<story><title>Symbolic mathematics finally yields to neural networks</title><url>https://www.quantamagazine.org/symbolic-mathematics-finally-yields-to-neural-networks-20200520/</url></story><parent_chain></parent_chain><comment><author>todd8</author><text>About 50 years ago I was fascinated to see a program that could do symbolic integration. Now, programs like Mathematica can do much harder, more complex integrals.&lt;p&gt;Professor Patrick Winston pointed out that most of the AI programs we were going to look at in his class (chess, natural language, 3D vision in block world, etc.) ended up, like integration, as simple code plus a database of facts.&lt;p&gt;Back then, there was general optimism about the future of AI. No one anticipated how slow progress would be while the capabilities of the hardware grew a million-fold.&lt;p&gt;The work referenced in the article is interesting. It appears to be another small step in advancing AI. It&amp;#x27;s a small, but difficult, step like almost every other advance in AI, and I admire the work done by those working in this field.&lt;p&gt;The problems of solving simple differential equations and symbolic integration at the first year calculus level are not really advanced math. Humans solve these problems with a relatively small bag of tricks that transform a symbolic integral into a simpler form. A program can do the same thing with an even more detailed database of transforms that can be attempted at each point in the search tree until a simple solution is reached.&lt;p&gt;The article claims that the new program can solve difficult integrals. This is interesting because hard to solve integrals are often associated with real physical phenomena. See for example the triple integrals of W. F. van Peype which arose while he was studying magnetism in different materials. These, relatively, plain looking definite integrals stumped some of the world&amp;#x27;s most famous mathematicians. See [1] and&amp;#x2F;or [2] for their interesting history.&lt;p&gt;[1] Paul J. Nahin, &lt;i&gt;Inside Interesting Integrals&lt;/i&gt;, Springer, 2015. Section 6.5, The Watson&amp;#x2F;van Peype Triple Integrals.&lt;p&gt;[2] I.J. Zucker, 70+ Years of the Watson Integrals, &lt;a href=&quot;http:&amp;#x2F;&amp;#x2F;www.inp.nsk.su&amp;#x2F;~silagadz&amp;#x2F;Watson_Integral.pdf&quot; rel=&quot;nofollow&quot;&gt;http:&amp;#x2F;&amp;#x2F;www.inp.nsk.su&amp;#x2F;~silagadz&amp;#x2F;Watson_Integral.pdf&lt;/a&gt;</text></comment>
<story><title>Symbolic mathematics finally yields to neural networks</title><url>https://www.quantamagazine.org/symbolic-mathematics-finally-yields-to-neural-networks-20200520/</url></story><parent_chain></parent_chain><comment><author>_0ffh</author><text>To me, the article somewhat misses the point of what&amp;#x27;s interesting here. Using ASTs to represent equations, or even whole programs has plenty of precedents in ML&amp;#x2F;AI. I&amp;#x27;d have liked to know how exactly they translate these trees to a representation suitable for an ANN. Fortunately, the paper seems to be easy to find and access (it&amp;#x27;s [1], I guess).&lt;p&gt;[1] &lt;a href=&quot;https:&amp;#x2F;&amp;#x2F;arxiv.org&amp;#x2F;abs&amp;#x2F;1912.01412&quot; rel=&quot;nofollow&quot;&gt;https:&amp;#x2F;&amp;#x2F;arxiv.org&amp;#x2F;abs&amp;#x2F;1912.01412&lt;/a&gt;</text></comment>