Not long ago, I shared a piece on how technical solutions evolve—think of it as the journey beyond REST in microservices. In that same spirit, the way AI handles computation has also undergone a transformation. Sometimes these models compute huge numbers or factorize massive integers at breakneck speed, other times they walk us through each methodical step. Below is a look at two real-world scenarios that highlight how and why these differences matter.
1. Why AI Computation Matters
When we talk about AI, most people envision chatbots or recommendation engines. But under the hood, these systems often need to perform intense mathematical operations. Whether it’s multiplying large numbers, factoring gargantuan integers, or evaluating complex expressions, how an AI performs these tasks reveals much about its design philosophy:
Fast, Tool-Assisted Computation: Calls upon specialized libraries or code runners for near-instant answers.
Manual, Step-by-Step Explanation: Emulates human reasoning, typically slower but offers transparency and deeper insight into each step.
2. The Multiplication Test
Our first example involved a seemingly straightforward arithmetic query:
Calculate 25665566*6778765556
ChatGPT’s Instant Approach
result = 25665566 * 6778765556
result
173980854776044696
The Strategy: Called a built-in “code runner” with a single Python snippet to multiply these large integers.
The Result: A near-immediate output.
The “Why?”: It recognized the task was purely computational and delegated it to a reliable tool.
Deepseek’s & Grok Methodical Route
DeekSeek R1 </think>
Alright, so I need to calculate the product of 25,665,566 and 6,778,765,556. Hmm, that's a pretty big multiplication. Let me think about how to approach this. I know that multiplying large numbers can be tricky, especially if I don't have a calculator handy. Maybe I can break it down using the distributive property or some estimation first to check my work later. First, let me write down the numbers to make sure I have them right: 25,665,566 and 6,778,765,556. Both are in the billions range, so their product is going to be really large. I might need to use some systematic method here. Let me recall that when multiplying two numbers, you can break them into parts. For example, using the standard algorithm where you multiply each digit and carry over. But doing that manually for such large numbers would be time-consuming and prone to errors. Maybe there's a smarter way. Alternatively, I can use the fact that 6,778,765,556 is close to 6.778765556 billion, and 25,665,566 is approximately 25.665566 million. But converting them into scientific notation might make it easier. Let's try that. 25,665,566 can be written as 2.5665566 × 10^7, and 6,778,765,556 is 6.778765556 × 10^9………………..
Grok Thinking
So I have this multiplication problem: 25,665,566 times 6,778,765,556. Hmm, those are pretty big numbers. I'm a bit rusty on multiplying large numbers, but I think I can handle it. Let me see. First, I remember that when multiplying two numbers, I can break it down into smaller parts. Maybe I can use the distributive property or something like that. Wait, actually, the standard way is to multiply each digit of one number by each digit of the other number and then add them up, right? But that seems tedious with such large numbers. Alternatively, perhaps I can simplify the numbers somehow. Let me check if there are any patterns or factors that can make this easier. Let's see, 25,665,566 and 6,778,765,556. Hmm, not sure if they share any common factors that I can factor out. Wait a minute, maybe I can approximate the numbers to get a rough estimate first. That might help me check if my final answer makes sense. So, 25,665,566 is roughly 25 million, and 6,778,765,556 is roughly 6.8 billion. Multiplying those, 25 million times 6.8 billion. Well, 25 times 6.8 is 170, and then million times billion is trillion, so roughly 170 trillion. But actually, wait, million times billion is 10^6 times 10^9, which is 10^15, so quadrillion. Wait, no: million is 10^6, billion is 10^9, so 10^6 10^9 = 10^15, which is quadrillion. But in the context of the numbers, 25 million is 2.510^7, and 6.8 billion is 6.810^9. So 2.510^7 6.810^9 = (2.56.8)10^(7+9) = 1710^16, which is 1.710^17. Wait, that doesn't seem right. Wait, 10^16 is ten quadrillion, but let's confirm: 10^15 is quadrillion, so 10^16 is ten quadrillion, but actually, in standard naming, 10^15 is quadrillion, 10^18 is quintillion, so 10^16 is 10 quadrillion. But perhaps it's better to think in terms of powers of ten…………
The Strategy: Simulated each step of long multiplication—similar to how you might solve it by hand, carrying digits and forming partial sums.
The Result: Accurate, but took a notable amount of time.
The “Why?”: Focused on clarity and a breakdown of logic at each phase, sacrificing speed for a teaching-like demonstration.
3. The Factorization Challenge
Soon after, we posed a tougher problem: factorizing a massive integer:
Prompt: Factorize 987654321987654321
Output :
$$987654321987654321=3^2 ×7×11×13×17^2 ×19×52579×379721$$
ChatGPT’s Swift Response
import sympy
num = 987654321987654321
factors = sympy.factorint(num)
factors
{3: 2, 7: 1, 11: 1, 13: 1, 17: 2, 19: 1, 52579: 1, 379721: 1}
Tool Used: A code snippet employing the sympy library in Python.
Time Taken: Just a couple of seconds—an immediate resolution of prime factors.
Key Insight: Similar to how advanced communication protocols drastically improve throughput, specialized libraries handle complex math in a fraction of the time.
Deepseek’s Longer Journey
DeepSeek R1 </think>
Okay, so I need to factorize 987654321987654321. Hmm, that's a pretty big number. Let me start by writing it down clearly: 987,654,321,987,654,321. Wait, I notice that this number seems to have a repeating pattern. It's 987654321 followed by another 987654321. So maybe it's constructed by repeating the sequence 987654321 twice. That might help in factoring it somehow. First, let me recall that numbers with repeating patterns can sometimes be expressed in a form that allows factoring. For example, a number like 123123 can be written as 123 1001. Similarly, maybe this number can be written as 987654321 multiplied by some factor. Let me check: If the original number is 987654321987654321, that's 987654321 followed by another 987654321. So, how many digits is that? The first part, 987654321, has 9 digits. So repeating it twice would make 18 digits. Let me confirm: 987,654,321,987,654,321 is indeed 18 digits. So, similar to the 123123 example, this can be written as 987654321 10^9 + 987654321. That simplifies to 987654321 (10^9 + 1). So, the number N = 987654321987654321 can be written as N = 987654321 (10^9 + 1). That seems like a good start. Now, if I can factor both 987654321 and (10^9 + 1), then I can combine their factors to get the full prime factorization of N. First, let's factor 987654321. Let me recall if I know anything about this number. Wait, 987654321 is a well-known number, it's the sequence of digits from 9 down to 1. I think this number has some factors. Let me try dividing it by small primes. Starting with 2: 987654321 is odd, so not divisible by 2. Next, 3: sum of digits. Let's calculate the sum: 9+8+7+6+5+4+3+2+1 = 45. 45 is divisible by 9 and 3, so the number is divisible by 9 and 3. Let's divide by 3 first.
Method: Gradual, possibly trial-division or more stepwise primality checks.
Time Taken: 298 seconds—nearly five minutes.
Why It Matters: Though it arrived at the same factorization, the approach highlights a commitment to manual or semi-manual problem-solving.
Final Output:
$$\boxed{3^2 \times 7 \times 11 \times 13 \times 17^2 \times 19 \times 52579 \times 379721}$$
4. Fast vs. Thorough: A Tale of Two Approaches
Whether it’s the multiplication or factorization scenario, the contrast stands out:
Tool-Based Calculation
Pros: Lightning speed, reliable results, minimal chance of slip-ups.
Cons: Limited transparency; the AI just “knows” the final answer without showing each step.
Manual “Thinking”
Pros: Explains every detail, ideal for teaching and verifying each arithmetic operation.
Cons: Time-consuming, higher risk of compounding errors if a single step is off.
Much like choosing RabbitMQ or gRPC for the right use case in microservices, deciding between tool-based or stepwise AI reasoning depends on your goals:
If you value speed and reliability— A tool based solution is more effective
If you need explanation and clarity—embrace the methodical, step-by-step breakdown.
Both approaches have their place, and both can produce the correct result. The key is understanding which strategy suits your scenario. When seconds matter, harness specialized libraries. When teaching or diagnosis is the main objective, a thorough, human-like walkthrough might be best.
