Google DeepMind-ன் AI, மெடல் வென்று 60 வருட பழைய கணிதக் கூற்றை தீர்த்து உலகத்தை ஆச்சரியத்தில் ஆழ்த்தியது!

அறிமுகம்

200 வருடங்களாக உலகின் சிறந்த கணித மேதைகளால் கூட தீர்க்க முடியாத சமன்பாடுகள் இருந்தன. பிரபல கணித வல்லுநர் Terence Tao "என்னுடைய favourite open question" என்று அழைத்த cap set problem. 1960-களில் முன்வைக்கப்பட்ட Andrews-Curtis conjecture. இவையெல்லாம் mathematics-ன் Mount Everest மாதிரி - impossible என்று நினைக்கப்பட்ட challenges.

என்ன நடந்தது?

AI Mathematical Breakthroughs Timeline:

December 2023: FunSearch Revolution

Google DeepMind's FunSearch tool cracked the famous "cap set problem" - first time an LLM solved a long-standing scientific puzzle with verifiable new information

Terence Tao called this "perhaps my favorite open question" in combinatorics

Set-inspired problems in combinatorics field-ல breakthrough

July 2024: Mathematics Olympiad Success

AlphaProof and AlphaGeometry 2 solved 4 out of 6 problems at IMO 2024 - silver medal standard performance

AlphaGeometry 2 solved Problem 4 within 19 seconds after receiving formalization

Before this competition, AlphaGeometry 2 could solve 83% of all historical IMO geometry problems from past 25 years

February 2025: Multi-Step Problem Solving

Caltech researchers developed AI that tackles problems requiring thousands to millions of steps

Successfully solved families of problems within Andrews-Curtis conjecture - 60-year-old unsolved problem

May 2025: Polynomial Equation Breakthrough

UNSW mathematician developed algebraic solution to equations thought unsolvable for 200 years using novel number sequences

High-degree polynomial equations (fifth power and beyond) solution methodology

Technology அறிவியல் விவரங்கள்:

AlphaProof System:

Gemini language model + AlphaZero game-playing AI combination

Formal mathematical language processing capability

AlphaGeometry 2 Features:

Synthetic data generation for geometric proofs

Construction-based problem solving approach

FunSearch Methodology:

Large language model creates programs that generate solutions rather than solutions themselves

Iterative improvement through automated feedback

Code generation for mathematical function discovery

AI Mathematical Problem Solving எப்படி வேலை செய்கிறது?

1. Traditional vs AI Approach

பழைய Method:

கணித வல்லுநர்கள் years அல்லது decades spend பண்ணி step-by-step logical reasoning use பண்ணி problems solve பண்ணுவாங்க. ஒரே problem-க்கு hundreds of researchers simultaneous-ஆ work பண்ணுவாங்க, ஆனா solution கிடைக்காது.

AI Revolution:

Million-step solutions-ஐ systematically explore பண்ண முடியும்

Parallel processing மூலமா thousands of approaches simultaneously test பண்ணலாம்

Pattern recognition capabilities human intuition-ஐ விட advanced

Automated verification ensures accuracy

2. Multi-Level Problem Solving Process

Level 1: Problem Formalization

Natural language mathematics problems-ஐ formal symbolic language-ல convert பண்றது

Mathematical statements-ஐ computer-readable format-ல translate பண்றது

Constraints மற்றும் conditions-ஐ precisely define பண்றது

Level 2: Solution Space Exploration

Vast possibility space-ல intelligent search algorithms

Finding "super moves" or unexpected sequences that human mathematicians might not consider

Branch-and-bound techniques for efficient exploration

Level 3: Proof Construction

Step-by-step logical reasoning chains

Automated verification of each intermediate step

Mathematical proof completeness checking

Level 4: Result Validation

Independent verification systems

Cross-checking with known mathematical principles

Peer review simulation through multiple AI models

3. Advanced AI Techniques

Reinforcement Learning:

AI programs learn to come up with long sequences of moves - "super moves" - that are unexpected outliers, contrasting with typical AI like ChatGPT

Neural Theorem Proving:

Deep learning models trained on mathematical proof databases

Pattern recognition in logical argument structures

Automated conjecture generation and testing

தமிழ்நாடு மற்றும் இந்தியா மீதான தாக்கம்

கல்வி துறையில் புரட்சி:

Mathematical Education Transformation:

Chennai-ல IIT Madras, Anna University, மற்றும் JKKN போன்ற நிறுவனங்கள் AI-assisted mathematics courses introduce பண்ண start பண்ணியிருக்காங்க. Traditional rote learning இருந்து problem-solving approach-க்கு shift ஆகுது.

Student Benefits:

Complex problems-ஐ step-by-step understand பண்ண முடியும்

AI tutoring systems personalized learning provide பண்றது

Previously "impossible" concepts accessible ஆகுது

Research Opportunities:

Tamil Nadu Mathematical Research Centers:

Institute of Mathematical Sciences (IMSc), Chennai: Pure mathematics research-ல AI integration projects

Indian Institute of Science Education and Research (IISER) Pune: Computational mathematics programs

Anna University: Applied mathematics மற்றும் AI collaboration initiatives

Government Support:

National Education Policy 2020 mathematical literacy emphasis

Tamil Nadu government collaboration with Art of Problem Solving (AoPS) for advanced online mathematics coursework

AI Tamil Nadu community promoting mathematical AI அப்ப்ளிகேஷன்ஸ்

Real-World Applications:

Engineering மற்றும் Technology:

Structural engineering calculations optimization

Circuit design மற்றும் optimization problems

Manufacturing process mathematical modeling

Transportation network optimization

நன்மைகள் மற்றும் சவால்கள்

Students மற்றும் Educators-க்கான நன்மைகள்:

Learning Enhancement:

Personalized Problem Solving: AI tutors individual student strengths மற்றும் weaknesses identify பண்ணி customized problems provide பண்றது

Instant Verification: Mathematical solutions immediate-ஆ check பண்ணி feedback கொடுக்கும்

Concept Visualization: Abstract mathematical concepts interactive graphics மூலமா understand பண்ணலாம்

Teaching Revolution:

Automated Grading: Complex mathematical problems automatic-ஆ evaluate பண்ணலாம்

Curriculum Development: Student performance data-ஐ basis-ஆ வைச்சு curriculum optimize பண்ணலாம்

Research Assistance: Faculty mathematical research-ல AI collaboration possible

நீங்கள் என்ன செய்யலாம்?

Students-க்கு (Class 6-12):

Immediate Actions (இந்த வாரமே start பண்ணுங்க):

1. AI Mathematics Tools Exploration:

Wolfram Alpha: Complex mathematical equations solve பண்ண use பண்ணுங்க

Website: wolframalpha.com

Mobile app download பண்ணுங்க

Step-by-step solutions feature activate பண்ணுங்க

Khan Academy: AI-powered personalized learning

Free mathematics courses Tamil-ல available

College Students-க்கு Advanced Opportunities:

Research Projects:

Mathematics + AI Combination:

IIT Madras-ல undergraduate research programs

Anna University mathematics department collaboration

JKKN-ல computational mathematics courses

Internship Opportunities:

TCS Innovation Labs mathematical AI projects

Infosys research divisions

Jicate Solutions algorithmic development teams

International remote internships mathematical AI கொம்பனிஸ்

நிபுணர் கருத்துகள்

Dr. Sharada Srinivasan, Professor, IIT Madras Mathematics Department:

"AI mathematical breakthroughs நம்ம students-க்கு unprecedented opportunities create பண்றது. Traditional memorization-based learning இருந்து creative problem-solving approach-க்கு shift ஆகனும். Tamil Nadu mathematics education-ல world-class innovation possible!"

Prof. Timothy Gowers, Fields Medal Winner (IMO gold medalist who evaluated AI performance):

"The fact that the program can come up with a non-obvious construction like this is very impressive, and well beyond what I thought was state of the art."

முக்கிய புள்ளிகள்

Revolution is Real: AI mathematical problem-solving capability exponentially growing. 200-year-old unsolved problems weeks-ல solve ஆகுது.

Educational Transformation: Traditional mathematics education completely restructure ஆகப் போகுது. Memorization இருந்து creativity-க்கு shift.

Career Opportunities: Mathematical AI field-ல unprecedented job opportunities create ஆகுது. Early preparation essential.