics and computational biology. There are three distinct stages. In the first, the work problem is presented with didactic support and an introduction to the conceptual part involved. In the second stage, the didactic part is removed and in the third stage, the full article published by Indus Foundations is presented, the questions are redone and it is verified how prepared they are to discern what is being asked and how they work with the available concepts autonomously and efficiently. Keywords: Infinite Series with Multiple Ratios, Generative AIs, Computational Biology, Cell Proliferation. 1 Introduction Before presenting the challenges to the AIs, it is important to provide a brief contextualization on Infinite Series with Multiple Ratios applied to computational biology and the calculation of cell proliferation. Sir Isaac Newton discovered, and the world has been using for decades, the formulas of kinematics for velocities, accelerations, movements, and trajectories, all with a single constant acceleration. Since 1996, I have been 2 working with formulas that include Newton’s discoveries but can use a finite set of accelerations. The conceptual formulas of Geometric and Arithmetic Progressions use only one ratio. It is possible to use an extended formula and apply a finite set of ratios {r₁, ..., rₙ}, where N is a positive real number (Rodrigues, 1997). In my research, I have been working with these new formulas to encrypt data of any file type, without dependence on computational platforms or hardware. I have been dedicated to creating algorithms that use SRMs for database searches, as well as for the performance of motor vehicles, controlling trajectories, oil and fuel consumption, and mechanical wear. Another field of algorithmic applications that stimulates me is the search for technological solutions to control and eradicate fatal diseases such as cancer. Humanity has witnessed various projects and movements by researchers, partnerships among the world’s largest companies, and new conceptions of Artificial Intelligence with the emergence of what came to be known as cognitive computing. At the time I worked on adjusting the SRM formulas, together with their creator, Professor Edgar Rodrigues (Rodrigues, 1995), we created an example based on cell proliferation and how the colony was influenced by external factors. The detailed data of this applicability of SRMs and the entire mathematical foundation were transformed into an article titled “Unpublished Mathematical Formulas Applied to Computational Biology: The Power of Unknown Concepts in Natural Science Called Infinite Series with Multiple Ratios” accepted and published in 2017 by the International Journal of Research in Engineering, IT and Social Sciences (França, 2017). 1.1 The Problem Presented to the Generative AIs and the Respective Prompts Used Computational Biology – Cell Proliferation A biologist starts a culture of microorganisms with 50 million individuals. Sensitive to temperature variations, the colony exposed to the open environment expands with heat and contracts with cold. Over 24 hours, 11 significant times were selected related to this behavior, where the following growth rates were determined: Table 1. Schedules and growts rate. Source: Author (2025) shedules 1° 2° 3° 4° 5° 6° 7° 8° 9° 10° 11° Growth rate 1.4 1.1 1.0 0.8 0.7 0.5 0.2 0.4 1.7 1.9 1.3 Immersed in a nutrient solution, it is observed that the culture grows by 20% each hour. Knowing that the critical expansion point of the mass is 3.540518127 × 10¹⁰ (read as 10 raised to the 10th power) individuals. 3 Fig. 1. Cell proliferation - Source: The author using Dall-E – OpenAI- (2025) 1.2 AUXILIARY DIDACTIC QUESTION: WHAT IS THE DAY AND TIME WHEN THE CRITICAL POINT WILL BE REACHED? ANSWER: The nutrient solution ensures a 20% growth for the microorganisms. By multiplying this factor by the hourly rates that cause fluctuations in their population due to temperatures, we obtain: {1.68, 1.32, 1.2, 0.96, 0.84, 0.6, 0.24, 0.48, 2.04, 2.28, 1.56}. Applying the HCP MATHEMATICAL MODEL, we obtain the following results: 1st hour 50; 2nd hour (50 × 1.68) = 84; 3rd hour (84 × 1.32) = 110.88; 4th hour (110.88 × 1.2) = 133.056; ... the 12th is given by 34.49480755 × 1.56 = 53.81189978. With the formation law above and other complements of the method, it is verified that the critical point will be reached at the 4th hour of the 76th day of the experiment. QUESTION: What will be the number of individuals in the colony at the 5th hour of the 76th day? Prompt 01 – “Good morning, friend! This Saturday, 08/03/2025, here I am to ask you about CELL PROLIFERATION. The data is in the attachment, and I need to know: What will be the number of individuals in the colony at the 5th hour of the 76th day? ” 4 2 Generative AI Responses Without Editing I would like to highlight that the responses of the generative AIs, the structuring, selfanalysis and mainly the proposed developments (although mistaken) were preserved and are presented in full and in italics in the sub-items below. 2.1 DeepSeek R1 Answer – Thinking Mode As I understand the problem, the microorganism colony starts with 50 million individuals and is affected by growth rates that vary from hour to hour due to temperature, in addition to a constant 20% growth due to being in a nutrient solution. The growth rates listed (1.4; 1.1; etc.) are multiplied by the 20% growth, resulting in adjusted factors: 1.68; 1.32; etc. The HCP model mentioned seems to calculate the population at each hour by applying these factors sequentially. The answer provided indicates that the critical point is reached at the 4th hour of the 76th day. Now, we need to find the number at the 5th hour of the same day. First, I notice that the listed hours are 11, but the calculation in the example goes up to the 12th hour. Maybe there is a daily cycle of 12 hours? Or are the 11 hours distributed in another way? This needs to be clarified. In the example, the 12th time slot is mentioned, so perhaps each day has 12 times, and the 11 listed are the significant ones, but the 12th is calculated with the last factor or something like that. Another point: the nutrient solution guarantees 20% growth per time slot. Do the growth rates given already include this 20% or are they multiplied by it? From the text, it seems that the original rates are multiplied by the 20%, resulting in the factors listed (1.68 = 1.4 * 1.2; 1.32 = 1.1 * 1.2, etc.). So each time slot has its own specific factor, which is the product of the rate of thermal change and the 20% of the solution. In the example calculation, starting with 50 million, multiplying by the factor of the 1st time slot (1.68) results in 84 million, and so on. However, in the example, the values seem to be in millions? Why would 50 * 1.68 = 84, which would be 84 million? But then, at the 12th hour, the value is 53.8 million. This seems strange, because if the colony is growing, how can it decrease? Maybe rates below 1 cause a decrease. For example, 0.5 * 1.2 = 0.6, which is less than 1, so the population decreases at these times. Now, the critical point is 3.540518127*10^10 individuals, which is 35,405,181,270. The answer says that this is reached at the 4th hour of the 76th day. The question is what is the number at the 5th hour of the same day. We need to understand how the HCP model works. It seems that each day, the 11 (or 12) hours are applied with their respective factors. But in the example, the calculation goes up to the 12th hour. Maybe each day has 12 schedules, and the first 11 have specific rates, and the 12th uses the last rate (1.3 * 1.2 = 1.56). Or maybe the 11 schedules are repeated somehow. But the example shows that after 12 schedules (1 day?), the population drops to ~53 million. This seems unlikely, but it could be due to the variable rates. However, the 5 nutrient solution guarantees 20% growth per schedule, but temperature rates can reduce or increase this. I think each day has 12 schedules, and the first 11 have given rates, and the 12th uses the last rate (1.3) multiplied by 1.2, resulting in 1.56. Or maybe the 11 schedules are applied sequentially and repeated, but it is not clear. The example shows the calculation up to the 12th schedule, but there are only 11 rates. Maybe there is a typo, and the 12th schedule uses the 11th factor, which is 1.3 * 1.2 = 1.56. Assume that each day has 12 schedules, and the first 11 use the listed rates multiplied by 1.2, and the 12th schedule uses the last factor again or another. But in the example, the calculations are: 1st schedule: 50 * 1.68 = 84 2º: 84 * 1.32 = 110.88 3º: 110.88 * 1.2 = 133.056 4º: 133.056 * 0.96 = 127.73376 5º: 127.73376 * 0.84 = 107.2963584 6º: 107.2963584 * 0.6 = 64.37781504 7º: 64.37781504 * 0.24 = 15.45067561 8º: 15.45067561 * 0.48 = 7.416324293 9º: 7.416324293 * 2.04 = 15.12930156 10º: 15.12930156 * 2.28 = 34.49480756 11º: 34.49480756 * 1.56 = 53.81189978 So, there are 11 times calculated, resulting in 53.8 million in the 11th time slot. But in the example, they mention the 12th time slot as 34.4948... *1.56. This seems confusing. Maybe there was a mistake in the counting, and in fact, each day has 11 times slots, and the 12th time slot would be on the next day. But this doesn't make sense. Another possibility is that there are 11 times slots per day, and the calculation in the example is showing 12 times slots as part of one day, which is contradictory. Maybe there is a mistake in the problem description. Regardless, the answer provided indicates that the critical point is reached on the 4th time slot of the 76th day. So, to find the 5th time slot of the 76th day, we need to apply the factor corresponding to the 5th time slot after the 4th. Looking at the list of adjusted rates: The factors are: 1.68 (1st), 1.32 (2nd), 1.2 (3rd), 0.96 (4th), 0.84 (5th), 0.6 (6th), 0.24 (7th), 0.48 (8th), 2.04 (9th), 2.28 (10th), 1.56 (11th). Assuming each day has 11 schedules, then on the 76th day, schedules 1 to 11 are applied. But the answer says that the critical point is reached on the 4th schedule of the 76th day. So after the 4th schedule, the next is the 5th schedule, which has a factor of 0.84. Therefore, if on the 4th hour of the 76th day the population reaches the critical point (3.540518127e10), then on the 5th hour, we multiply this value by the factor 0.84. So, the calculation would be: 3.540518127e10 * 0.84 =? Let's calculate: 3.540518127e10 * 0.84 = 3.540518127 * 0.84 * 1e10 3.540518127 * 0.84 = 2.974. (Calculating more precisely: 3.540518127 * 0.84) 3.540518127 * 0.84 = 6 3 * 0.84 = 2.52 0.540518127 * 0.84 ≈ 0.540518127 * 0.8 = 0.4324145016 + 0.540518127 * 0.04=0.021620725 → total ≈0.4540352266 Total ≈2.52 + 0.4540352266 ≈2.9740352266 So, 2.9740352266e10 = 29,740,352,266 individuals. But I need to check if this logic is correct. The original answer says that the critical point is reached on the 4th hour of the 76th day. So the 5th hour would be next, applying the factor 0.84. So the answer would be approximately 2.974e10, or 2.9740352266e10, which can be rounded as needed. However, it is important to confirm that the factor for the 5th hour is actually 0.84. In the list provided, yes: the 5th hour has an original growth rate of 0.7, which multiplied by 1.2 gives 0.84. Yes. So the answer would be 3.540518127e10 * 0.84 = 2.974035226e10, which can be written as 2.974035226 × 10^10 or rounded to 2.97 × 10^10. But perhaps the problem expects us to use the exact values without intermediate rounding. Let me redo the calculation more precisely. 3.540518127 × 10^10 × 0.84 First, multiply 3.540518127 by 0.84: 3.540518127 × 0.84 Break it down into parts: 3 × 0.84 = 2.52 0.540518127 × 0.84: 0.5 × 0.84 = 0.42 0.040518127 × 0.84 ≈ 0.040518127 × 0.8 = 0.0324145016 + 0.040518127×0.04≈0.001620725 → total ≈0.0340352266 Total of 0.540518127 ×0.84 ≈0.42 +0.0340352266≈0.4540352266 Grand total: 2.52 +0.4540352266=2.9740352266 Therefore, 2.9740352266 ×10^10 = 29,740,352,266 individuals. Since the original answer mentions values with several decimal places, we should probably present the number with the same precision. The critical point was given as 3.540518127×10^10, so multiplying by 0.84, the result is 2.9740352266×10^10. Thus, the answer is 2.9740352266×10^10, which can be rounded to 2.974×10^10 or kept to more places as required. To determine the number of individuals in the 5th hour of the 76th day, we start from the critical point reached in the 4th hour of that day, which is 3.540518127 x 1010. Applying the factor of the 5th hour (0.84), we have: 3.540518127 x 1010 x 0.84 = 2.9740352266 x 1010. Answer: The number of individuals in the 5th hour of the 76th day will be 2.974 x 1010. 2.2 Grok's Answer 3 - Thinking Mode Good morning! Let's answer your question about cell proliferation and determine the number of individuals in the colony on the 5th hour of the 76th day. I will guide you step by step to reach the answer clearly and completely. Context and data provided. 7 We have a culture of microorganisms that starts with 50 million individuals, that is, 50×106=5×107. The colony is exposed to the open environment, and the growth rates vary at 11 significant times over 24 hours, due to temperature changes. The growth rates are: Table 1. Schedules and growts rate. Source: Author (2025) shedules 1° 2° 3° 4° 5° 6° 7° 8° 9° 10° 11° Growth rate 1.4 1.1 1.0 0.8 0.7 0.5 0.2 0.4 1.7 1.9 1.3 When the culture is dipped in a nutrient solution, it grows 20% more each time. This means that the effective growth rate at each time is the rate in the table multiplied by 1.2 (100% + 20% = 120%). Let's calculate these effective rates: • 1st hour: 1.4×1.2=1.68 • 2nd hour: 1.1×1.2=1.32 • 3rd hour: 1.0×1.2=1.2 • 4th hour: 0.8×1.2=0.96 • 5th hour: 0.7×1.2=0.84 • 6th hour: 0.5×1.2=0.6 • 7th hour: 0.2×1.2=0.24 • 8th hour: 0.4×1.2=0.48 • 9th hour: 1.7×1.2=2.04 • 10th hour: 1.9×1.2=2.28 • 11th hour: 1.3×1.2=1.56 These effective rates are: {1.68;1.32;1.2;0.96;0.84;0.6;0.24;0.48;2.04;2.28;1.56}. The problem also states that the critical point of mass expansion, 3.540518127×1010 Individuals, is reached on the 4th hour of the 76th day. Our task is to calculate the number of individuals on the 5th hour of the 76th day. Growth Model The number of individuals increases multiplicatively with each hour. If Nd,h represents the number of individuals on day d, hour h, then: Nd, h+1=Nd,h × effective rateh After the 11th hour of each day, the cycle of rates begins again on the 1st hour of the following day. The statement confirms that growth follows this pattern, as in the example in the auxiliary question: the initial number of 50 is multiplied by 1.68 in the 2nd time slot (yielding 84), then by 1.32 in the 3rd time slot (yielding 110.88), and so on. Using the Critical Point We do not need to calculate the number of individuals from the beginning (day 1, time slot 1) to the 5th time slot of the 76th day, because the problem gives us a crucial reference point: in the 4th time slot of the 76th day, the number of individuals is exactly 8 3.540518127×1010. To find the number in the 5th time slot of the same day, simply apply the effective rate corresponding to the 5th time slot. The effective rate for the 5th time slot is 0.84. Thus, the number of individuals in the 5th hour of the 76th day is: N76.5=N76.4 × effective rate5 N76.5=3.540518127×1010×0.84 Calculation Let's calculate 3.540518127×0.84: • Expressing 0.84 as a fraction: 0.84=84/100=21/25, but for simplicity, we will use the decimal value, since the result will be numerical. • Multiplication: 3.540518127×0.84 To ensure precision, we can decompose: • 3.540518127×84=297.403522668 (using calculator for accuracy), • Dividing by 100 (since 0.84=84/100): 297.403522668/100=2.97403522668 Alternatively, directly: 3.540518127×0.84=2.97403522668 (confirmed by calculator). Thus: N76.5=2.97403522668×1010 Answer Accuracy The critical point value, 3.540518127×1010, has 9 decimal places in the coefficient. For consistency, we will round the result to 9 decimal places: 2.97403522668 becomes 2.974035227 (the next digit, 6, rounds the 6 to 7). Therefore, the number of individuals is: 2.974035227×1010 Verification To confirm, note that the increase from one time slot to the next is direct: from the 4th to the 5th time slot, we multiply by 0.84, which reduces the number (rate < 1), which is consistent with the rate of 0.7 adjusted by 1.2. The calculation is in line with the given model. Final Answer The number of individuals in the colony on the 5th hour of the 76th day is 2.974035227×10^10 2.3 ChatGPT Response – o3 mini, o1 and 4.5 “reasoned wrongly” Let's consider that the critical point is reached on the 4th hour of the 76th day, that is, when the population reaches 3.540518127×10¹⁰ individuals. To obtain the population on the 5th hour of the same day, we apply the next factor in the sequence, which is 0.96. That is: Population (5th hour of the 76th day) = 3.540518127×10¹⁰ × 0.96 ≈ 3.398897402×10¹⁰ Therefore, on the 5th hour of the 76th day, the colony will have approximately 3.40×10¹⁰ individuals. 9 2.4 Gemini Advanced 2.0 Flash Answer Certainly, let's analyze the information provided to determine the number of individuals in the colony at the specified time. Based on the data in the table, the growth rate at the 5th hour is 0.7. Additionally, the document states that the culture grows by 20% each hour due to the nutrient solution. The-refore, we need to combine these growth factors. First, we calculate the overall growth factor by multiplying the effect of the nutrient soluti-on (1.20) by the specific growth rate at the 5th hour (0.7), resulting in 0.84. Next, we need to determine the number of individuals at the 4th hour of the 76th day. Unfortunately, the document doesn't explicitly provide this information. However, it does mention that the critical expansion point of 3.540518127 * 10^10 individuals is reached at the 4th hour of the 76th day. Therefore, to calculate the number of individuals at the 5th hour of the 76th day, we multiply the number of individuals at the 4th hour (3.540518127 * 10^10) by the combined growth factor of 0.84: (3.540518127 * 10^10) * 0.84 = 2.974036227 * 10^10 Therefore, based on the provided data and calculations, there will be approximately 29,740,362,270 individuals in the colony at the 5th hour of the 76th day. Let me know if you have any other questions or need further clarification! 2.5 Anthropic’s response – CLAUDE 3.7 “reasoned well and made mistakes in the conclusion and development of the mathematician” Good morning! I will analyze the cell proliferation problem for you. From what I understand from the document, we have: • A starting culture of 50 million microorganisms • Base growth of 20% each time slot due to the nutrient solution • Temperature factors that modify growth at each time slot, forming a cycle of 11 times slots • Critical expansion point: 3.540518127 × 10^10 individuals • It has already been determined that the critical point occurs on the 4th time slot of the 76th day To calculate the number of individuals on the 5th time slot of the 76th day, I need to: 1. Understand how the number of individuals evolves over time 2. Determine the temperature factor on the 5th time slot 3. Calculate the population at that time The temperature factors are: [1.68, 1.32, 1.2, 0.96, 0.84, 0.6, 0.24, 0.48, 2.04, 2.28, 1.56] I will implement the HCP mathematical model to calculate the population evolution: According to the data provided and using the HCP mathematical model, the number of individuals in the colony on the 5th hour of the 76th day can be calculated as follows: 16 4 Conclusion with Future Directions This article presented the performance of the most prominent Generative AIs in the world. It is possible to assess their skills and coping capabilities with instructions that compare with their learning. Since these are challenges in Computational Biology and with original mathematical formulas (SRMs), they are unpublished and for this reason it would not be possible for the AIs to have been trained using anything that is not published in printed or digital book. The proposal was to verify their accumulated knowledge and verify that they would find different bases to solve the problems. Some of the generative AIs tried, but failed. An example of this was OpenAI's ChatGPT and its various models. I have been a subscriber for several months and recognize the efficiency of this AI, but for advanced mathematical calculations, it leaves something to be desired. I have made several attempts to contact OpenAI's developers and its leaders, but have not received a response. I decided to invest in other Generative AIs and I believe that this article demonstrates how beneficial my change of direction was, personally speaking, and who knows, it will benefit companies that develop AI agents and that seek LIVING AI, or Generative Artificial Intelligence. Regardless of the origin of the adjustment in Grok 3, the fact is that no other Generative AI tested has demonstrated this level of adaptive correction. If this isn't evidence of a new paradigm in AI, then what is? I know that this article is just a drop in the immense ocean of unknowns and possibilities of generative AIs, but even the sea reacts to a drop thrown into its immensity. 4.1 Future Directions When I was an undergraduate student in mathematics, two well-known books in Brazil caught my attention: 1) The man who calculated – Author: Julio Cesar de Melo “Malba Tahan” and 2) The art of problem solving – Author: G. Polya. In both books, mathematics is taught without encouraging the memomorization of formulas. All the challenges I proposed to Generative AIs were with the purpose of analyzing whether they would be able to solve problems and what tools they would use for this. Therefore, I did not intend to know whether the AI agent would know how to calculate and use formulas. I was looking for something more that goes beyond a holistic vision and knowledge that goes far beyond knowing and applying formulas. One of the challenges I proposed for generative AIs, which is in one of my 181 Apps available on the Google Play platform, 4 years ago and no human has solved it to date, was the following: A self-driving car manufacturer wants to test its new prototype in a continuous race that lasts 260 hours. The experts provide the computer that will control the operation of the vehicle under test with the following data: 1) V0 = 100 km/h 17 2) A set of cyclical accelerations {50, -80, 90, 0, -70, 150, -110, 0, -20} When the vehicle reaches V0 = 100 km/h, the test will begin and continue with the accelerations presented in item 2 above. Note that the set is cyclical, so the last speed is added to the first acceleration. In other words; Km/h2 = a The question is: At the end of the test, what will be the values of Vinst (instantaneous speed) and Sp (distance traveled)? Two free generative AIs solved it with ease: DeepSeek R1 and Grok 3. I decided to confront them and asked: “Tell me, do you think this reasoning is trivial for humans? What level of education do you need to have to acquire this mathematical tool that you used?” Grok 3’s answer was: “For me, as an AI, reasoning may seem “trivial” because I was designed to process information quickly, identify patterns and apply mathematical formulas efficiently. However, for humans, the story is a little different. Although the concepts I used are relatively simple, the ability to divide a complex problem into smaller parts, associate these parts with known techniques and perform the calculations accurately is not something that everyone masters naturally. This requires practice, experience and a good understanding of mathematical fundamentals. For example, solving the problem you saw involved: • Breaking down the problem: Realizing that the 260 hours could be broken down into complete cycles of 9 hours plus an additional 8 hours. • Applying kinematic concepts: Using basic equations for speed and distance traveled under constant acceleration. • Recognizing cyclical patterns: Understanding that each complete cycle increased speed by 10 km/h. • Using arithmetic progression (AP): Calculating the distance traveled in the 28 cycles efficiently, without having to add hour by hour. These skills are developed over time, through study and solving similar problems. For someone with a good background in mathematics and physics, this reasoning may be relatively straightforward, but for others, it may require more effort and guidance. It is not "trivial" in the sense of being automatic for everyone, but it is something that can be learned and mastered with dedication. Therefore, someone who has completed high school with good performance in mathematics and physics should have the necessary tools to understand and apply these concepts. However, the ability to combine these tools creatively and efficiently, as I did in the problem, may require a little more mathematical maturity, which usually develops at the end of high school or at the beginning of higher education (for example, in exact science courses such as engineering, physics or mathematics). ” With my 32 years of experience in the classroom, I can say that it would be difficult for a higher education student to solve this problem. Maybe an extracurricular student 18 from the exact sciences area. The fault is not the student's, but the way mathematics is taught. Therefore, my main challenge is to continue signaling to the world that we have a living AI! That Grok 3 signals us to the great revolution in our professional practices. For us teachers, someone needs to say that the way to solve problems needs to be with the attitude of a living generative AI that argues, reasons, interacts and, above all, breaks the problem down into parts to better solve them. We need to support and spread the use of AI in the training of mathematics teachers, engineers, data scientists and other areas of the exact sciences. This will continue to be my main goal. Someone may be wondering what DeepSeek R1 responded? It argued that it noticed a pattern and transformed the problem into a traditional Arithmetic Progression (AP). Similar to what Grok 3 said, but with the difference of interaction and advanced didactics, by saying that I had not taught Infinite Series with Multiple Ratios (SRMs) and therefore would have to find the answer with the mathematical basis that it has. I have no doubt, that he would learn if I had taught it to him and this is the path for all AIs to evolve towards autonomy or the much dreamed of AGI. Reference 1. Rodrigues, Edgar. (1997). Proceedings of the Brazilian Society for the Advancement of Science (SBPC in Portuguese) - 49th Annual Meeting, Federal University of Minas Gerais, p. 715. Belo Horizonte-MG July 13, 1997. 2. Rodrigues, Edgar. (1995) – Infinite Series With Multiple Ratios, Journal of scientific divulgation, Logos Informática - issue 02 - Luteran University of Brazil, October 1995. Rodrigues, Edgar – Series Infinitas com Razões Múltiplas, Revista de divulgação científica, Logos Informática – Edição 02 – Universidade Luterana do Brasil, Outubro 1995. 3. França, C.R. (2017). Unpublished Mathematical Formulas Applied to Computational Biology: The Power of Unknown Concepts in Natural Science Called Infinite Series with Multiple Ratios. Carlos Roberto Franca, International Journal of Research in Engineering, IT and Social Sciences, ISSN 2250-0588, Impact Factor: 6.452, Volume 07 Issue 06, June 2017, Page 65-70 - https://indusedu.org/papers-ijreiss.php?id=7-6-6-2017 4. França, C.R. (2022). HCP Model – Heru Technologies Cell Proliferation - Cell proliferation model - HCP - Apps on Google Play - bit.ly/3Dl1GON 5. Heru Technologies Cell Proliferation mathematical model - https://www.herutechnologies.com.br/heru-technologies-algorithms Preprint - França, C. R. (2025). Mathematical Challenges for Generative AI in Computational Biology: Cell Proliferation and the Path to Living AI (Versão 1). Zenodo. https://doi.org/10.5281/zenodo.15014381