Ludwig Wittgenstein Quotes
Philosophy is like trying to open a safe with a combination lock: each little adjustment of the dials seems to achieve nothing, only when everything is in place does the door open.
Rhees, Rush, editor. Ludwig Wittgenstein: Personal Recollections. Rowman and Littlefield, 1981, p. 69.
For many scientists, this is the goal of each area of inquiry. For others, the science is crude and really not understood unless the mathematical model exists and can be verified experimentally. For Thompson, this was the difference between understanding and not.
Feynman generally emphasized the importance of a scientist understanding the mathematics of his/her subject, especially where nature's complexities abounded. At the time few appreciated the importance in the biological sciences of mathematics which we know today is so essential.
Ludwig Josef Johann Wittgenstein was an Austrian-British philosopher who worked primarily in logic, the philosophy of mathematics, the philosophy of mind, and the philosophy of language.