# Microsoft AI to participate in the International Olympic Games! Small goal: gold medal in Mathematics

Qubit report official account No. QbitAI

This year, it may be the last pure human IMO (International Olympic Games).

u25b3 participating in the IMO China team in 2020 (Li Jinmins official age information is wrong)

Because next year, AI may also join the gold medal race and become a seed player..

The AI that sneaked into the IMO event, called lean, was developed by Microsoft researchers.

At present, they are planning to let lean participate in the International Olympic Games next year.

In other words, it will compete with Olympians from all over the world for IMO gold medals.

Lean ready to show his skills on IMO

In fact, the reason why Microsoft researchers let AI participate in IMO is that it is a good experimental tool.

Selsam, a Microsoft researcher and co-founder of the challenge imobrand challenge, said the aim of the competition was to train an artificial intelligence system to win gold medals in the worlds top mathematics competitions.

Because there are not only the simplest problems in Mathematics (even higher mathematics cant be used, but they just cant do it), but also bring together top experts from all over the world.

If AI can prove these mathematical theorems like human beings, it can also show that it is not too difficult to make it think like a human being.

Based on this idea, Microsoft researchers began to develop lean in 2013, hoping to enable AI to have the ability to judge independently and deduce according to assumptions.

In other words, it is an open source project aimed at narrowing the gap between interactive theorem proving and automatic theorem proving.

Automatic theorem proving: to find a method to prove or disprove a theorem or conjecture in mathematics. The system not only can deduce according to the hypothesis, but also has certain judging skills.

Interactive theorem proving: with the help of computer-aided proving tools, understand and test the correctness of mathematical theorems, and complete the proof of mathematical theorems.

Lean has launched three versions, and lean4 is still in the process of improvement. The current logic system is based on the dependency type theory and is powerful enough to prove all the conventional mathematical theorems.

That is to say, it is still very difficult for it to prove by itself the mathematical problems raised in IMO that have not been seen before.

Lean4 is not fully prepared, and author leonardodemoura said that if it was to participate in this years IMO, it may only get 0 points..

Because, at present, lean cant even understand what concepts are involved in some mathematical problems, and what these concepts mean by themselves.

The first step of proof is difficult to solve the algorithm

For many people, mathematics is very abstract and difficult to learn.

In fact, AI feels the same as you do.

In general engineering application problems, AI is handy, because in the pre training stage, the algorithm model already knows a class of problems.

In other words, AI is still limited at the present stage. It usually needs to give conditions and data, and after continuous brush questions, it can do more complex calculation.

This is a process from 1 to 2, 3, and even infinite.

But the essence of proof of mathematical problems is not the same. To prove an axiom or a complex equation, we need to start from scratch.

The first step of proof: put forward a reasonable proof path. The key from 0 to 1 is that only human brain can do it.

Most AI, it is difficult to give the first step of proof.

Take one of the simplest and oldest mathematical axioms. In 300 BC, Euclid proved that there are infinitely many prime numbers.

To prove this conclusion, the key is to realize that a new prime number can always be found by multiplying all known prime numbers and adding 1. With this idea, the next proof is very simple.

But the behavior of thinking about this idea itself is very difficult for AI.

Back to IMO, although the three questions in the official competition do not involve calculus and other advanced mathematics, they all require the players to use all the mathematics knowledge in middle school to make ingenious ideas and give solutions.

For example, this 2005 IMO real Title:

At that time, contestants from different countries gave at least three different proofs. Among them, the solution widely accepted and discussed adopted the idea of simplifying Cauchys inequality, which required about half a page of A4 paper.

Another player from Moldova creatively completed the proof in two lines

The top line is because and the bottom line is so. Its simplicity, accuracy and even rude and effective shocked the audience.

Ingenious thinking also won the IMO special award of that year.

It should be noted that the IMO special award does not depend on the total score, but is awarded to the players with unique problem-solving methods.

This first step is almost impossible for AI today.

This may be why Microsoft researchers set the goal of gold medal impact..

How does lean learn mathematics?

Like all AI algorithms, lean needs to feed data for training.

At present, lean cant design a complete IMO topic proof process, and even cant understand the concepts involved in some of the problems.

So leans first task is to learn more mathematics.

But mathlib still has some gaps in high school mathematics, and the team is completing the mathlib database.

Mastering knowledge is only the first step, and how to use it flexibly is the key.

The team takes the same approach as chess, go AI, etc. - follow the decision tree until the algorithm finds the optimal solution.

The key to many IMO topics is to find a pattern of proof. Going deep into the bottom of mathematical proof is a series of very specific and logical steps.

The researchers tried to train lean through all the details of the IMO topic proof.

However, there are limitations in this method. Each specific topic proof is too specialized for the algorithm, and the next different type of problem still can not be solved.

To solve this problem, the team needed mathematicians to write a detailed formal proof of the previous IMO topic. The team then refines the different strategies used in the proof.

Next, leans task is to find a winning combination of these strategies.

This task is actually much more difficult than described. The team compares it as follows:

In go, the goal is to find the best move. In mathematics, the goal is to find the best game, and then find the best move in the game.

The team said it might still be difficult to win a gold medal next year, but at least, lean has a chance to compete.

In this regard, some netizens lament the rapid progress of AI in recent years: first chess, then go Now, AI will come again to win the gold medal in the International Olympic Games.

However, some netizens hold a pessimistic attitude that AI can only approach the level of human beings in some aspects at this stage.

At present, AI algorithms are all based on human cognition So I take a negative attitude on special tasks like (proving mathematical theorems). After all, only a few people in the world can help.

The problem is surprisingly difficult to explain. When mathematicians try to solve new problems, the activity of the brain is hard to describe, let alone implemented in algorithms.

Although some AI teams have taken a step towards the depth of mathematical thinking, from the perspective of their strategies, they still learn from the past ideas and choose the permutation with the highest success rate.

Such AI algorithms are far from hot to surpass human creativity and breakthrough.

The GPT in the next door has also achieved preliminary results in the direction of mathematical proof.

Recently, openai has introduced gpt-f for mathematical problems, which uses the generation ability based on transformer language model for automatic theorem proving.

The 23 short proofs discovered by gpt-f have been received by metamath master library, which is the first time that AIs mathematical proofs have been recognized in the industry.

GPT is really going to kill everyone, even mathematicians.

So, lean or gpt-f, which one do you prefer?

Project link:

https://leanprover.github.io/

Online play:

https://leanprover.github.io/live/master/

Reference link:

https://leodemoura.github.io/

https://www.quantamagazine.org/how-close-are-computers-to-automating-mathematical-reasoning-20200827/

https://www.quantamagazine.org/at-the-international-mathematical-olympiad-artificial-intelligence-prepares-to-go-for-the-gold-20200921

Source: Quantile editor: Wang Fengzhi_ NT2541