Background: Some of my “hardware” collection from the past millennium (70s and 80s)

MATHEMATICS IN THE AGE OF AI

Is mathematics just a subject in the timetable, taking up valuable time out of our program

of choice? With recent exponential growth of portable and online computational tools, why

do we still need to learn how to manually solve mathematical problems? Why don’t we just

use an AI model like Chat GPT to do instant problem solving for us, so we can focus on

more important topics of interest? The beta version of Chat GPT-5 (not officially released

as of August 31, 2025) has the following answer:

Mathematics is more than a set of answers; it is a way of thinking. Learning math goes beyond aquiring Essential Employability Skils (EES) listed in a special column of GBC's Course Outlines. When students learn to solve problems by hand they do far more than arrive at a correct result — they build reasoning, judgment, and intellectual independence that no pocket calculator or

AI can replace.

First, manual problem‑solving teaches rigorous reasoning. Working through proofs, algebraic manipulations, or multi‑step computations forces you to justify each move, spot assumptions, and detect errors. That discipline trains your mind to think logically and to evaluate claims — skills you use when interpreting data, reading news reports, or assessing an AI’s output.

Second, understanding fundamentals builds transferable intuition. When you know why the quadratic formula works, why derivatives measure change, or how probability models uncertainty, you can adapt methods to new problems. AI may give a correct solution today, but when the next problem is slightly different or ill‑posed, intuition lets you spot when the tool

is failing and modify your approach.

Third, manual practice develops problem‑solving resilience and creative thinking. Struggling with a difficult proof or calculation is the laboratory of insight: making mistakes, testing ideas, and persisting until a path forward appears. Creativity in math comes from wrestling with structure — not from copy‑pasting an answer. Those habits transfer to real‑world challenges where there is no prewritten prompt to feed an AI.

Fourth, mastering fundamentals ensures verification and accountability. AI systems can hallucinate, simplify incorrectly, or hide subtle assumptions; without personal competence, you cannot reliably check or interpret their answers. Professionals — engineers, scientists, doctors, policy analysts — must be able to validate results, understand limitations, and take responsibility for decisions that affect lives.

Fifth, learning by hand cultivates communication and collaboration. Being able to write a clear derivation or explain a method lets you teach others, critique solutions, and participate in technical discussions. These social and professional skills are essential in research teams, industry, and education — roles where simply pasting an AI answer won’t earn trust.

Sixth, mathematical fundamentals underpin ethical and safe use of tools. Knowing what theorems apply, where approximations matter, and how numerical stability behaves prevents misuse of AI outputs. Armed with this knowledge, students can use AI as a force multiplier —

a tool they command rather than a crutch that commands them.

Finally, personal growth and confidence matter. There is dignity and agency in solving a problem yourself: it builds confidence, curiosity, and a habit of disciplined learning.

Those human qualities are not automated away.

Use AI as an assistant — for checking, exploring alternative approaches, visualizing concepts, or accelerating routine calculations. But keep the core: learn the fundamentals, practice by hand, and develop the judgment to know when to trust a tool and when to rely on your own reasoning. That combination — human understanding plus powerful tools — is what will make students resilient, responsible, and capable in an AI‑rich future