Is There a Free Way to Learn Math and Science?

The quest to master mathematics and the natural sciences can seem daunting, but with the right tools and determination, it is possible to journey from the most fundamental concepts to the most complex fields.

Enter the World of Khan Academy

Khan Academy is an invaluable resource for those looking to embark on this journey. It offers a comprehensive curriculum that begins from the basics, such as simple equations, and progresses to more advanced topics including college-level math and statistics. While it may not take you to the peak of difficulty, the platform is designed to significantly enhance your understanding and skills.

Khan Academy is constantly expanding its offerings, with new modules and resources being added regularly. As of my last update, you can navigate through nearly 1500 modules covering a vast range of subjects including mathematics, physics, chemistry, biology, and even art. For instance, I've completed several cycles through their world of mathematics, reaching a current mastery level of over 96% (1422/1496). This platform truly democratizes access to high-quality education and is a testament to the power of learning through interactive and engaging content.

Beyond Khan Academy: Pursuing Expertise

While Khan Academy is an excellent stepping stone, achieving the peak of difficulty, especially in mathematics, requires a deep love and dedication to the subject. Recreational math can be a delightful way to explore mathematical problems that are easily understandable but fiendishly difficult to solve. For instance, Martin Gardner's "Mathematical Games" column in Scientific American introduced a generation to such problems. Other areas like Combinatorial Game Theory, as detailed in Winning Ways by Berlekamp, Conway, and Guy, can also be a rewarding experience.

Specialization and Advanced Learning

To truly specialize in a field, you will eventually need to immerse yourself in more formal educational settings or advanced courses. Many top universities and platforms like Coursera and EdX offer free advanced courses at any age. For example, 11-year-olds have successfully completed college-level courses, demonstrating the accessibility and potential of these resources.

When diving deep into pure mathematics, the focus is often on proving theorems. Books like General Topology by and Modern Algebra by van der Waerden provide a foundation for this. The "Bourbaki" style of rigorous proofs is among the most respected in this discipline. For applied mathematics, the emphasis shifts to calculations and justifications, often involving complex differential equations.

Experimental Sciences and Practical Work

In the experimental sciences, particularly in fields like physics and chemistry, hands-on experience is crucial. While the theoretical aspects can be learned for free, the process of experimentation and observation is indispensable. Nature itself is the ultimate judge of the accuracy of scientific theories. Don't shy away from getting your hands dirty; practical work often reveals flaws in our understanding and allows for continuous refinement.

As the great physicist once said, "The difference between theory and practice is that in theory, there's no difference, but in practice, there is." This mantra emphasizes the importance of practicality and empirical evidence in scientific pursuits. Stay open to new perspectives and always be ready to challenge your own assumptions.

Conclusion

Breaking down the journey from basic to advanced levels in math and science is about embracing the learning process. Whether it’s through the structured modules of Khan Academy, the theoretical rigor of specialized texts, or the practical experimentation of the natural sciences, the key is to stay curious and committed. With the right resources and dedication, anyone can explore the peaks of mathematical and scientific knowledge.