Calculus

In this chapter, you will see the important preliminary steps taken before the full power of Newton and Leibnitz would be felt only a few decades later. Both Newton and Leibnitz, who we shall consider in the next chapter, gave full acknowledgment to their predecessors and freely used their results. You will see early work, much of it appearing rather familiar though somewhat different.

Goals

Among the many features you should regard are:

Philosophy and Mathematics.

• Calculus. What significant early approaches seem remarkable. For example, note how infinite series played a much greater role in early calculus that functions such as the trigonometic family and the exponential functions. Note as well the sheer bulk of contributions. In fact, you may begin to question if Newton and/or Leibnitz actually invented calculus. Did they?
• Carefully note what was a function to these mathematicians. Is is in anyway a modern notion?
• The players. Are the mathematicians of this day truly professional or are they of the class of wealthy (or poor) practitioners of their craft dependent on other employment to earn money.
• Note the power and importance of symbolism at this juncture.
• Note also the major "false-start" in calculus, that of infinitesimals, a potentially powerful tool that did not survive.
• Note the subjects taught in the schools. Not the training of many of the mathematicians. Note the stature of the intellectual in the European community.
• What did Newton and Leibnitz bring to this new theory that was absent before them?
• What was their legacy, mathematically and philosophically? Has the nature of mathematics changed forever, or does it have merely some extrordinarily powerful new tools?

References