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In the sciences, mathematics serves as nothing less than a convenient notation for expressing (and manipulating) certain principles: it is an invaluable tool, b
by thegenius2000 11y ago
In the sciences, mathematics serves as nothing less than a convenient notation for expressing (and manipulating) certain principles: it is an invaluable tool, both for analysis and exposition.
That being said, in my opinion, great science is largely about insight, and this does not necessarily depend on maths. For example, consider the contributions Faraday made to our understanding of electromagnetism. Although he never mastered maths, he broke the ground for many that followed him, most notably Maxwell. With Maxwell, you have almost the opposite situation, as he was a highly skilled mathematician: his insights were largely borne of mathematical abstraction.
So I think the best answer to the question is sometimes. Faraday's insights were not (directly) dependent on advanced knowledge of mathematics, but Maxwell's were. We needed the genius of both these men, but mathematics was only required of the second.
What should we do, then? Definitely require hard science majors to learn mathematics, even more so then currently. Encourage mathematicians to think about science problems, and vice-versa. But let us not make the mistake of closing the scientific doors on the so-called 'mathematically illiterate.' For all we know, they carry the solutions to some of our most difficult problems.
Edit: changed 'where' to 'were'
- lutusp 11y ago> But let us not make the mistake of closing the scientific doors on the so-called 'mathematically illiterate.' Fair enough, but it can lead to a very serious problem -- how do we compare the results of different studies? Day-to-day experimental results can be collected with only a little math, but any theories that might be shaped on the basis of those results, that might end up defining new fields, usually have a mathematical form that summarizes the experimental work and creates new principles and paradigms. Those theories that last the longest and have the largest effect on science, tend to be more mathematical than anecdotal. > Faraday's insights were not (directly) dependent on advanced knowledge of mathematics, but Maxwell's were. We needed the genius of both these men, but mathematics was only required of the second. This example supports the role of mathematics in science. Faraday described some results that arose in laboratory experiments, then Maxwell explained those results using mathematics. Faraday's results were fascinating, but Maxwell's results were portable and later served as a foundation for relativity -- which was also very mathematical.
- forgetsusername 11y ago>Faraday described some results that arose in laboratory experiments, then Maxwell explained those results using mathematics. The issue is with expecting a single person to be able to do both; people with incredible insight who are also great at mathematics are inherently rare. If you require the latter you're going to miss out on much of the world's stock of the former. I think the future of science rests on the coordination of both.
- lutusp 11y agoI agree completely, but by 1915, Einstein had reshaped himself into exactly the multidisciplinary person required to write the general theory. The real tragedy in science are those with only physical intuition and little mathematical foundation, like Nicola Tesla, who wasted much time on notions that flatly contradicted the mathematical underpinnings of physical theory.
- akyu 11y agoMaxwell wrote that Faraday was "a mathematician of a very high order" despite his lack of formal education. I always found that fascinating.