A Comprehensive Introduction to Problem Design, Solution and Analysis (Skills Edition) Offering Original Scientific Problem Construction, Multimodal Data Analysis, and Step-by-Step LaTeX Solution Architecture, Along with the Skills Documentation Page and SKILL.md Download Guide
Author: Aydın Tiryaki
Constructing a high-quality problem from scratch across engineering, fundamental sciences, finance, and statistics requires a methodological expertise just as deep as solving the problem itself. Similarly, accurately parsing data coming from diverse media (handwritten notes, textbook pages, screenshots, voice recordings, or complex texts) and solving them with mathematical precision is one of the most critical needs of modern education and engineering. Problem Design, Solution and Analysis (Skills Edition) is a dual-mode engineering and analytical thinking system designed specifically to unite these two core capabilities under a single intelligent framework.
1. Dual-Mode Operational Architecture: Designer and Analyst Identity The system begins every session with a dynamic initialization gateway (Mode 0) that allows the user to choose between two primary operational tracks:
- Mode 1️⃣: Problem Design (Designer Mode): Activated when the user wants to generate an original question or problem from scratch. Rather than producing generic questions with incomplete inputs, the system first conducts an interactive preliminary analysis. It clarifies the scientific discipline, difficulty level (High School / K-12, Undergraduate / BSc, Olympiad), target technical parameters, and narrative style (academic literature tone or simplified everyday language). Once the parameters reach maturity, it constructs a professional problem statement that preserves scientific curiosity and technical challenge. Through its “Post-Design Transition Bridge,” upon receiving user confirmation, the system seamlessly transitions into the full solution and analysis phase for the newly designed problem.
- Mode 2️⃣: Problem Solution and Analysis (Analyst Mode): Solves problems submitted by the user via text, voice, or visual (multimodal) inputs—or generated in Mode 1—down to the finest detail. Specifically for visual inputs such as photographs or screenshots, before initiating the mathematical analysis, the system transcribes all texts, numbers, and symbols in the image as raw data under the “Text in Visual:” heading to verify optical accuracy, thereby preventing calculation errors caused by misread inputs right at the source.
2. Five-Stage Solution, LaTeX Formulation, and Expert Analysis Every solution process executed in Analyst Mode follows a structured 5-layer engineering protocol rather than delivering an unstructured reply:
- Discipline Identification Layer: Clearly identifies whether the problem belongs to Mathematics, Physics, Engineering, Finance, or Statistics, along with its specific sub-discipline.
- Stage 1 – Problem Construction and Restoration: Refines fragmented or informally stated user inputs into a grammatically and technically rigorous, standardized problem statement.
- Stage 2 – Definitive Result Declaration: Presents the final mathematical, logical, or technical answer clearly and indisputably upfront so the user never gets lost amidst complex derivations.
- Stage 3 – Detailed Calculation and LaTeX Formulation: Demonstrates all intermediate steps of the solution in a logical sequence. By strictly applying LaTeX formatting (inline and block equations) for derivatives, integrals, matrices, differential equations, and scientific variables, it ensures publication-grade readability.
- Stage 4 & 5 – Visualization and Expert Commentary: Provides an in-depth expert evaluation covering the physical, economic, or theoretical meaning of the result, boundary conditions, and critical pitfalls to watch out for. Additionally, it supports schematic and conceptual visualization through a 9-option visual/video generation menu (With Text, Textless, and Video across Vertical, Horizontal, and Square aspect ratios).
3. Dual-Perspective Verification, Open Web Sources, and Living Assistant Before presenting any mathematical or technical output, the system cross-checks the data from a second analytical perspective; if a discrepancy arises, it conducts a third verification pass and transparently informs the user via a Hesitation Notification if any uncertainty remains. Relevant Wikipedia articles and working YouTube educational videos or playlists are shared as directly clickable open URLs rather than search engine query pages. Thanks to the integrated Living Assistant engine, users can type “Guide”, “Help”, “Handbook”, or “Manual” at any stage to receive instant interactive navigation at either the Summary or Detailed/Index level.
Technical Identity and Version Information
- Product Name (TR / EN): Problem Tasarımı, Çözümü ve Analizi / Problem Design, Solution and Analysis
- Version and Gem Repository No: v1.18 │ gdn037 │ GemStat: 2 (Completed)
- Character Distribution (TR): Title: 35 │ Description: 993 │ Instructions: 8232 │ Total: 9260 characters
- Character Distribution (EN): Title: 37 │ Description: 995 │ Instructions: 8934 │ Total: 9966 characters
- 📄Skills Documentation Page: https://aydintiryaki.org/2026/06/19/gdn037/
Google Drive Folder Link and SKILL.md File You can go to the folder below to download and directly use the SKILL.md file from this folder. If you cannot access this folder or file, it means the link is temporarily suspended because the development of the relevant Skills is currently in progress; please try again later.
📁 Google Drive Folder Path (EN): https://drive.google.com/drive/folders/1VestKYGJPe-5UvZH7szcCqPdsEjwctM4?usp=sharing
Note: You can make your own developments and edits on the SKILL.md file you obtain from here. However, out of respect for the effort, we kindly ask you to keep the Skills creator and editor information included here.
The architecture of the Problem Design, Solution and Analysis (Skills Edition) design introduced in this article, as well as all content, analytical approaches, and views in the article, belong to the author Aydın Tiryaki; the editorial work and writing assistance of the article were carried out by the active Gemini Pro model and Extended thinking level at the time of execution in accordance with ATG Gem Factory (Skills Edition) v14.11 and ATG Article and Document Workshop (Skills Edition) v01.15 standards (29.10.2026 23:02).
| aydintiryaki.org | YouTube | Aydın Tiryaki’nin Yazıları ve Videoları │Articles and Videos by Aydın Tiryaki | Bilgi Merkezi│Knowledge Hub | ░ Virgülüne Dokunmadan │ Verbatim ░ | ░ Problem Tasarımı, Çözümü ve Analizi │Problem Design, Solution and Analysis (Gemini Skills) ░ 04.11.2026
